POPULATION SYNTHESIS AND ITS CONNECTION TO …

The Pennsylvania State University

The Graduate School

The Eberly College of Science

POPULATION SYNTHESIS AND ITS

CONNECTION TO ASTRONOMICAL

OBSERVABLES

A Thesis in

Astronomy and Astrophysics

Michael S. Sipior

c© 2003 Michael S. Sipior

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

May 2003

We approve the thesis of Michael S. Sipior

Date of Signature

Michael EracleousAssistant Professor of Astronomy and AstrophysicsThesis AdvisorChair of Committee

Steinn SigurdssonAssistant Professor of Astronomy and Astrophysics

Gordon P. GarmireEvan Pugh Professor of Astronomy and Astrophysics

W. Niel BrandtAssociate Professor of Astronomy and Astrophysics

L. Samuel FinnProfessor of Physics

Peter I. MeszarosDistinguished Professor of Astronomy and AstrophysicsHead of the Department of Astronomy and Astrophysics

Abstract

In this thesis, I present a model used for binary population synthesis, and

use it to simulate a starburst of 2×108 M� over a duration of 20 Myr. This

population reaches a maximum 2–10 keV luminosity of ∼ 4 × 1040 erg s−1,

attained at the end of the star formation episode, and sustained for a pe-

riod of several hundreds of Myr by succeeding populations of XRBs with

lighter companion stars. An important property of these results is the min-

imal dependence on poorly-constrained values of the initial mass function

(IMF) and the average mass ratio between accreting and donating stars in

XRBs. The peak X-ray luminosity is shown to be consistent with recent

observationally-motivated correlations between the star formation rate and

total hard (2–10 keV) X-ray luminosity. Recent calculations published by

other groups fail to account for the aforementioned sustained high X-ray

luminosity from different mass companions. Model cumulative luminosity

functions show increasing steepness at the high end, as the most luminous

systems die off.

I also consider those XRBs with massive companions that survive the

second supernova, and go on to become double compact object binaries.

Depending upon the initial configuration at the time the second compact

object is formed, the system may go on to experience a merger through

iii

the loss of orbital energy to gravitational radiation. We show that with a

detection threshold of h ∼ 10−21 for gravitational radiation (comparable to

the expected sensitivity of LIGO I), a total merger rate of 6×10−3–10−2 yr−1

can be expected. This means that detection of gravitational wave sources

through this formation channel will have to wait for LIGO II, with an order

of magnitude improvement in sensitivity, and a commensurate thousand-fold

increase in search volume and event rates.

In an attempt to compare model predictions with observations, I analyze

a sample of 41 nearby mildly-active galaxies observed in a snapshot survey

during Cycles 1 and 2 of the Chandra X-ray Observatory. Using the observed

X-ray images, 33 nuclei are detected, and diffuse nuclear X-ray emission is

found in 25% of the targets. Substantial XRB populations are detected in

all but a few fields, many with luminosities in excess of 1039 erg s−1. Over

four hundred sources were detected overall, with fourteen in the latter high

luminosity category. All but one of these sources is found in a spiral host

galaxy, implying that such sources are generally tied to higher star formation

rates.

iv

Contents

List of Figures vii

List of Tables x

1 Introduction 1

1.1 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Physics of Binary Evolution . . . . . . . . . . . . . . . . 10

1.2.1 Gravitational Waves . . . . . . . . . . . . . . . . . . . 12

1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Simulating the X-ray luminosity evolution of a stellar pop-

ulation 18

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.1.1 X-ray binaries revealed by Chandra . . . . . . . . . . 18

2.1.2 Observables for reconstructing a star formation history 19

2.2 Population modeling . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.1 History and authorship of the population synthesis code 22

2.2.2 Population code theory of operation, choice and extent

of parameter space . . . . . . . . . . . . . . . . . . . . 23

2.2.3 Implementation of mass transfer in the code . . . . . . 31

v

2.2.4 Mass accretion and resulting X-ray luminosity . . . . 37

2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . 44

2.4 Comparison with other theoretical work . . . . . . . . . . . . 69

2.4.1 Numerical simulations by Van Bever & Vanbeveren . . 69

2.4.2 Analytic calculation by Wu (2001) . . . . . . . . . . . 72

2.4.3 Semi-analytical calculation by Ghosh & White (2001) 73

2.4.4 Comparison with observations . . . . . . . . . . . . . . 74

2.4.5 Further applications of the simulation results . . . . . 76

3 A snapshot survey of nearby mildly-active galaxies with

Chandra 84

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.3.1 Target descriptions and notable trends . . . . . . . . . 97

3.4 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4 Nova Sco and coalescing low mass black hole binaries

as LIGO sources 149

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

4.2 Example of Nova Sco . . . . . . . . . . . . . . . . . . . . . . . 155

4.3 Population synthesis . . . . . . . . . . . . . . . . . . . . . . . 158

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Bibliography 176

vi

List of Figures

2.1 Evolution of total X-ray luminosity . . . . . . . . . . . . . . . 56

2.2 Evolution of BH/XRB population, Salpeter IMF, low q . . . 57

2.3 Evolution of NS/XRB population, Salpeter IMF, low q . . . . 58

2.4 Evolution of BH/XRB population, Miller-Scalo IMF, low q . 59

2.5 Evolution of NS/XRB population, Miller-Scalo IMF, low q . . 60

2.6 Evolution of BH/XRB population, Salpeter IMF, flat q . . . 61

2.7 Evolution of NS/XRB population, Salpeter IMF, flat q . . . . 62

2.8 Evolution of BH/XRB population, Miller-Scalo IMF, flat q . 63

2.9 Evolution of NS/XRB population, Miller-Scalo IMF, flat q . . 64

2.10 Luminosity function at five epochs, Salpeter IMF, low q . . . 65

2.11 Luminosity function at five epochs, Miller-Scalo IMF, low q . 66

2.12 Luminosity function at five epochs, Salpeter IMF, flat q . . . 67

2.13 Luminosity function at five epochs, Miller-Scalo IMF, flat q . 68

2.14 Hα luminosity evolution for the first 2 Gyr after star formation 80

2.15 X-ray luminosity versus Hα compared to Ho et al. . . . . . . 83

3.1 LX vs. BT and (B − V )T . . . . . . . . . . . . . . . . . . . . 106

3.2 LX frequency by host galaxy type . . . . . . . . . . . . . . . 107

vii

3.3 Colour-magnitude diagram and luminosity function for NGC 253,

404, 660 and 1052 . . . . . . . . . . . . . . . . . . . . . . . . 127


1058, 2541 and 2683 . . . . . . . . . . . . . . . . . . . . . . . 128


2841, 3031 and 3368 . . . . . . . . . . . . . . . . . . . . . . . 129


3489, 3623 and 3627 . . . . . . . . . . . . . . . . . . . . . . . 130


3675, 4150 and 4203 . . . . . . . . . . . . . . . . . . . . . . . 131


4314, 4321 and 4374 . . . . . . . . . . . . . . . . . . . . . . . 132


4414, 4494 and 4565 . . . . . . . . . . . . . . . . . . . . . . . 133


4579, 4594 and 4639 . . . . . . . . . . . . . . . . . . . . . . . 134


4736, 4826 and 5033 . . . . . . . . . . . . . . . . . . . . . . . 135


5195, 5273 and 6500 . . . . . . . . . . . . . . . . . . . . . . . 136

3.13 Colour-magnitude diagram and luminosity function for NGC 6503137

3.14 NGC 253, 404, 660 and 1052 . . . . . . . . . . . . . . . . . . 138

3.15 NGC 1055, 1058, 2541 and 2683 . . . . . . . . . . . . . . . . 139

3.16 NGC 2787, 2841, 3031 and 3368 . . . . . . . . . . . . . . . . 140

3.17 NGC 3486, 3489, 3623 and 3627 . . . . . . . . . . . . . . . . 141

3.18 NGC 3628, 3675, 4150 and 4203 . . . . . . . . . . . . . . . . 142

3.19 NGC 4278, 4314, 4321 and 4374 . . . . . . . . . . . . . . . . 143

viii

3.20 NGC 4395, 4414, 4494 and 4565 . . . . . . . . . . . . . . . . 144

3.21 NGC 4569, 4579, 4594 and 4639 . . . . . . . . . . . . . . . . 145

3.22 NGC 4725, 4736, 4826 and 5033 . . . . . . . . . . . . . . . . 146

3.23 NGC 5055, 5195, 5273 and 6500 . . . . . . . . . . . . . . . . 147

3.24 NGC 6503 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

4.1 a vs. e for BH-BH and BH-NS systems . . . . . . . . . . . . . 171

4.2 Two mass distribution histograms for bound BH-BH systems 172

4.3 Chirp mass distribution for merging systems . . . . . . . . . . 173

4.4 Merger time vs. final binary velocity . . . . . . . . . . . . . . 174

ix

List of Tables

2.1 Simulation parameters summary . . . . . . . . . . . . . . . . 46

2.2 Power-law index of model cummulative luminosity function

at five epochs . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.1 Observed sample of nearby LLAGN galaxies . . . . . . . . . . 92

3.1 Observed sample of nearby LLAGN galaxies . . . . . . . . . . 93

3.2 Summary of source properties . . . . . . . . . . . . . . . . . . 108













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xi

Acknowledgements

It is my great pleasure to thank the members of my thesis committee for

their insightful comments and accumulated scientific wisdom. Thanks go

most especially to my advisor(s), Herr Doktor Professors Mike Eracleous

and Steinn Sigurdsson. Without their encouragement and (ahem) stern

discipline, I should likely still be writing this thesis, and only half as well at

that.

Comraderie is the bulwark of any graduate student’s morale, and I have

been indeed fortunate to have had some exceptional peers during my tenure

at Penn State. First and foremost among these is Dave Andersen, my drink-

ing mentor, without whom I should today be completely sober, and utterly

boring. But I have been truly blessed with many exceptional friends here at

Penn State, and I should like to thank them all for making the trip worth-

while. Johannes Ruoff and William Krivan for an enormous amount of fun

auf Deutsch. Ann Hornschemeier for her razor wit, and exceptional insight

into the human condition. Sarah Gallagher, for always being willing to chat,

even if I am much younger than she. Her wisdom and beer-quaffing skills

never failed to brighten my day. Chris Smeenk for being so damned clever,

and always fascinating to talk to. Rajib Ganguly for always laughing at my

jokes. Mike Weinstein for his enormous passion for pedagogy (and I have

xii

almost forgotten that his father gave me a “B” in Thermodynamics all those

years ago. . . ) Jason Best, for being inimitable. Eric Cardiff for breaking all

my stereotypes about those crazy engineers (in a good way). Karen Lewis

for being there (and letting me beat up her stuffed frog, which is a great

stress reliever, if you ever get the chance).

Anna Jangren and Bertil Olsson are still the very definition of European

Cool for me, even if Bertil isn’t really an Arctic Ninja. John Debes for his

hearty sense of humour, and for not telling me to piss off when I really, really

deserved it. John Feldmeier for actually being willing to share an office with

me (for more than one year, even!)

The Sipior Distinguished Service Medal goes to John Wise, Britton

Smith, Miroslav Micic and Simos Konstantinidis. Thank you, gentlemen,

for taking in a stray graduate student, and for letting an old geezer drink

with you young whippersnappers.

Without my parents, none of this, quite literally, would have been pos-

sible, and I thank them for their love and unfailing support for these seven

years.

Lastly, I should like to send my sincere thanks to the distant stars of

aeons past that perished, casting their enriched atmospheres into the Void,

allowing all this to come to pass. Special heartfelt thanks for all of the

Silicon, which has made my work possible.

Michael S. Sipior

Amsterdam

April 2003

xiii

Chapter 1

Introduction

1.1 Historical Perspective

X-ray astronomy began with the now-legendary rocket launch on 18 June

1962 at White Sands Missile Range, New Mexico (Giacconi et al., 1962).

This provided the first cogent evidence for extra-solar X-ray sources. The

field blossomed rapidly from this point, with Bowyer et al. (1964) making use

of a lunar occultation to show clearly that the Crab Nebula was a distinct

source of X-rays. By 1966, no less than eight distinct X-ray sources were

known to exist (Fisher et al., 1966).

A fresh surprise came with a rocket launch from Woomera, Australia in

April 1967. A source was detected with a brightness comparable to that

of Scorpius X-1 (the most luminous source known at that time), but which

had not been seen on a previous flight (Harries et al., 1967); as well, the

intensity of the source dropped off by nearly two orders of magnitude over

the next four months (Chodil et al., 1968). The first X-ray nova had been

discovered (and is now known as the X-ray transient source Cen X-2). A less

dramatic variability (factors of several in intensity) was found in Sco X-1

on time scales of roughly ten minutes (Lewin et al., 1968). Interestingly,

1

this discovery could not be made by rocket flight observations, which share

ten minutes or less of exposure time between several targets. Instead, the

variability was found by a long (∼ 7 hours) balloon observation.

The identification of these X-ray sources with binary systems came sev-

eral years later, and required a great deal more ancillary data. With the

launch of the Uhuru X-ray satellite in December 1970, dramatically im-

proved positions (0.5◦ uncertainty, down from several degrees with previous

detectors) were established for a number of X-ray sources. This made mul-

tiwavelength source correlations much easier, leading to the discovery of

a variable radio source in close proximity (less than the Uhuru resolution

limit) to Cyg X-1 (Braes & Miley, 1971; Hjellming & Wade, 1971). The error

in the radio position was on the order of a few arcseconds, and, remarkably,

contained a brilliant B0 supergiant star.

At this point, optical observations of the supergiant (Webster & Murdin,

1972; Bolton, 1972) determined that the star possessed a 5.6 day orbital pe-

riod around an unseen companion. From the radial velocity curve a mass

function was established, with a probable companion mass of more than 2

M�. That a star this massive was undetected at the distance of the super-

giant strongly implied that the companion was a compact object, possibly

even sufficiently massive to be a black hole, heretofore a purely theoretical

construct.

Shortly thereafter, Schreier et al. (1972b) demonstrated the binary na-

ture of the X-ray source Cen X-3 by showing that the source underwent

an X-ray eclipse every 2.1 days, and that X-ray pulsations exhibited by

the source every 4.8 seconds experienced a Doppler shift that could not be

explained except as coming from one element of a binary system. Similar

analyses were performed, with the same conclusion, on Her X-1, which is

2

also an X-ray eclipsing system (Tananbaum et al., 1972), as well as SMC

X-1 (Schreier et al., 1972a), among others.

Even before so many X-ray sources were shown to be in binary systems,

theorists attempted to explain the mechanism by which this luminosity was

produced. Shklovsky (1967) put forward the first neutron star binary model

for the source Sco X-1, showing that the optical and X-radiation could not

be from the same source. Moreover, he showed that the energy distribution

of the X-rays was consistent with thermal bremstrahlung arising from the

accretion of an optically-thin plasma onto a neutron star surface. Joy (1954)

and Crawford & Kraft (1956) had already introduced models of accretion

disks in binary systems, albeit in the context of CVs. Shakura & Sunyaev

(1973) and Shakura (1973) extended this to detailed modeling of accretion

disks around black holes.

These theoretical milestones were rapidly followed by the discovery of

X-ray sources with even more unusual properties. These were X-ray burst

sources with recurrence time scales on the order of a few hours; however,

all exhibited a dramatic softening of the X-ray spectrum after only a few

minutes after each flash. Hoffman et al. (1977) showed that the typical

emission radius for such objects were on the order of ∼ 10 km, comparable

to the size of a neutron star. Later observations would uncover another class

of bursting source, this time with recurrence times of only a few minutes (the

accurately-named “Rapid Burster”, Lewin et al. 1976). These rapid bursts

showed none of the spectral softening seen in longer bursts. Further study

of this source, however, revealed that, in addition to these rapid bursts, it

also exhibited the less frequent bursts seen elsewhere, and that these bursts

did display spectral softening (Hoffman et al., 1978).

This discovery, coupled with theoretical advances in the understanding

3

of helium thermonuclear flashes made by Joss (1978) led to a simple picture

to describe both types of X-ray bursts. The bursts with longer recurrence

times and spectral softening after the burst (type-I) were the result of helium

flashes on the surface of the neutron star, made possible as the accreting

material built up in sufficient quantities that the temperature and pressure

allowed for a rapid burst of fusion. These bursts softened as the material

cooled adiabatically after each burst. The short-period bursts (type-II) were

attributed to rapid variations in the rate at which material was accreted onto

the neutron star. No softening was observed because the change in the rate

of thermal bremstrahlung varied the total power emitted, but not the power

distribution. This picture has remained essentially unchanged to the present

day.

Another major result to come out of this period was the distinction

between low-mass and high-mass X-ray binaries, referring to the mass of

the companion (mass donor) star. This distinction was first clearly made by

Canizares (1975), who noted the similarity between the optically-identified

companions of X-ray sources in the galactic bulge and in several globular

clusters. These sources, embedded in an old stellar population, contrasted

strongly with many sources in the galactic disk with a luminous O- or B-star

companion to the unseen compact object. It rapidly became clear that the

X-ray properties of these two groups were similarly distinct. For example,

all of the known X-ray burst sources belong to the former group of low-

mass X-ray binaries (LMXBs), whereas high-mass X-ray binaries (HMXBs)

frequently display pulsations which are rare in LMXBs. The spectra of

HMXBs tend also to be harder than LMXBs, and are generally brighter.

HMXBs include both systems that accrete via Roche-lobe overflow, and

those systems accreting part of a strong stellar wind produced by a massive

4

companion.

Generally speaking, HMXBs have companion stars with masses above

∼ 8M�, and LMXBs have companions lighter than ∼ 1.4M�. This latter

requirement comes out of an accretion stability criterion for a neutron star

primary. In this case, a more massive donor star would undergo accretion

on a dynamical time scale, with a rapidly contracting orbit driving unstable

mass transfer. However, for systems with a more massive black hole primary,

this is no longer the case, and a class of medium- or intermediate-mass X-

ray binaries (MMXBs) should also exist (though not many, given the initial

stellar mass required to form a black hole). As well, Pylyser & Savonije

(1988) showed that, provided the donor’s convective envelope doesn’t extend

too deeply, accretion on a 1.4 M�neutron star will be stable for donor masses

up to ∼ 2M�. Tauris & Savonije (1999) later extended this result for giant

stars below this limit. So MMXBs with neutron star primaries also exist, for

borderline donor masses. Indeed, the binary Her X-1 is thought to be such a

system, with a companion mass of 2.3±0.3M� (Reynolds et al., 1997). Such

systems may also play an interesting role in solving the “birthrate problem”

regarding binary millisecond pulsars, further discussed below.

In the galactic population, there are now over 200 known XRBs, two-

thirds of which are LMXBs (Lewin et al., 1997). The number of MMXBs

at present is unclear, as there is considerable confusion with the LMXB

population. Accurate companion masses are not available for many LMXBs,

making it difficult to segregate the two populations. For the reasons given

above, not many MMXBs are expected, and only a handful are known, with

Her X-1 being the primary example. The X-ray luminosity produced by

each of these binaries, when active, runs from 1036–1039 erg s−1, making

XRBs the principal contributors to the X-ray luminosity of normal galaxies

5

lacking an active nucleus.

In 1974, a binary pulsar was discovered using the Arecibo radio telescope

by Hulse & Taylor (1975a), which was quickly shown to have some unusual

properties. Unlike every other pulsar in a known binary system at that time,

no optical companion could be discerned. Pulsar timing analysis confirmed

the mass of the pulsar PSR 1913+16 at 1.442±0.003M� , and the mass of the

companion at 1.386± 0.003M� . The orbit of the system was later shown to

be contracting at precisely the rate predicted by Einstein’s General Theory of

Relativity(Taylor & Weisberg, 1982), simultaneously demonstrating that the

companion was itself a neutron star or black hole (most likely the former).

While a powerful test of General Relativity, it also raised the question of

how such a system came to form in the first place. It is unlikely that the

pulsar has remained unchanged since its initial formation, given the spin

period (59 ms) and the observed magnetic field strength (∼ 3×1010 G). The

most probable explanation for this is that, after the more massive primary

evolved off the main sequence and became a pulsar, it received an infusion of

mass from the companion, either from Roche-lobe overflow accretion or by

passing through a common-envelope evolution phase. The resulting transfer

of angular momentum will spin up (recycle) the central pulsar; however,

this mechanism is not available to the second star, and it remains either an

ordinary neutron star or a short-lived pulsar.

A variant of this mechanism comes into play in the binary pulsar system

PSR 1534 + 12, discovered by Wolszczan (1990). Interestingly, radio pulse

timing indictates a pulsar mass of 1.32 ± 0.03M�, with a companion mass

of 1.36 ± 0.03M�; that is, the pulsar and its companion are of comparable

masses. As in the case of PSR 1913 + 16, the pulsar period and weak

magnetic field strongly indicate that the pulsar was recycled by an episode of

6

mass transfer. In this system, however, the pulsar progenitor seems to have

evolved last, which raises the question of how the pulsar could experience

mass transfer. The likely scenario in this case is analogous to that of a

classic “paradox” of binary evolution, the evolution of the eclipsing binary

Algol (β Persei). This system consists of a main sequence star orbiting an

evolved sub-giant. The assumption was that the sub-giant was the more

massive of the pair, as it had evolved off the main sequence first. Later

measurements showed that this was not the case, and it was eventually

understood that the system had experienced at least one episode of mass

transfer, and that the sub-giant had initially been the more massive star. As

departure from the main sequence is driven by the consumption of hydrogen

in the stellar core, the loss of a sizable amount of its envelope did not

significantly affect the amount of time the mass donor remained on the main

sequence. For PSR 1534 +12, the pulsar progenitor may initially have been

more massive, evolving first even after transferring a significant amount of

mass to it companion. After becoming a neutron star, the reverse occurred,

with mass flowing from the evolving companion to the neutron star, spinning

it up.

Binary evolution is also critical to our understanding of the fastest-

spinning pulsars currently known, the millisecond pulsars. Generally de-

fined to have a spin period of around 10 ms or less, millisecond pulsars are

overwhelmingly found in binary systems. Of those millisecond pulsars in

the galactic disk, ∼ 90% are known to be members of a binary, along with

about half of those discovered in globular clusters (see Bhattacharya 1997,

and references therein). Contrast this with the binarity rate among the radio

pulsar population as a whole, where the value is closer to 5%. In addition

to their short spin periods, millisecond pulsars are characterised by weak

7

magnetic fields, typically on the order of 109 Gauss or less, compared with

the 1011–1012 Gauss that is normal for slower pulsars. This weak field means

both that the neutron star is old, and that it spins down slowly compared

to stars with stronger fields. This implies that pulsar recycling has occurred

at some point in the past, as the neutron star would have had a stronger

field when newly-formed, and would not still be spinning with a millisecond

period so long after formation. A fresh infusion of angular momentum onto

an old neutron star from its companion could produce such systems, as the

weaker magnetic field means that the star will not spin down quickly. Also,

the weak field permits a higher initial (recycled) spin to be reached, since

strong-field objects tend to abruptly terminate mass transfer upon reaching

a critical spin period, becoming “magnetic propellers”, and rejecting further

accretion.

To spin a neutron star to such periods requires that an amount of mass

on the order of 0.1 M�be transferred. Even for systems accreting at or near

the Eddington rate (MEdd ∼ 10−8M� yr−1), it would take around 107 years

to transfer the requisite amount of material. Assuming the Eddington rate

applies generally, this implies that HMXB systems cannot be the progenitors

of such systems, as they do not transfer mass for a long enough period of

time, and the companion stars do not themselves live long enough. LMXBs,

on the other hand, can transfer mass stably for many hundreds of Myr, de-

pending upon the companion mass. This has led to the commonly-held view

that millisecond pulsars are an evolutionary end state of LMXB systems.

The difficulty with the above scenario was pointed out by van den Heuvel

et al. (1986) and Kulkarni & Narayan (1988), and is now known as the

“birthrate problem”. Extrapolating from current observations, and adjust-

ing for the opaque zone of avoidance towards the Galactic center, it is es-

8

timated that there are around 100 LMXB systems throughout the Galaxy.

Extensive radio campaigns to locate millisecond pulsars have borne con-

siderable fruit, and currently there are believed to be nearly 104 millisec-

ond pulsars in our Galaxy. The typical lifetime of an LMXB is roughly

τLMXB ∼ 109 years. The correspinding lifetime for a millisecond pulsar

is around 1010 years. Roughly, the formation rate of LMXBs, then, is

100/109, or 10−7 yr−1. For millisecond pulsars, the resulting formation

rate is 104/1010 = 10−6 yr−1, an order of magnitude greater. A number of

theories have been put forward to bring these rates into closer agreement.

For example, the estimate of τLMXB may be too large, if X-ray irradia-

tion of the companion star during mass transfer substantially shortens the

duration of mass transfer (Tavani, 1991). Other pathways for creating mil-

lisecond pulsars may exist; for example, it may be that some neutron stars

are naturally born with weak magnetic fields and fast spins. As mentioned

above, medium- (or intermediate-) mass X-ray binaries may provide an ad-

ditional formation channel. The lifetime of such systems is shorter than that

of LMXBs by nearly an order of magnitude, but they still live long enough

to transfer the required amount of mass. There is some evidence that this

channel produces at least a few systems, with several binary millisecond

pulsars discovered in the Parkes multibeam Galactic plane survey (Camilo

et al., 2001) showing deviations from the canonical millisecond pulsar. Their

companion stars are white dwarfs with unusually high masses, indicative of a

CO star from a more massive progenitor than those found in LMXBs. Also,

the spin periods are slightly longer than usual, indicating a smaller amount

of mass transfer than what is typical. A theoretical discussion, including

attempts to model the final evolved system can be found in Li (2002).

9

1.2 The Physics of Binary Evolution

A detailed discussion of the mechanics of evolving binaries will appear in

Section 2.2, below. For this introduction, the principal concepts will be

touched on, with the specifics of implementation delayed until the population

synthesis model is detailed.

There are four primary quantities that uniquely specify the future evolu-

tionary sequence of a binary star system. The quantities are the mass of the

primary star (M1), the mass ratio between the primary and its companion

(q), the initial eccentricity of their mutual orbit (e), and the initial semi-

major axis of the orbit (a). There are a number of other parameters that

govern the physics of the model proper, such as the efficiency with which

orbital energy can expel a common envelope, or the intensity of winds gener-

ated by stars of varying brightness on the main sequence and giant branch.

Once the rules of the physical environment have been established, however,

the output is strictly a function of the four fundamental parameters.

All of the binary star modeling considered in this work is carried out in

the Newtonian regime, with the exception of merger timescales via gravita-

tional radiation, a principal result from Chapter 4. As the binary systems

of Chapter 2 evolve out to a maximum of 2 Gyr, graviational radiation is

considered only abstractly, and is applied in a separate processing step on

systems that have reached the evolutionary endpoint of two closely-bound

compact objects.

For a binary system described in a co-rotating reference frame, the total

potential energy of the system can be written as the sum of the gravita-

tional potential and a centrifugal term arising from the choice of reference

frame. For a binary with stars of masses M1 and M2, at positions R1 and

10

R2, rotating with a common angular velocity ω, the potential field can be

expressed as (Pringle, 1985)

φ (R) = −(

(ω ×R)2

2

)

−G

(

M1

|R −R1|+

M2

|R−R2|

)

(1.1)

This relation defines a continuous series of equipotential surfaces. Of

particular interest is the unique equipotential surface which encompasses

both stars, and tapers to a single point at exactly one place along the line

which joins the centers of the two stars. This is the first, or inner Langrange

point, and the surface defines the Roche lobe of each star. If neither star

fills its lobe, the system is detached (no mass transfer). If one star fills its

lobe, material can travel along the Roche surface and through the L1 point,

transferring from one star to the other. This is a semi-detached system. If

both stars fill their respective Roche surfaces, the system is said to have a

common envelope, with the outer layers of both stars commingling freely.

The Roche surface is usually described by a Roche radius, which is de-

fined as the radius of a sphere with the same volume as the Roche lobe. An

approximation for this radius was derived by Eggleton (1983). In units of

the semi-major axis of the orbit, a, the Roche-lobe radius is given by

RL

a=

0.49 q2/3

0.6 q2/3 + ln(1 + q1/3)(1.2)

For semi-detached systems, the stability of mass transfer essentially de-

pends on how the donor’s radius changes in response to mass loss (whether

it is partially or fully convective, etc.), and the mass ratio between the donor

and the accretor. If the star expands in response to mass loss, it will con-

tinue to overfill its Roche lobe in a positive feedback loop, resulting in a

rapid burst of mass transfer. This can quickly change the orbital radius of

11

the system, often resulting in a merger of the two stars. If the star contracts

in response to mass loss, it will barely fill its Roche lobe, and will only

transfer mass in response to external stimuli; e. g., the radius expands due

to nuclear evolution, or the orbital radius shrinks via gravitational radiation

and/or magnetic braking. In addition, if the donor is the more massive star

of the pair, the orbit will contract if the mass transfer is conservative (no

material is expelled from the system). This can quickly lead to a runaway

mass transfer episode if the donor’s Roche lobe shrinks faster than the stellar

surface contracts.

In the case of common envelope systems, orbital parameters change

rapidly and dramatically, as viscous drag rapidly diminishes the orbit. Many

of these systems will end up merging during this phase. Those systems that

survive end up in a very close orbit, with a greatly improved chance of

undergoing a later phase of mass transfer. As well, if the end system is

comprised of two compact objects, the narrow separation makes these pairs

strong potential sources of gravitational radiation, with the potential for a

merger in the distant future via this process.

1.2.1 Gravitational Waves

Gravitational radiation is a direct prediction of Einstein’s General Theory.

Just as electromagnetic waves are generated by the acceleration of electrical

charges, gravitational waves are produced from the acceleration of matter.

Electromagnetic (EM) waves are self-sustaining oscillations of the electric

and magnetic fields. Gravitational waves are oscillations in the space-time

metric which defines local notions of distance. As gravitation is a vastly

weaker force than electromagnetism, so too are gravitational waves much

weaker than their electromagnetic counterparts. As such, only the most

12

powerful sources of gravitational radiation can potentially be detected.

The small wavelength of EM radiation compared to the size of the emit-

ting object allows them to be used to image the source in a detector. The

smallest wavelength expected from astronomical sources of gravitational ra-

diation is on the order of tens of kilometers, meaning that the size of the

emitter is at best comparable to, but usually much smaller than the grav-

itational waves. Thorne (1997) makes the interesting point that the infor-

mation carried by these very different radiations will be largely orthogonal,

as most sources detected via one radiation will be invisible in the other.

From General Relativity, a gravitational wave has two quadrupole po-

larisations, typically labelled “+” and “×”. Associated with these are the

two amplitudes h+ and h×, each of which is a function of time and position

that completely describe the wave. The effect of a gravitational wave is to

change the distance between two points in space, which can be thought of

as a “strain” acting on the space between the two reference points. This

strain can be quantified in terms of the fractional change in the distance,

so if the resulting length change is denoted by the function ∆L(t), then the

corresponding strain parameter h is defined as

h(t) =∆L(t)

L= F+ h+(t) + F× h×(t) (1.3)

where the F coefficients range from zero to unity and denote the projec-

tion of each component onto an arbitrary distance vector (i. e., the detector,

or one arm of the detector).

The strength of a gravitational wave source is typically given in terms

of the strain parameter it produces at the detector. Using the Newtonian

approximation to the Einstein field equations allows us to estimate the order

13

of magnitude of the strain parameter. If the astrophysical source has a mass

quadrupole moment denoted by Q, then this approximation gives a value for

the strain parameter proportional to the second derivative of the quadrupole

moment

h ∼ GQ

r c4(1.4)

Note that the strain is inversely proportional to the source distance, not

to the square of the distance. This is an important point in calculating

the expected rate of gravitational wave events and will be raised again in

Chapter 4. Clearly, sources with a rapidly changing quadrupole moment

yield the largest signal, and this gives a clue to the astrophysical systems

that should comprise the bulk of the detector signal. The gravitational

interaction of compact objects should provide the brightest sources. This

includes not only the gravitational collapse of the object at formation, but

closely orbiting neutron star and black hole binaries as well. As such a

bound system loses orbital energy to gravitational radiation, the orbit will

shrink and the quadrupole moment will vary even faster, resulting in more

radiation. This cascade culminates in the merger of the two compact objects,

an event which would project an enormous amount of gravitational energy.

Of course, these brightest sources are also very short-lived (the final stage of

inspiral may last only a few minutes), and so really luminous gravitational

wave sources will be very rare. The canonical source would be a neutron star-

neutron star coalescence, which would typically produce a strain h ∼ 10−21

at a distance of 200 Mpc.

The detection of gravitational waves similar to those predicted by theory

would be yet another verification of General Relativity, and has been the

14

focus of numerous intensive experimental efforts over the past four decades,

beginning with the bar detectors developed by Weber (1960), a pioneer of

gravitational radiation detectors. The passing of a gravitational wave causes

the bar to oscillate in response to the external strain, which can then be

calculated. Unfortunately, it is not clear that such techniques can obtain

the sensitivity needed to detect strains on the order of 10−20.

Recent advances over the last two decades in laser interferometry, how-

ever, mean that detectors capable of detecting strains of 10−21 can now be

constructed on size scales that, while not exactly compact, can at least be

termed “fundable”. The LIGO laser interferometer is the best and most

recent example of this technology, encompassing two remote sites with 4 km

interferometer arms. Even at this scale, a strain of 10−21 represents an os-

cillation on the order of several ×10−16 cm, much smaller than an atomic

nucleus. Thus, efforts are underway to construct wave “templates” using

numerical techniques to predict the waveforms seen in a variety of possible

source configurations (binary coalescence, for example). By convolving these

patterns with the data garnered from the interferometer, it is hoped that

this will greatly enhance the signal-to-noise ratio, allowing clear detections

to be made and increasing the available search volume, with a commensurate

increase in observed event rates.

1.3 Overview

Chapter 2 talks about the assumptions that went into the binary model,

and why they were chosen. After describing the process by which binaries

are evolved from the zero age main sequence (ZAMS) through to the final

end state, I detail the mass transfer procedure used by the code. Finally, I

15

show the results produced during a simulation of a starburst with a stellar

formation rate of 10 M� yr−1, and a duration of 20 Myr. The focus of this

simulation is on the time evolution of the X-ray luminosity produced by vari-

ous classes of X-ray Binaries (XRBs), and the individual contributions made

by high-mass (HMXB), low-mass (LMXB) and intermediate-mass (MMXB)

populations. The onset time for each population to reach a peak luminos-

ity is shown and the physical basis for that onset delay is discussed. A

comparison is then made to a number of recent theoretical models of X-ray

luminosity evolution, as well as observational data in the context of a re-

lationship between star formation rate and the 2–10 keV luminosity of the

host galaxy. Lastly, an application of the model investigating how the ratio

between the hard X-ray and Hα luminosity of a star-forming galaxy changes

with time.

Chapter 3 details a snapshot survey of 41 nearby galaxies with the Chan-

dra X-ray Observatory. The data reduction process is detailed, and a com-

plete target list (host galaxies) and source list are given. A summary of the

source populations in each host galaxy is included, along with plots showing

that there is little or no correlation between the optical luminosity or B−Vcolour and the total X-ray luminosity of the host galaxy.

Massive binaries can become interesting astrophysical sources again, long

after their X-ray emission is over. If both members of a binary are sufficiently

massive to become compact objects, and remain bound through the second

supernova, there is a possibility that they may become significant sources of

gravitational radiation in the distant future, after their orbital energy has

been slowly dissipated emitting gravitational waves. Chapter 4 gives a dis-

cussion of this process in terms of the evolutionary history of the system, and

uses population synthesis to estimate merger rates. The role of natal kicks

16

is discussed in terms of the effect on merger rates, as well as the importance

of the IMF, initial binarity fraction and assumptions about the fraction of

mass retained by a black hole during collapse. Rates are couched in terms

of detectability with the LIGO laser interferometer, the most sensitive to

date. Alternative merger channels are briefly discussed.

17

Chapter 2

Simulating the X-rayluminosity evolution of astellar population

2.1 Introduction

2.1.1 X-ray binaries revealed by Chandra

There is now a considerable corpus of evidence that, for “normal” galaxies

(i. e. with no active nucleus), the principal component of the X-ray lumi-

nosity above 2 keV arises from the associated population of X-ray binaries

(XRBs). This is especially true in the presence of vigorous starburst activity,

and has been further established with the advent of the Chandra X-ray Ob-

servatory, where high-resolution imaging allows an accurate source census

and luminosity function to be constructed for a diverse sample of host galax-

ies. Specific examples of large, luminous XRB populations that have been

revealed with Chandra include the vigorous starbursts in NGC 4038/4039

(the Antennae, Fabbiano et al., 2001), M82 (Zezas et al., 2001; Griffiths

et al., 2000), and the ULIRG NGC 3256 (Lira et al., 2002). Perhaps more

interesting, however, has been the discovery of sizable XRB populations

18

in non-starbursting galaxies, with inactive or mildly-active galactic nuclei,

comparable to those found in some starbursts. The implication, given the

generally slow stellar formation rate, is that a significant fraction of X-ray

binaries can remain luminous for many gigayears affecting the X-ray emis-

sion of a galaxy long after their formation. By way of example, NGC 1291

(Irwin et al., 2002), IC 5332, M83 (Kilgard et al., 2002), and NGC 4736

(Eracleous et al., 2002) all sport several dozen point sources with 2–10 keV

X-ray luminosities well in excess of 1037 erg sec−1. The first two of these

are undistinguished spirals; however, M83 is known to exhibit highly lo-

calised starburst activity in the nucleus and bar regions (Telesco et al.,

1993), though the observed XRB population is not limited to these areas.

The nucleus of NGC 4736 is known to contain a LINER (Low-Ionisation

Nuclear Emission Region, see Heckman 1980).

While a commonly-held view is that some LINERs populate the low-

power regime of the active nucleus continuum that encompasses QSOs,

Seyferts and the like, many are also associated with starburst activity (e. g.

NGC 404, NGC 4736, see Eracleous et al. 2002). I shall defer further dis-

cussion of the LINER-XRB connection to the end of the present chapter,

but raise the issue now both to emphasise the utility of the Chandra ob-

servatory (allowing individual X-ray sources to be tabulated even when in

close proximity) and to establish the role of star formation as the princi-

pal determinant of a galaxy’s X-ray properties in the absence of a strong,

presumably accretion-powered, nuclear source.

2.1.2 Observables for reconstructing a star formation history

More than any other quantity observable in the X-ray band, the luminosity

distribution of an XRB population gives great insight into the star forma-

19

tion history of the host galaxy. It is true that measurements of soft X-ray

superwinds provide a great deal of information on recent episodes of star for-

mation; however, XRBs (specifically low-mass X-ray binaries, or LMXBs)

are durable records of the distant past, and can be studied long after the

star formation driving the superwind has faded. This is doubly true for

quiescent galaxies, where a measurable superwind may simply never form.

The shape of the luminosity distribution is determined primarily by two

factors; namely, the age of the population, and the distribution of mass

ratios between the system primary (accretor) and companion (donor) star.

The normalisation of the luminosity distribution is directly proportional to

the star-formation rate (SFR) of the population in question, save for noise

resulting from counting statistics when there are few active sources. These

points are borne out by recent observations. The analyses of Eracleous et al.

(2002) and Kilgard et al. (2002), comparing the source luminosity functions

of a number of starburst and non-starburst galaxies show two significant

trends. Specifically, the luminosity function in starburst galaxies tends to

be substantially flatter, with high-luminosity sources in greater abundance.

Second, the slope of the luminosity function shows a strong correlation to

the observed 60 µm and Hα luminosities, direct measures of star formation.

This trend can be understood in terms of a stellar population’s age, which

determines which elements of the population will become luminous at some

epoch.

The simulations undertaken here allow the variation of luminosity func-

tion with Hubble type to be predicted directly, from fundamental principles

of stellar evolution coupled with a sophisticated treatment of mass trans-

fer. The generated luminosity functions can then be compared against data

from the Chandra and XMM/Newton observatories. This is a new approach

20

and allows for substantial iteration, whereby the latest observational results

inform the next, refined iteration of the code, enhancing its predictive capa-

bilities and simultaneously improving our understanding of the underlying

input variables.

The relationship between the shape of the luminosity function and the

age of the underlying population is driven by the timescale over which the

donor star in the binary begins to transfer mass. For low-mass XRBs

(LMXBs), mass transfer is driven by either the nuclear evolution of the

donor (expanding to fill its Roche lobe), or the loss of angular momentum

through gravitational radiation and magnetic braking processes (shrinking

the Roche lobe of the donor). All three of these mechanisms develop over

long timescales. In contrast, high-mass XRBs (HMXBs) begin mass transfer

on the shorter nuclear timescale of the massive donor star. HMXBs pow-

ered by Roche-lobe overflow tend to be brighter, on average, than LMXBs,

as the accretor is more likely to be a black hole when the donor is massive (a

consequence of the stellar mass function and mass ratio distribution). The

result is a flat luminosity function (more numerous bright X-ray sources) for

young stellar populations, which slowly becomes steeper as the short-lived

HMXBs give way to long-lived LMXBs.

To extract more physical insight from recent XRB data, it is natural to

consider a simplified system; where, by taking a simple set of rules to govern

star formation and evolution, and by inferring a set of input parameters from

available observations, a “binary machine” can be constructed. Synthetic

populations can be created and evolved in time, observables calculated and

then fed back as input in further iterations. Once there is confidence that the

machine can be made to closely match observed XRB populations, the next

step is to investigate the long-term evolution of synthetic XRB populations.

21

In particular, the evolution of the X-ray luminosity of a galaxy can then

be modeled. Star formation rates can be inferred from photometry in var-

ious bandpasses (see, e. g., Condon, 1992; Kennicutt, 1998; Rosa-Gonzalez

et al., 2002). Coupled with a few other assumptions, detailed below, this

is sufficient to generate an approximate picture of the XRB population at

an arbitrary epoch. Periods of mild or intense starburst activity can be

introduced, and the effect of these events quantified. Indeed, in its most

general form, the population synthesis undertaken here can be viewed as

an “integrator” of the SFR, itself a function of time, between the epoch of

galaxy formation and the current lookback time. Thus, it provides a use-

ful connection between the cosmological star formation rate as a function

of lookback time, and the population of XRBs seen at increasing redshift.

This problem has been approached in a seminumerical fashion by Ghosh &

White (2001); Ptak et al. (2001); White & Ghosh (1998), in addition to an

analytic formalism expressed in Wu (2001). Our goal is to approach the

study of the evolution of galactic X-ray properties from a numerical stand-

point, which requires fewer simplifying assumptions than a seminumerical or

purely analytic formulation. Coupled with an understanding of the relation-

ship between a galaxy’s current star-formation rate and its X-ray properties,

this work enhances the power of modern X-ray observatories to document

the historical star-formation rate.

2.2 Population modeling

2.2.1 History and authorship of the population synthesiscode

We make use of a binary evolution code detailed in part by Pols & Marinus

(1994), and modified for use in neutron star-neutron star (NS-NS ) systems

22

by Bloom et al. (1999). Our extension of the code allows for evolution

to the black hole state, with assumptions about the mass function of such

objects at the time of collapse; in addition, the technique for computing

mass transfer rates was refined considerably, by coupling it more directly to

the underlying physics, as discussed below.

For purposes of the numerical model, an initial binary system is con-

sidered to be completely described by four parameters: the mass of the

system’s primary (more massive) star, M1, which is chosen from the spec-

ified initial mass function; the primary to secondary mass ratio, q, defined

to lie between zero and unity; the initial orbital eccentricity, e; and the ini-

tial orbital semi-major axis, a. The code then evolves the binary in time,

taking into account the orbital changes caused by mass transfer, wind loss,

etc. These four quantities are tracked, as is the evolutionary state of each

star, and any mass exchanges that take place. The code terminates when

both stars have reached their respective evolutionary end points, which are

a strict function of the initial core mass.

2.2.2 Population code theory of operation, choice and extentof parameter space

The evolution of a binary pair starts with the choice of a primary mass

from an assumed initial mass function (IMF). For this work, we consider

two power law IMFs (where dN = m−αdm); the first index is α = −2.35

(the Salpeter IMF; Salpeter 1955), the second is α = −2.7, approximating

the high end of a Miller-Scalo IMF (Miller & Scalo, 1979). In both cases,

we established a lower cutoff of 4M� for the primary star’s mass, confining

the code to an interesting range of initial masses; i. e., where at least one

supernova is possible in principle. This is because our interest is in systems

23

with a neutron star or black hole, as these are the potentially luminous X-

ray sources. Our stellar models are taken primarily from Maeder & Meynet

(1989). The helium star models used are a mix of models from Habets

(1986) and Paczynski (1971), and the reader is referred to these for a detailed

discussion and evolutionary tracks.

We define the initial mass ratio q to be the initial mass of the secondary

divided by that of the primary (hence 0 ≤ q ≤ 1). The distribution of q is a

topic of some controversy, given the observational biases involved in studying

systems with diverse mass ratios (Hogeveen, 1992). A “flat” distribution,

where all values of q are equally likely, is often chosen given the difficulty

in reconstructing the underlying function. An extensive inventory of obser-

vational data was compiled by Kuiper (1935) in an attempt to address the

mass ratio distribution question. These data, coupled with the more recent

data of Batten et al. (1989), and the analysis found in Hogeveen (1992),

point to two principal results. First, in the case of single-lined spectroscopic

binaries, the distribution of q is a two-part function, where:

ψ(q) ∝

q−2 for q > 0.3

1 for q < 0.3(2.1)

For double-lined spectroscopic systems, the observed q distribution was

found to be driven almost completely by selection effects, albeit consistent

with the q-distribution of single-lined binaries above. See Elson et al. (1998)

for a further discussion of this problem in the context of massive binaries in

a young LMC cluster, where a q distribution biased towards companions of

equal mass is found, but the detection limit prevents an accurate census of

low-q systems. We consider both the flat and the low-skewed q-distributions

in our simulations below, accepting that reality likely lies somewhere be-

24

tween these two points.

The initial binary separation is chosen after Abt (1983), with a distribu-

tion that is flat in the logarithm of the semi-major axis , and in the range

10R� < a < 106R�. This distribution fits well with existing spectroscopic

surveys of nearby stars. Duquennoy & Mayor (1991), describe another sep-

aration distribution, based upon a CORAVEL spectroscopic survey of 181

Gliese catalogue stars. The function they derive is Gaussian, with a mean

of 8 × 103 R� and σ = 8 × 102 R�. We use Abt’s prescription here, but

wished to make clear that this is not a settled issue. Related population

synthesis studies currently use the former distribution almost exclusively,

often with little comment. If the Duquennoy & Mayor (1991) result holds

when expanded to a larger survey size (preferably including a few non-local

systems) then this issue will have to be revisited. Given the dramatically

wider initial separations implied by the Duquennoy & Mayor (1991) distri-

bution, one can at least make the prediction that far fewer X-ray binaries

would result, since the common-envelope phase would be less likely to occur.

This in turn would imply wider systems with larger Roche surfaces, making

Roche-lobe overflow unlikely.

The eccentricity is chosen from the standard thermal distribution, ξ(e) =

2e. This choice for the distribution of initial eccentricities is ubiquitous in

binary population synthesis. The mathematics justifying this relation can

be found in Heggie (1975), and interested readers are referred there for all of

the details. Briefly, consider a phase space of fourteen dimensions defined by

the positions q1,q2 of two particles, their velocities v1,v2 and their masses

m1,m2. Let f be a function on this space that gives the number density of

particle pairs (per unit volume of phase space) with the specified state. In

general, the pair distribution function can be written in terms of the single

25

particle distributions as

f(q1,v1,q2,v2,m1,m2) ≡ f(1, 2) = f(1) f(2) + g(1, 2) (2.2)

where g is a correlation function. If the particles do not interact at all,

the function g goes to zero. Obviously this cannot be strictly true for real

stars, but it is sufficiently accurate if the binary forms at a large distance,

a very common case. If the ensemble of stars is in thermal equilibrium, the

single particle distribution functions converge towards the Maxwell distri-

bution. After some manipulation (Heggie, 1975), it can be shown that in

the resulting f(1, 2), the eccentricity parameter is not correlated with any

other variable, and is distributed according to the relation ξ(e) = 2e.

After the initial parameters have been selected, each binary system is

evolved along the stellar tracks referenced above until both components have

reached their final degenerate form, accounting for mass-transfer-induced

stellar regeneration and stellar winds. Stellar winds from helium stars are

accounted for using the relation developed in Langer (1989), where the mass

loss rate is M = 5× 10−8M2.5 M� yr−1. This wind lasts for the duration of

the star’s helium main sequence lifetime.

When the more massive primary leaves the main sequence and ascends

the giant branch, the rapidly-swelling star may engulf its companion with

its outer envelope. This common-envelope phase will rapidly shrink the

orbital radius of the binary on a timescale of only a few orbital periods.

Those systems that avoid a merger event at the end of the CE phase will be

more likely to engage in mass transfer, as the size of the companion’s Roche

lobe shrinks along with the orbital separation. A CE phase can also result

as the secondary leaves the main sequence, though systems are unlikely to

26

survive two such events without merging. For our purposes here, during

the common-envelope phase, the orbit is circularised, and the orbital energy

is reduced by the binding energy of the envelope divided by the common-

envelope efficiency parameter, which we take to be 0.5. In other words, the

orbital energy is reduced by twice the envelope binding energy.

Neutron stars are formed from progenitors with zero-age main sequence

(ZAMS) masses of between 8 and 20 M�, inclusive, and are always given a

mass of 1.4 M�. More massive stars end up as black holes. This boundary

is unlikely to be a sharp one, as it is strongly coupled to the spin state of

the pre-collapse object (Fryer, 1999). Even assuming this was known to

perfect accuracy, the effects of magnetic fields and rotational support on

the compact object’s end state are not well understood. This point also

bears upon the magnitude and direction distribution of natal kicks received

by the neutron star at birth, from an asymmetric emission of neutrinos or

core material. The role of and justification for asymmetric natal kicks is

discussed below, including the appearance of assymetric kicks during black

hole formation.

The black hole mass function (i. e., the post-collapse mass of a BH, given

its mass just prior to the explosion) is highly speculative at this point, and

is almost certainly not merely a function of initial mass, but also of angular

momentum, to the extent that this determines the fraction of material falling

back onto the collapsing star. In order to experience a kick, the black hole’s

formation must be delayed somewhat, either due to rotational support, or

because event horizon formation occurs only after delayed fallback of mass

initially ejected from the core. Fryer (1999) has performed core-collapse

simulations in order to explore the critical mass for black hole formation,

and the final masses of the resulting black holes. As a best working scenario,

27

we have constructed a mass relation from a quadratic fit to the limited data

set found in Fryer (1999). Our fit shows that the mass of the black hole at

formation (MBH ) is related to the ZAMS mass of the progenitor (M0) by

MBH = (M0/25M�)2×5.2M�. This relation is accurate to about 10% of the

black hole initial mass at each of the values resulting from a hydrodynamic

simulation. It should be noted that this relation is almost certainly depen-

dent upon metallicity (see, for example, Fryer et al. 2002). The assumed

relation is appropriate for systems with approximately solar metallicity, but

would need to be adjusted to investigate metal-poor progenitors.

The importance of the black hole IMF in XRB formation extends beyond

the obvious effect on a system’s orbital elements. The maximum luminosity

from future mass transfer onto the black hole is a function of the hole mass.

The Eddington limit of LE = 1.3×1038× M/M� erg s−1 is frequently invoked

for this luminosity cutoff; however, this limit applies strictly only in the case

of spherically symmetric accretion. The black hole IMF is important because

it is one of two important factors that set the maximum luminosity of the

most luminous XRBs (the other is the range of mass transfer rates from the

companion star). Thus, the high-luminosity end of the resulting luminosity

function depends quite sensitively on the black hole IMF.

Of course, the Eddington assumption can be relaxed, allowing us to

test the models that have been put forward to explain the significant num-

ber of extremely-luminous XRBs now known to exist. Models that explain

these events through bona fide super-Eddington accretion (Begelman, 2002)

should result in a different distribution of luminosities and event rates (per

unit SFR) than models involving randomly-directed relativistic beaming

(King et al., 2001). Careful population synthesis can provide a means to

discriminate between these hypotheses, and we hope to report the result in

28

the near future.

Another relevant parameter concerns the magnitude of natal kicks to

be imparted to a neutron star or black hole at formation. I discuss more

fully the mechanism and justification for including natal kicks in Chapter 4,

but a brief overview is warranted here. There are two mechanisms for natal

kicks. Blaauw-Boersma kicks (Blaauw, 1961) result from a conservation of

momentum after the supernova which gives birth to the compact object. In

this scenario, the supernova ejecta are released approximately isotropically,

in the rest frame of the explosion. The remaining mass in the system receives

a kick in the direction opposite the velocity of the exploding star, with a

resulting speed change comparable to the orbital velocity of the supernova

progenitor (assuming roughly half of the total binary mass is expelled from

the system), and proportional to the mass ratio of the ejecta to the binary

(post explosion).

Asymmetric kicks arise from the anisotropic emission of neutrinos and/or

core material in the supernova event. Compared to symmetric Blaauw-

Boersma kicks, a smaller amount of mass loss is needed to generate a compa-

rable velocity change, and this is especially true if the bulk of the momentum

is carried away in an anisotropic neutrino flux. For neutron stars formed

in a supernova, this scenario is sufficient. However, if the star is massive

enough to form a black hole, there is a potential problem for the natal kick

scenario. Gourgoulhon & Haensel (1993a) convincingly demonstrate that, if

the event horizon forms on the dynamical timescale of the collapsing core,

an insufficient number of neutrinos escape to drive a supernova explosion

through envelope heating. This implies a maximum mass for a supernova

progenitor, above which the supernova is quenched by the event horizon

before it begins. We have chosen a simple criterion for whether a black hole

29

will receive an asymmetric kick during collapse; namely, all objects below

40 M� (referring to the ZAMS mass) experience a random kick. Above

this limit, objects collapse directly to a black hole, with no kick. This is a

simplification consistent with hydrodynamical simulations such as those of

Janka & Mueller (1996), Fryer (1999) and Fryer & Heger (2000).

The magnitude and direction of the asymmetric kick are still matters

of considerable debate. One strong possibility is that of neutrino-induced

convection, as discussed in Janka & Mueller (1994); Fryer & Heger (2000),

and references therein. In this process, the angular momentum acts to sta-

bilise the forming compact object, so that rapidly-rotating progenitors pro-

duce substantially-weakened explosions. The neutrino convection in rapid-

rotators is concentrated at the slowly-rotating poles, driving an asymmetri-

cal supernova. It is interesting that the kick vector depends not only upon

the rotation of the progenitor, but that an inverse correlation is posited

between the magnitude of the supernova event and the asymmetry of the

explosion. Unfortunately, the binary evolution code does not track the rota-

tion state of the progenitor, and so while the above theoretical predictions

are an interesting path for future investigations, they cannot be effectively

applied here. Therefore, I take asymmetric kicks to be oriented randomly

and isotropically. The imparted kick speed is selected from a Maxwellian

distribution with an energy corresponding to a 1.4 M�neutron star with a

speed of 90 km s−1. The distribution is truncated at the high end, with a

maximum kick speed of 500 km s−1(again, for a 1.4 M�neutron star). All

kick speeds are scaled to the mass of the recoiling object; e. g., a 7 M�black

hole will receive a speed change one-fifth the size that would be imparted to

the aforementioned neutron star.

A more complete discussion of the effects natal kicks have on binary evo-

30

lution can be found in Chapter 4. For the present discussion, it is important

to note that, in order for a system to become an XRB of any type, it must

first survive the natal kick produced when the compact object is formed.

The likelihood of this obviously drops dramatically as the imparted kick

speed increases. Since the kick speed is inversely proportional to the mass

of the compact object progenitor, an immediate prediction is that XRBs

with a black hole accretor should be more common than the assumed IMF

would indicate, as these systems will survive the first natal kick more easily

than systems with a neutron star primary. A similar effect holds for the mass

of the donor star, though in this case the effect is independent of the kick

magnitude. Systems which retain a larger fraction of their total mass have

a greater chance of surviving the first supernova; this implies that binaries

with more massive secondaries are also more resistant to disruption. The

overall effect is to increase the ratio of HMXB to LMXB systems compared

to what would be predicted on the basis of the initial IMF alone.

2.2.3 Implementation of mass transfer in the code

The code itself tracks changes of state, which means that instead of evolving

a binary system along a smoothly-flowing time axis, the next evolutionary

“event” (for example, a star may leave the main sequence, or become a

helium star after casting off its envelope through a stellar wind) is found

from the input stellar evolution tracks, and the code advances the time in-

dex accordingly. At this point the code extrapolates mass loss from winds

for each star for the elapsed time, and recalculates orbital parameters ac-

cordingly. Sudden mass loss (from supernova events) is handled identically,

with the code writing out the evolutionary state and orbital parameters

immediately before the explosion, and immediately after. If, after advanc-

31

ing to the next evolutionary state, the code determines that the two stars

should have interacted via mass transfer at some point, the system is backed

up to the immediately previous state, and the orbital parameters are set

such that (at least) one star is barely in contact with its Roche-lobe. An

episode of mass transfer is then resolved, ending with both stars inside their

respective Roche-lobes (or with a spiral-in, if the system was undergoing

common-envelope evolution and lost sufficient orbital energy to bring the

stellar cores into contact, after ejecting the envelope). The code is modu-

lar in the sense that the means by which mass transfer is resolved can be

completely redefined without affecting any other aspect of the evolution.

The original evolution code made use of a crude technique for mass

transfer, insufficient for our purposes. After interpolating on the appropri-

ate stellar evolution track, the donor’s core mass (mcd) was found. The

difference between this and the total donor mass md gave the envelope mass

of the donor, which was considered to be completely transferred to the accre-

tor over a discrete number of mass-transfer steps (twenty, by default). The

amount of mass transferred in any given step was constant, so in the default

case 5% of the envelope mass was moved to the accretor each time. After

each mass element was moved, the orbital elements were recalculated. This

low-resolution method gives a reasonable first approximation of the orbital

elements after mass transfer has concluded, but obviously is a poor choice

for studying X-ray binaries, where mass transfer is the phenomenon under

consideration.

Settling on a mass transfer routine was easily the most difficult aspect

of the simulation, and was the greatest single modification that I made to

the original code base. A commonly-used technique in Cataclysmic Variable

modeling (Meyer & Meyer-Hofmeister, 1983; Ritter, 1988) is the following:

32

Letting ρL1be the density of the mass flow through the inner Lan-

grangian (L1) point, vs the isothermal sound speed, and Q the effective cross-

sectional area of the flow, then the mass transfer rate is given as (Pringle,

1985)

−M = ρL1vsQ (2.3)

Next, consider Bernoulli’s theorem, along a path from the donor photo-

sphere, to the L1 point

1

2v2 +

∫ L1

ph

dP

ρ+ Φ = constant (2.4)

where P is the pressure, Φ the gravitational potential, and v the flow

velocity. The result is the flow density at the L1 point, given by

ρL1=

1√eρph exp

(

−φL1− φph

v2s

)

(2.5)

and the isothermal sound speed can be expressed in terms of the mean

molecular weight, gas constant, and photospheric temperature

vs =

√

TphRµ

(2.6)

From the above, the mass transfer rate can then be expressed as

−M =1√eρph vsQ exp

(

−φL1− φph

v2s

)

(2.7)

The above equation demonstrates the principal difficulty in employing

this technique. Note that the mass transfer rate depends on an exponential

function of the gravitational potential difference between the L1 point and

the edge of the donor’s photosphere. This means that even a small error

33

in estimating the potential difference will result in a very large error in the

resulting mass transfer rate. To know the precise extent of the photosphere

would require detailed knowledge of the star’s physical and chemical struc-

ture. Chemical structure is not tracked in any way by our binary evolution

code, and physical structure is generally interpolated between points on the

stellar evolution grids that are taken from a library. The result is that we

cannot know the potential difference in the mass transfer rate equation to

sufficient accuracy.

While not usable directly, the mass transfer equation makes sense at an

intuitive level. It essentially states that the resulting mass transfer rate is

strongly dependent on the extent to which the donor’s photosphere exceeds

its Roche radius. A star that just barely fills its Roche surface will exhibit a

low mass transfer rate, while a donor that would otherwise be much larger

than the resulting Roche surface will support a much higher transfer rate.

The model used in the final version of the binary evolution code in-

corporates the above principle, as described in Hurley et al. (2002), and

references therein. To determine the stability and timescale of mass trans-

fer, adiabatic coefficients are employed, which describe the response of the

donor star’s radius to mass loss. These coeffiecients are defined in Webbink

(1985), as follows:

ζad ≡(

∂ lnR

∂ lnM

)

X,s(2.8)

ζL ≡(

d lnRL

d lnM

)

(2.9)

ζeq ≡(

∂ lnReq

∂ lnM

)

X(2.10)

ζad is a logarithmic derivative of the donor’s radius with respect to mass,

34

at a constant chemical composition and specific entropy. ζL is the logarith-

mic derivative of the donor’s Roche lobe radius with respect to its mass, and

ζeq is the logarithmic derivative of the radius of the donor in thermal equi-

librium, when held at a fixed chemical composition, with respect to mass.

The mode of accretion can be determined from the following inequalities

between the coefficients

ζL < (ζad, ζeq) Nuclear timescale mass transfer. Mass transfer is not self-

sustaining, and is strongly dependent on the degree to which the Roche

lobe is overfilled. The resulting mass transfer rate is

−M2 = f(M2) ln

(

R2

RL

)3

M�yr−1 (2.11)

where M2, R2, and RL refer to the mass, radius and Roche lobe radius

of the donor star, and f(M) is given by

f(M2) = 3 × 10−6 min (M2, 5.0)2 (2.12)

This relation is chosen to ensure steady mass transfer (Hurley et al.,

2002, and references therein).

ζeq < ζL < ζad Mass transfer occurs on the thermal timescale of the donor’s

envelope. IfM is the donor mass, Mc is the core mass of the donor, and

τkh is the Kelvin-Helmholtz timescale (in years) of the donor envelope,

then the mass transfer rate is

−M2 =M2 −Mc

τkhM�yr−1 (2.13)

35

ζad < ζL Dynamical mass transfer. In this situation, the radius of the pri-

mary expands more quickly than the Roche surface after transferring

a mass element. Thus the mass-loss rate is limited only by the sound

speed in the envelope of the donor, and is a runaway process. If τdyn

is the sound-crossing time of the donor (the donor’s radius divided by

the envelope sound speed), then the mass loss rate is just

−M2 =M2 −Mc

τdynM�yr−1 (2.14)

A number of HMXBs exhibit a very different mode of mass transfer;

namely, accretion from a strong stellar wind coming off of a massive com-

panion, typically a Be- or O-star. We do not consider these systems for a

number of reasons. First, the X-ray luminosity of such an XRB is highly

variable, and strongly tied to the positions of the two stars relative to the

line of sight, as the absorption column density is far from isotropic. Second,

these systems tend to be very faint (below 1035erg s−1), unless in a rare out-

burst from an instability in the companion. While these sources have a hard

X-ray spectrum, they are never present in sufficient numbers to dramatically

alter the outcome of the simulation.

Pulsars and the associated supernova remnants (SNRs) also contribute

to the overall X-ray luminosity. While SNRs energised by a young, rapidly-

spinning pulsar can attain luminosities of 1037erg s−1 and above, much of

this radiation is emitted below 2 keV, while we are more interested in the

hard X-ray emission from 2–10 keV. Van Bever & Vanbeveren (2000) have

an interesting discussion about the small contribution of these objects in

their own synthesis work, and claim that, for the SNR contribution to be

significant, the bulk of newly-formed pulsars would require spin periods of

36

10 ms or less. Hence, we ignore this group of objects in our tally of X-ray

photons.

2.2.4 Mass accretion and resulting X-ray luminosity

For the Roche-lobe overflow systems we are considering here, the accretion

flow, collimated through the inner Lagrange point, naturally forms into a

disk structure around the accretor, as it cannot shed angular momentum

quickly enough to permit a direct impact onto the primary (Shakura &

Sunyaev, 1973). A distinction must be drawn between the mass transfer

rate (the rate of material passing through the inner Lagrange point), and

the mass accretion rate (the rate of material accreting on to the compact

object). Clearly, the X-ray luminosity depends strongly upon the latter. In a

conservative mass transfer scenario, no matter is lost from the system, and

the two transfer rates should be equal if the disk remains in equilibrium.

This is not generally true, however, and we must quantify the extent to

which mass transfer is non-conservative. We can establish a relation defined

in terms of the Eddington luminosity limit of the accretor; so the mass

transfer rate −M2, and mass accretion rate M1, are related by

M1 = (αEdd − 1) M2 (2.15)

where

αEdd = max

(

0 , 1 − MEdd

M2

)

(2.16)

The MEdd term is the mass transfer rate that generates a luminosity

equal to the Eddington luminosity of the accretor (assuming for the moment

that M1 = −M2). In other words, as the mass transfer rate climbs above

37

MEdd, the mass transfer becomes increasingly non-conservative, as αEdd

approaches unity.

The procedure for converting a mass transfer rate into a bolometric lumi-

nosity follows from energy conservation. If r1 is the radius of the accretor,

and a is the semimajor axis of the binary, then the power generated by

an accretion rate M on to a compact object of mass M1 is the bolometric

luminosity

Lbol = GM1M

(

1

r1− 1

a

)

(2.17)

For accretion onto compact objects, it is safe to assume that a� r1, so

that

Lbol =GM1M1

r1(2.18)

Half of the potential energy liberated by the infalling material is re-

leased in the accretion disk before making contact with the compact object

(Pringle, 1985). Precisely where this energy is emitted becomes important

when considering accretion on to a black hole, where energy crossing the

event horizon is lost from the system. Consider that a mass element falling

from infinity begins with zero binding energy. Upon reaching the innermost

region of a circular, Keplerian disk, the binding energy for an element of

mass m is just one half of the kinetic energy, with opposite sign

T = K + U = −K = −1

2mv2 (2.19)

= −m2

GM

R(2.20)

= −GMm

2R(2.21)

38

=1

2U(∞) (2.22)

(2.23)

Thus, we introduce the efficiency parameter ηc, with a value of 0.5 for

black hole accretors, representing the fraction of energy released before the

“accreted” material disappears across the event horizon. For neutron star

accretion, we take this value to be unity, with essentially all of the energy

radiated from either the innermost ring of the accretion disk, or from the

accretion column on to the neutron star proper. The amount of energy emit-

ted from these two regions is equal only in the special case of an accretion

disk that is truncated at the radius of the neutron star. As the magnetic

field of the neutron star acts to truncate the disk at much larger radii, the

bulk of the energy is in fact emitted from direct accretion on to the neutron

star surface.

A second efficiency factor that must be considered is the duty cycle of the

accreting sources. In many X-ray binaries, the accretion disk is vulnerable

to an instability analogous to the so-called “dwarf nova” instability seen in

many cataclysmic variables. A thorough analysis of the physics that drives

the instability can be found in Frank et al. (1992, p. 104). Recall that

for a disk comprised of annuli with temperature T and surface density Σ,

steady accretion across the annulus will only occur if the derivative ∂T/∂Σ

is positive. The functional form of T (Σ) in each annulus is a solution of

the diffusion equation, with an equilibrium solution T0(Σ0) for a specified

mass transfer rate. If the derivative ∂T/∂Σ is positive at the equilibrium

solution, then the mass accretion rate will equal the mass transfer rate, and

steady accretion will occur, with no instability. If, however, the derivative

at the equilibrium point fails this condition, the system can never achieve

39

equilibrium. As the mass accretion rate gets closer to the mass transfer rate,

the surface density of the disk climbs (as there is still a net flow of material

into the ring), with a corresponding increase in temperature. When the

temperature no longer increases with surface density, the system jumps to

a much higher temperature and mass transfer rate at the same Σ, and the

temperature derivative is again positive. However, the mass accretion rate is

now much higher than the mass transfer rate, and the ring steadily empties of

material as the system again attempts to attain equilibrium. The disk cools

until the temperature derivative reaches zero once more, at which point the

system again drops into the previous low temperature, low viscosity (hence

low mass accretion rate), and returns to the beginning of the cycle.

Reproducing this process in our numerical simulation is difficult, as the

physical parameters of the accretion disk are not tracked. As well, the

accretor itself plays a significant role in determining whether instabilities

will be seen. From a large volume of observations, it is known that LMXB

systems with black hole accretors, for example, almost always exhibit the

dwarf nova instability. For NS-LMXBs this is much less common. It is

thought that significant X-ray emission from accretion on to the neutron

star illuminates and heats the disk, maintaining the high-viscosity state and

allowing stable accretion.

For the purposes of our simulation, we have broken down this problem

into three possible cases. The first, accretion onto a neutron star primary

from a massive companion (either an NS/HMXB or NS/MMXB in the clas-

sification scheme), is the simplest case. The generally high mass transfer

rates from massive companions, coupled with the radiation from the surface

of the neutron star, act to prevent the dwarf nova instability. We therefore

take the duty cycle of such systems to be unity.

40

The second case is that of accretion onto a neutron star by a low-mass

companion (NS/LMXB). Here, the lower mass transfer rate means less il-

lumination of the accretion disk by accretion onto the neutron star. To

determine if the instability manifests itself in a given system of this type,

we employ a period criterion inferred from a plot in Li & Wang (1998). The

critical period Pcrit is defined as:

log Pcrit(days) = 6.5 ×(

M2 − 0.6

M�

)

(2.24)

where M2 is the donor mass, as before. If the donor mass is below

0.6M�, the energy released by mass transfer is judged to be insufficient

to stabilise the disk, regardless of the orbital separation of the system. If

0.6M� < M2 < 0.8M�, then the system is taken to be stable if the orbital

period is less than the critical period Pcrit above. If M2 exceeds 0.8M�, then

the system is stable only if its period is less than twenty days. All systems

with larger periods are assumed to exhibit the dwarf nova instability, and are

assigned a duty cycle of 0.1, meaning that only ten percent of the luminosity

from such systems is counted in the results showing the time evolution of

the luminosity.

The final case covers black hole accretors with a companion of any mass.

Because there is no radiation from the accretion column illuminating the

disk, a black hole system must be closely bound to avoid the disk instability.

The criterion for this case is taken from King (2001), where it is derived from

estimating when the luminosity required to suppress disk outbursts exceeds

the Eddington luminosity. The critical period for the system in this case is

Pcrit ' 3.3

(

fdisk

0.7

)−1.5(

M2

0.5MEdd

)0.75 (M1

M2

)0.125

days (2.25)

41

The fdisk term refers to the disk filling fraction, which is the ratio of

the disk radius to the radius of the accretor’s Roche lobe. We estimate

this radius as the point at which the disk is disrupted by the tidal forces

exerted by the donor star. Those systems with periods above Pcrit are

flagged as subject to the dwarf nova instability. The duty cycle of such

systems is known to be dramatically shorter than for neutron star accretors

with this disk instability. This is because, in the absence of illumination

from accretion onto a stellar surface, more material must be added to the

disk to raise the temperature to the point where steady accretion can occur,

and this material takes more time to accumulate. Typical recurrence times

are on the order of a decade or longer, implying duty cycles of 0.01 or lower.

With such extended recurrence times, it is difficult to estimate a mean time

between outbursts, as few transient systems have been observed in outburst

more than twice. For now, we assume a duty cycle of 0.01, keeping in

mind that this will likely change as more black hole transient systems are

catalogued.

The relationship between accretion mode and the observed luminosity

and spectrum from a binary has been covered by numerous authors (see

Lewin et al., 1997, and references therein). The dramatic high-luminosity,

soft-spectrum and low-luminosity, hard-spectrum states observed in Galactic

HMXBs such as Cygnus X-1 and GS 1124–68 can be understood as a tran-

sition between a bright, optically-thick disk and a dim advection-dominated

accretion flow structure (ADAF) (Meyer et al., 2000). Interestingly, from ob-

servations of state changes in Galactic HMXBs it is commonly held that the

transition occurs when the luminosity is in the neighbourhood of 1037 erg s−1

(Lewin et al., 1997, pg. 165); this corresponds to the maximum ADAF lu-

minosity of a ∼ 5 M� black hole, a representative mass for currently-known

42

black hole candidates.

Irrespective of what causes the hard-soft variability in XRBs, whether

from ADAF formation or other disk instabilities, the variation in luminosity

must be accounted for in our calculation of XRB X-ray luminosities. For a

population of XRBs, the luminosity fluctuations can be parameterised by a

single duty cycle, the fraction of time a binary spends in its high/soft state.

This duty cycle is, of course, the average of the duty cycles for each XRB in

a population, each a function of at least the orbital elements of the system,

along with poorly-understood quantities like disk viscosity. Therefore, when

presenting model results in section 2.3 I make no attempt to adjust for the

duty cycle. Results given therein are for systems which are in a continual

high (soft) state, and it must be understood that another factor should be

applied to account for this. Unfortunately, the number of XRBs for which

detailed variability information is available (that is, nearby Galactic sources)

is somewhat small; until a more detailed understanding of XRB variability

is developed, the duty cycle will remain as one of the tunable parameters

of the model. Equivalently, the results herein can be adjusted post facto

by applying a duty cycle scaling factor. Note that this factor is in addition

to that imposed by considerations of the dwarf nova instability discussed

above. Note also that this correction factor will be different each binary

considered, as it is the result of a convolution of many factors, including

orbital period, orbital radius, variability in the donor star, and so forth.

A final efficiency parameter is employed to convert the calculated bolo-

metric luminosity to the power radiated between 2–10 keV. This factor varies

with the type and spin of the accreting compact object. For simplicity (and

because the code does not track spin), we assume that 40% of the bolometric

luminosity from accreting onto a black hole is emitted in this band. For neu-

43

tron star accretion, that value is 20%. This adjustment is used everywhere

that an X-ray luminosity is quoted herein.

2.3 Simulation results

Four simulation runs were performed, each simulating a 20 Myr episode of

star formation, at a constant rate of 10M� per year. Of the four simulations,

two were performed using the Salpeter initial mass function (Salpeter, 1955),

and two with the Miller-Scalo IMF (Miller & Scalo, 1979). For each IMF,

one run was performed with a flat mass ratio (“q”) distribution, and the

other draws the mass ratio from the distribution φ(q) = 2/(1 + q)2, which

approaches the spectroscopically-determined distribution shown in equation

2.1. For ease of reference these shall be referred to hereafter as Salpeter/flat-

q, Salpeter/low-q, MS/flat-q, and MS/low-q.

The first question to address is the normalisation of the simulations; that

is, how one converts from a desired star formation rate and duration to a

total number of binaries generated. One difficulty is that the code draws the

primary mass from an IMF that is truncated at 4M� at the low end. This is

done because two such stars combined have the minimum mass necessary to

undergo a supernova; lighter primaries will never become XRBs and hence

are not considered. We therefore need a weighting factor, w, which is the

number of generated stars of all masses divided by the number of generated

stars above the 4M� cutoff. In other words,

w =

∫

∞

0.1 dN∫

∞

4 dN(2.26)

where dN is the differential number of stars with mass m. For example,

dN = m−2.35 dm for the Salpeter mass function. Performing this integration

44

for a general power law IMF of the form dN = m−α dm gives w = 40α−1 =

145.5 for the Salpeter IMF. The value of w for the Miller-Scalo IMF can

be found in an analogous fashion, by considering the three separate power

laws, giving w = 69.2 for this case.

Next, a definition of the binarity fraction is needed. We take the binarity

fraction b to represent the fraction of systems that contain two stars. For

example, if a sample of three stars exists as a binary pair and one single

star, the binarity is taken to be one-half (as opposed to two-thirds).

If we let m and q represent the average primary mass (in M�) and binary

mass ratio, respectively, and let n denote the total number of binaries formed

in a 1 Myr period, then the total star formation rate for the 1 Myr interval

is the sum of three parts; the mass contributed by the primary stars, the

mass contributed by the companion stars (weighted by q), and the mass

of the single stars which are not considered in the code but are generated

according to the binarity b. Assuming a binarity of b = 0.5, we can then

write

SFR(

M� Myr−1)

= nwm+ nwmq + nwm

(

1 − b

b

)

(2.27)

= nwm(1 + q) + nwm (2.28)

= nwm(2 + q) (2.29)

m and q are functions of the IMF and mass ratio distribution, respec-

tively. w is also a function of the IMF, and the values of each of these

parameters for the four runs are shown in Table 2.1. The last column of

the table shows the number of binary systems generated for each Myr of the

simulation, representing a constant 10 M� yr−1star formation rate. The star

formation rate varies linearly with the number of binaries formed in each

45

Simulation m (= m/M�) q w n (Myr−1)

Salpeter/flat-q 0.39 0.5 145.5 71300Salpeter/low-q 0.39 0.386 145.5 74700MS/flat-q 0.6 0.5 69.2 96300MS/low-q 0.6 0.386 69.2 101000

Table 2.1 A summary of the parameters used to normalise the four starburstsimulations. The first column gives the simulation identifier, which showsboth the mass function and mass ratio distribution used. The other fourcolumns are the mean mass of a star with the given IMF (in Solar units),the mean mass ratio of a companion to the primary, the conversion factorgiving the total number of stars formed for every star formed above 4M�,and the number of binary systems generated in each 1 Myr interval to givea 10M� yr−1 formation rate.

interval, allowing the results to be adjusted for an arbitrary SFR by simple

proportionality. This proportionality breaks down at large times, however,

when large scatter is introduced by small-number statistics, as only one or

two sources are active at any given moment.

Figures 2.1–2.13 detail the final output of the investigation. One of the

principal results of the simulations are the curves showing the time evolution

of the bolometric luminosity and population size of the X-ray luminous pop-

ulation. The bolometric luminosity is the total amount of radiated power,

over all wavelengths. To obtain the hard (2–10 keV) luminosity from this,

we must apply a correction factor of 0.2 to the neutron star accretors and

a factor of 0.4 to the black hole accretors. For this purpose, the population

is subdivided into six categories, based on two intrinsic properties of the

system. First, the accretor is classified as either a black hole or a neutron

star. Second, the donor is placed in one of three mass categories. Donors

with a mass less than 1.4M� are low-mass X-ray binaries (LMXBs), donors

with a mass between 1.4 and 8M� (the minimum mass necessary to form a

46

neutron star) are considered to be medium-mass X-ray binaries (MMXBs),

and more massive donors are, naturally, high-mass X-ray binaries (HMXBs).

Plots showing the evolution of the luminosity and size of each population

subset are shown, one set for each of the four possible parameter sets.

Figure 2.1 gives the most important and directly observable result; namely,

the total 2–10 keV X-ray luminosity for the population, evolved over the first

2 Gyr after the star formation episode. Panels (a) and (b) show the results

for a Salpeter IMF, with a low-skewed and flat q-distribution, respectively.

(c) and (d) show the analogous plots for a Miller-Scalo IMF.

The first thing that is immediately apparent from Figure 2.1 is that

the input IMF and mass ratio distribution have little or no effect on the

X-ray luminosity evolution of the population. This is an interesting and

important result, because it implies that the output depends little upon

uncertainties in the IMF, or choice of q-distribution, both parameters with

significant uncertainties. Conversely, however, this also means that it would

be difficult to constrain these parameters through a comparison of the results

with observational data.

Along these lines, an important question is the overall robustness of the

output in terms of several other variables that are not explicitly listed as

input variables, but comprise assumptions made in the implementation of

the population synthesis code. We now describe each of these in detail,

along with probable effects on the output, and a justification for the choice

of parameter value employed.

As mentioned previously, our choice for mass loss through winds during

the main sequence phase is taken from the work of Langer (1989). This is the

canonical treatment of winds used in a majority of the literature. A more

recent formulation by Hamann & Koesterke (1998) dramatically lowers the

47

wind-loss rate on the main sequence, and is used in the numerical simulations

of Van Bever & Vanbeveren (2000). This has the consequence of keeping the

orbital size smaller throughout main sequence evolution (as a larger mass

loss would widen the system dramatically). As well, stars retain a larger

fraction of mass prior to the supernova, resulting in larger compact object

masses. The end result are closer, more massive systems that are better

able to survive the first supernova without becoming unbound. This results

in a greater number of potential XRBs, and a correspondingly larger X-ray

luminosity. As an example, the Van Bever & Vanbeveren (2000) results are

several times greater than our own, with wind mass loss reduced by a factor

of four. The wind prescription of Hamann & Koesterke (1998) has only

been applied to a few systems. Until confirmed by futher observations, the

formulation of Langer (1989) is still the most reasonable choice for describing

winds.

The mapping between the mass of a black hole progenitor and the final

mass of the hole (the black hole “IMF”) is another poorly-constrained quan-

tity. We make use of the IMF derived by Fryer (1999), using hydrodynamic

collapse models. Critical to the end result is the mass at which a progenitor

will collapse directly to a black hole, with no intervening supernova (and

hence no asymmetric kick, discussed below). This limit strongly influences

the average resulting black hole mass, as objects above the limit tend to

retain most or all of their pre-collapse mass, and objects below this limit

lose a substantial fraction of this mass through a supernova. If the criti-

cal collapse limit is high, most black holes will experience a supernova at

formation, with a lower resulting mass. If it is set low, the average black

hole mass will be much greater, with correspondingly narrower orbits and

larger Eddington accretion limits. The results in Fryer (1999) do approxi-

48

mate the typical observed mass in black hole candidates (averaging around

∼ 6–7M�). However, this observable is likely influenced by selection effects

dependent on the mass of the black hole.

The magnitude and distribution of natal, asymmetric supernova kicks

strongly influences the survival of binaries past the first supernova. As the

magnitude of the kicks increase, of course, the number of XRBs goes down,

as more systems are disrupted by the initial supernova. But this effect also

changes the relative numbers of black hole and neutron star accretors, as

the lighter neutron stars will be more strongly affected by the kick. The

orientation of the kick is also important as retrograde kicks will tend to

keep the system intact (and, indeed, shrink the orbit significantly), whereas

prograde kicks disintegrate the system optimally. It is likely that the kick

orientation is influenced by the spin of the progenitor. However, this rela-

tionship has yet to be worked out in any detail, and the code does not track

spin information in any event.

Chapter 4 discusses at length the effect of kick magnitude on the survival

of a binary. Tables 4.1 and 4.2 show the change in the number of bound

BH-BH, BH-NS and NS-NS systems as the average kick magnitude changes

from 90 km s−1to 190 km s−1, and then 450 km s−1. As can be seen, systems

with black hole progenitors are only mildly affected by even strong kicks,

with bound system rates dropping by roughly 30%. Neutron star systems,

however, almost completely vanish in the presence of strong (450 km s−1)

kicks. The kick distribution chosen for our simulations approximates that

of Podsiadlowski et al. (2002), where a mix of low (∼ 90 km s−1) and strong

(∼ 450) kicks is shown to reproduce the distribution of observed neutron

star velocities.

The Eddington limit is a somewhat contentious restriction on the maxi-

49

mum accretion rate of a compact object. In our models, we assume that the

Eddington rate applies weakly; that is, the mass transfer rate is throttled

back dramatically above this limit, with no abrupt cutoff. Still, this only

permits a minor violation (typically of a few tens of percent) of the Edding-

ton limit. However, there is observational evidence of systems that exceed

this boundary by factors of several. For example, three X-ray pulsars in the

SMC are known to exhibit substantial super-Eddington accretion. Neverthe-

less, most galactic XRBs are at or below this limit, so this is representative

of most known sources.

Lastly, consider the parameter governing the efficiency of common-envelope

evolution. Webbink (1984) introduced the idea of simulating a phase of

common-envelope evolution by decreasing the orbital energy by the binding

energy of the envelope. The efficiency parameter was assumed to be unity,

so that the two quantities were equal. Later work by de Kool (1990) showed

that when compared against reasonable stellar models, the average efficiency

parameter dropped to around 0.5, and this is the value we use. This value

means that the orbit must lose twice the binding energy of the envelope

in order to dissipate it. It is true, however, that the precise value of the

efficiency parameter depends strongly on the structure of the evolving star.

More recently, Dewi & Tauris (2000) showed that the efficiency value ranged

between 0.2 and 0.8 for the vast majority of stellar evolution tracks. While

we should technically make use of the more precise values provided in this

paper, the code does not track the structure of the star closely enough for

this to be practical. Nevertheless, it is clear that the mean parameter value

is a good choice overall for calculating the end results of a common-envelope

evolution phase. Increasing the parameter would result in wider systems,

and hence fewer XRBs. However, the fact that fewer systems would merge

50

under these conditions would mitigate this somewhat. A lower value of the

efficiency parameter would dramatically increase the number of mergers,

with fewer systems surviving this phase to become XRBs.

Figure 2.2 shows the evolution of XRBs with black hole accretors, given

an initial Salpeter IMF, and a low q distribution after equation 2.1. Each

point represents the luminosity and population size for a 1 Myr interval.

Star formation progresses at a constant rate for 20 Myr; the end of star

formation is shown as a vertical dashed line on each of the plots. The

left three panels (a, c and e) show the luminosity evolution of the HMXB,

MMXB and LMXB populations, respectively. The corresponding plots on

the right side show the number of emitting systems of each type at the

indicated epoch. The evolution of all systems was tracked out to a maximum

of 2 Gyr, though massive systems evolve on more rapid timescales, and are

only tracked until the second compact object is formed. Panel (a) shows

the luminosity evolution for the BH/HMXB systems, with a peak at about

1041 erg s−1. More importantly, the peak coincides with the end of the star

formation episode. This is understood to be the result of massive donor

stars, with short main sequence lifetimes. HMXBs thus form vary quickly

after the creation of the initial binary, as the second (donor) star leaves

the main sequence. The HMXB population tracks star formation closely,

with accreting systems accumulating until star formation stops, at which

point the remaining systems quickly die off; 20 Myr after the end of the star

formation episode, no HMXBs remain. One final point: comparing the peak

luminosity in panel (a) with the peak BH/HMXB population size in panel

(b) of the same figure, we see that the mean luminosity of a binary is around

6–7 × 1038 erg s−1. This corresponds to the Eddington luminosity limit for

an accretor of roughly five solar masses, a typical black hole mass given the

51

assumed IMF and the mapping, discussed above, between the pre-collapse

mass of a black hole progenitor and the final hole mass. We conclude that

the bulk of BH/HMXB systems accrete at or near the Eddington limit, as

they are driven by massive stars with rapid evolutionary timescales.

Continuing with figure 2.2, panels (c) and (d) detail the evolution of

BH/MMXB population, with companion masses ranging from 1.4–8 M�.

The first and most important thing to notice is the delay in the onset of

this population. The first such systems do not appear until more than 10

Myr have elapsed, and their numbers do not peak until about 30 Myr after

the end of star formation. This is due, of course, to the longer evolution-

ary timescales of these less-massive companion stars. The black hole forms

quickly, but the binary will only enter the accretion stage on the nuclear

timescale of the donor star. The reader may wonder why, if this is true,

that there is a concentration of sources at ∼ 40–50 Myr. What about lower

mass companions? This peak is the result of two effects. First, because of

the choice of mass ratio distribution, a primary massive enough to form a

neutron star (at least 8 M�) is less likely to have a light companion. For a

flat mass ratio distribution, the average companion mass for an 8 M� star is

4 M�. For the low-skewed mass ratio distribution, this value drops to just

under 3 M�. So this is a selection effect of sorts, arising from the minimum

mass necessary to form a neutron star. The second factor to consider is that

the duration of a typical mass transfer episode occupies a larger fraction of

the life of a massive star than one at the light end of the MMXB category

(∼ 1.4M�). Since massive companions are formed on a timescale compara-

ble to their main sequence lifetimes, they all tend to leave the main sequence

and fill their Roche lobes in a similarly short period. This contributes to the

luminosity peak in panel (c). Longer-lived stars are less likely to leave the

52

main sequence in closely-timed groups, spreading out the resulting X-ray bi-

naries in time. These sources are not concentrated in time, but XRBs from

this group continue to be formed even at very large times (several Gyr).

One other feature of note in panel (c) is the bifurcation in the luminosity

evolution that at occurs about 70 Myr into the simulation. This population

oscillates rapidly between a low-luminosity and a high-luminosity state. A

glance at the number evolution plot shows that, at this epoch, less than ten

sources (and at times as few as two) comprise the entire MMXB group. The

variation is therefore partly due to small number statistics, as single sources

ficker in and out of mass transfer episodes. As well, the systems comprising

the upper branch of the bifurcation are almost entirely XRBs being driven

by a companion crossing the Hertzprung Gap, implying a rapid expansion

and commensurately high mass transfer rate and luminosity. The lower

systems tend to be accreting on the nuclear timescale of the companion,

with a lower resulting luminosity per system.

Panels (e) and (f) show the BH/LXMB systems. One might expect that

no such systems would be present in the first 2 Gyr of the simulation, as

the main sequence lifetime of even the most massive companions in this

category (1.4M�) is significantly longer than that. These systems are not

accreting because the companion has left the main sequence; rather, the

companion is transferring mass on its nuclear timescale. This requires a

very small orbital separation for the companion to fill its Roche-lobe, and

is unlikely to occur ab initio given the choice in the distribution in initial

orbital separations. These systems are all survivors of an episode of common

envelope evolution, when the system primary ascended the giant branch, and

enveloped the secondary star. The dramatic reduction in orbital separation

during this phase meant that, after the primary went through a supernova,

53

the secondary was close enough to begin transferring mass onto the nascent

neutron star. This explains the concentration of such XRBs seen 20–40 Myr

after the end of star formation, the time necessary for the primary to ascend

the giant branch and go supernova. The small probability of this outcome

explains the relatively small number of systems in this catgeory. If sufficient

resources had allowed the simulation to be extended to several Gyr, more

BH/LMXBs would begin to appear as the donor stars evolve off the main

sequence, in the usual fashion.

Figure 2.3 is analogous to figure 2.2, and shows the evolution of popu-

lations accreting onto a neutron star instead of a black hole. All run pa-

rameters remain identical. Panels (a) and (b) are almost precisely the same

as those of the previous figure, with the exception of a noticeable delay in

the rise-time of the NS/HMXB population. This is directly related to the

longer main sequence lifetime of the lighter neutron star progenitors.

Panels (c) and (d) show the evolution of the NS/MMXB set. This is the

most numerous population, and, at its peak value is the most luminous as

well, for a brief period from roughly 40–80 Myr into the simulation. The

evolution curves are quite regular, until around 200 Myr, when the XRB

population size fluctuates rapidly between several and ten or twenty sources

at a time, with a corresponding dramatic fluctuation in the luminosity. The

slow decrease in the maximum luminosity as the population ages results

from fewer accreting systems, and also lower mass transfer rates from in-

creasingly lighter, longer-lived companion stars. It is interesting to note,

however, that the luminosity of this subset of XRBs remains significant well

beyond even 2 Gyr. This means that populations of NS/MMXBs formed in

long-vanished starbursts continue to contribute to the X-ray luminosity of

their host galaxy, long after the galaxy returns to quiescent star formation.

54

This also means that successive waves of rapid star formation may allow

NS/MMXBs and NS/LMXBs to accumulate in a sort of hysteresis loop, so

that the total number of such systems observed in the present era represents

a number of individual starbursts taking place in the distant past. The rela-

tionship between the high-mass and lower-mass XRB systems, could best be

summarised as follows. The BH/HMXB and NS/HMXB popuations track

the current, or recent star formation rate. MMXBs and LMXBs, however,

better track the time-integrated star formation in a galaxy’s history, i. e.,

the total mass of stars formed.

Panels (e) and (f) show the NS/LMXBs. Note that they also attain a

significant luminosity, at a later epoch than the MMXB population. Like

the BH/LMXBs at this early time, these systems are the result of common-

envelope evolution. The offset in time is larger, again, because of the longer

main sequence lifetime of the neutron star progenitor. There are many

more systems here than in the BH/LMXB plot, as they are formed more

frequently from the assumed IMF.

Figures 2.10–2.13 show the luminosity function at five epochs (10 Myr,

20 Myr, 50 Myr, 100 Myr and 200 Myr) after the beginning of star formation.

The luminosity function is expressed in terms of the fractional amount of the

population that exists above the given luminosity. One interesting aspect of

these functions is that, because they represent a time-slice of the luminosity

evolution, longer-lived systems are more likely to be included. This makes

them representative, but ignores the high-luminosity sources, which are only

active for a short time. This means that the high end of all of the displayed

luminosity functions is subject to a considerable amount of variability as

short-lived, high-luminosity systems flicker on and off.

55

Figure 2.1 The evolution of the total X-ray luminosity of a simulated pop-ulation over 2 Gyr, from a star formation rate of 10 M� yr−1, extendingfor 20 Myr (vertical dashed line). Panel (a) shows the results of a SalpeterIMF with a low-skewed q-distribution. (b) also uses the Salpeter IMF, witha flat mass ratio distribution. Panels (c) and (d) use the Miller-Scalo IMFwith a low-skewed and flat mass ratio distribution, respectively.

56

Figure 2.2 The evolution of the bolometric luminosity of the BH/XRB com-ponent of the population over 2 Gyr, from a star formation rate of 10 M�

yr−1, extending for 20 Myr (vertical dashed line). Note the short delaybetween the start of the simulation and maximum luminosity, roughly cor-responding to the nuclear lifetime of the secondary (donor) star. The lumi-nosity evolution for the BH/HMXB (a), BH/MMXB (b) and BH/LMXB (c)populations are shown, alongside the evolution track of each population’ssize (d,e,f).

57

Figure 2.3 The evolution of the NS/XRB component of the population over2 Gyr, from a star formation rate of 10 M� yr−1, extending for 20 Myr. Thisis the analogue of figure 2.2. The luminosity evolution for the NS/HMXB(a), BH/MMXB (b) and BH/LMXB (c) populations are shown, alongsidethe evolution track of each population’s size (d,e,f).

58

Figure 2.4 Same as figure 2.2, but for a Miller-Scalo IMF (the mass ratiodistribution remains the same).

59

Figure 2.5 Same as figure 2.3, but for a Miller-Scalo IMF (the mass ratiodistribution remains the same).

60

Figure 2.6 Same as figure 2.2, but for a flat mass ratio distribution (all valuesof q equally likely).

61

Figure 2.7 Same as figure 2.3, but for a flat mass ratio distribution (all valuesof q equally likely).

62

Figure 2.8 Same as figure 2.2, but using the Miller-Scalo IMF, and replacingthe low-skewed q with a flat distribution.

63

Figure 2.9 Same as figure 2.3, but using the Miller-Scalo IMF, and replacingthe low-skewed q with a flat distribution.

64

Figure 2.10 The cumulative function for the population derived from theSalpeter IMF, and a low-skewed q distribution. The five epochs are 10 Myr(a), 20 Myr (b), 50 Myr (c), 100 Myr (d), 200 Myr (e). These were chosen toshow the dramatic change as star formation ends and massive stars no longerdominate (a and b), as the X-ray luminosity becomes driven by increasinglylighter companions (c, d and e).

65

Figure 2.11 Same as for figure 2.10, but using a Miller-Scalo IMF in placeof the Salpeter function.

66

Figure 2.12 Same as for figure 2.10, but using a flat mass ratio distribution.

67

Figure 2.13 Same as for figure 2.10, but using the Miller-Scalo IMF, and aflat q distribution.

68

2.4 Comparison with other theoretical work

Recently, a number of attempts have been made by various groups to use

population synthesis techniques to estimate the X-ray luminosity of a star

formation episode at various epochs. We discuss three of them here, and

draw a comparison between the results and methodology.

2.4.1 Numerical simulations by Van Bever & Vanbeveren

The simulations of Van Bever & Vanbeveren (2000) are nearest to our own

work in terms of technique. A sizable population of binary systems was

generated, using a library of stellar evolution calculations detailed in Van-

beveren et al. (1998a,b,c). Winds, in particular, receive a great deal of

attention, as the precise mass loss formalism used can greatly affect the fi-

nal evolutionary outcome of massive stars. In particular, the choice of wind

strength will change the mass distribution of black holes seen in the popu-

lation, as the black hole progenitor loses a different amount of mass prior to

collapse. As mentioned above, our simulations make use of the wind mass

loss formalism of Langer (1989). Van Bever & Vanbeveren (2000) make use

of the mass loss rates of Hamann & Koesterke (1998), which are roughly

four times smaller than those predicted by Langer, and include the effects

of line blanketing and clumping in determining wind strengths. The result

of these stronger winds should be wider binaries, but with a larger fraction

surviving the initial supernova. More black hole mass measurements are

needed to lend support to the low wind mass loss rates; in particular, a

large population of black holes with confirmed masses above ∼ 10M� would

require winds considerably weaker than those predicted by Langer (1989).

Another significant difference in the assumptions made by Van Bever &

69

Vanbeveren (2000) involves the final collapse of a massive star into a black

hole. They assume that all such objects (those with an initial mass of above

25M�) collapse directly to a black hole, with no associated supernova event.

This again has the effect of increasing the mean black hole mass, as no ma-

terial can be lost from the system via a supernova. They themsevles note

that there is observational evidence contravening this assumption; specifi-

cally, the dramatic overabundance of O, S, Mg and Si in the atmosphere of

the optical component of the LMXB GRO J1655-40, reported by Israelian

et al. (1999a). The primary in this system is a strong black hole candidate,

with an inferred mass of 6± 2M�. Our simulations assume that a star with

a zero age main sequence (ZAMS) mass of 20M� or more will become a

black hole. Those progenitors with a ZAMS mass of less than 40M� will

undergo a supernova upon black hole formation. Above this limit, the hole

forms via direct collapse, with no explosion. The difference is important,

because black holes that form through direct collapse should experience no

natal kicks, which can act to disrupt the system. If no black holes receive

kicks, then a greater fraction of systems with a black hole component will

survive to become X-ray binaries. For the same reason, a greater fraction

of the observed XRB population will comprise accreting black holes, since

neutron stars will still experience kicks at the same rate as before.

Van Bever & Vanbeveren (2000) generate a single burst of 3× 105 stars,

selecting the masses of single stars and binary primaries from the Salpeter

initial mass function. A flat mass ratio distribution is used to choose the

mass for the companion star. Single stars are tracked in this model because

the hard (2–10 keV) X-ray contribution from supernova remnants (SNRs) is

included in the total. To do this, neutron stars are assigned a magnetic field

strength and initial spin period chosen from a random distribution, which

70

allows the rotational energy loss rate to be calculated. A small fraction

(∼ 0.03) is then used to determine the amount of this energy that comes

out as X-rays. We do not include young supernova remnants in our own

calculations, for two reasons. First, the assignment of a magnetic field and

rotational period at formation ignores the importance of the evolutionary

history of the progenitor star, and so is fairly arbitrary. Second, the contri-

bution of remnants to the total X-ray luminosity should be quite small for all

but the shortest period pulsars. Indeed, after completing their simulation,

Van Bever & Vanbeveren (2000) come to very much the same conclusion,

claiming that SNRs contribute to the total starburst X-ray luminosity only

when most or all neutron stars are born with an initial period of less than

10 ms.

Van Bever & Vanbeveren (2000) plot the X-ray luminosity evolution for

the first 10 Myr after the starburst. The onset time for the X-ray luminous

phase is 3–4 Myr, precisely the same as in our own simulations. The peak

luminosity of around 1033erg s−1M−1� is reached shortly thereafter (around

5 Myr), and remains constant through the 10 Myr that are plotted. This is

very different from our own results, which show that the X-ray luminosity

continues to rise nearly 100 Myr after the end of star formation, though

the rate of increase slows dramatically after star formation ends. By only

tracking the population out to 10 Myr, Van Bever & Vanbeveren (2000)

missed the important contribution of neutron star accretors to the overall

X-ray luminosity over an extended period of time. Note that the luminosity

is given in terms of a power per unit solar mass of stars generated. If we scale

the luminosity results shown in Figure 2.1 by dividing the peak luminosity

by the total mass of stars formed, which is 2 × 108M� for each simulation,

we obtain a “specific luminosity” of approximately 5 × 1032erg s−1M−1� .

71

Interestingly, this rate is almost exactly the peak rate given by Van Bever

& Vanbeveren (2000).

One last thing to note about both the results of Van Bever & Vanbev-

eren (2000) and our own simulations is the strongly stochastic behaviour of

the luminosity evolution. This is noticeable throughout the 10 Myr range

considered by the former, and can be seen in our results at longer timescales

(typically above 100 Myr). This is the direct result of small-number statis-

tics, when few systems are in an active state at a given time. The Van

Bever & Vanbeveren (2000) results are based on a relatively small initial

population of 3 × 105 stars, many of which will not become XRBs. Our

larger population size of 2×106, and the fact that the star formation occurs

over a significant interval, helps to smooth out dramatic fluctuations in the

luminosity until a much larger period of time has elapsed.

2.4.2 Analytic calculation by Wu (2001)

As an alternative to the population modeling shown heretofore, where indi-

vidual systems are tracked from birth to evolutionary end state, Wu (2001)

views a population of XRBs in terms of differential equations governing birth

and death rates. Unfortunately, to formulate such a system of equations

requires a slew of simplifying assumptions. In particular, Wu assumes per-

fectly circular initial orbits to calculate gravitational radiation and magnetic

braking timescales, and completely ignores the effects of natal kicks from su-

pernovae. In addition, no allowance is made for disk instability effects. As

well, the parameterisation of many input quantities make comparison with

observables difficult, with no clear coupling to a star formation rate. Still,

the method has the advantage of rapidly exploring a wide parameter space,

as well as providing analytic relations between certain parameters that would

72

not be immediately obvious from numerical population synthesis.

A comparison of the results from Wu (2001) is complicated by the fact

that no easy way exists to adjust his results to a specific star formation rate.

Wu presents a number of luminosity functions representing the distribution

of XRBs at a given epoch, but no normalisation is possible. Nevertheless, it

is interesting to note that the bulk of the curves display a distinct turnover

at a luminosity of around 6 × 1037erg s−1, a turnover which is also clearly

visible in many of the luminosity functions to come out of our simulations,

and roughly one-third of the Eddington luminosity of a typical neutron star.

As more work making use of this technique appears, a better comparison of

these two dramatically different approaches to population synthesis should

be possible.

2.4.3 Semi-analytical calculation by Ghosh & White (2001)

Ghosh & White (2001) make use of a related methodology through which

they use X-ray survey data to infer the long-term evolution of cosmic star

formation rates. They also establish a system of differential equations de-

scribing the population of X-ray binaries, though their approach is more

rooted in experimental data, and is couched in terms of a real star forma-

tion rate, as opposed to the parameterised version found in Wu (2001).

The goal of this study is quite different from our own, and is focussed on

the X-ray luminosity evolution over scales of a Hubble time. Our work is in

rough agreement in a qualitative sense; that is, the relative contribution of

the various XRB species is similar, and the shape of the luminosity curves

are analogous. We differ in one major prediction, however. Ghosh & White

predict that the LMXB population will not become a significant contributor

to the total X-ray luminosity until several Gyr have passed; in other words,

73

when the companion stars either begin evolving off the main sequence, or lose

sufficient orbital energy to magnetic braking and/or gravitational radiation.

Our prediction is that a large number of LMXB systems will become active

in the first 200 Myr or so after a vigorous star formation episode; e. g.,

panels (e) and (f) on any of figures 2.2–2.9. These systems are survivors

of a stage of common-envelope evolution, which shrank the orbital radius

and permitted Roche-lobe overflow to occur several billion years before it

would otherwise be possible. Ghosh & White do not consider the effect of

common-envelope evolution in their equation set, and so do not predict this

feature.

2.4.4 Comparison with observations

Recently, Ranalli et al. (2002) extended the well-known correlation between

a galaxy’s far-infrared (and radio) luminosities and the underlying star for-

mation rate to the 2–10 keV energy regime. Making use of ASCA and Bep-

poSAX observations of nearby actively-star forming galaxies, they proposed

that the star formation rate could be expressed in terms of the 2–10 keV

luminosity of the host galaxy as

SFRM� yr−1 = 2.0 × 10−40 L2−10keV (2.30)

For our simulated galaxy experiencing an SFR of 10 M� yr−1, we found

that the peak hard X-ray luminosity, reached at the time star formation

ceases and sustained for several tens of Myr, was around 4 × 1040 erg s−1.

As discussed earlier, this result is largely independent of the choice of IMF

or binarity fraction. By the above relation, such a galaxy should have an

underlying star formation rate of 8 M� yr−1, which is in good agreement

with the actual rate used in the simulation. This reinforces our original

74

claim that the principal output of the code is in good agreement with reality,

i. e., that the estimated luminosity and relative population sizes are robust

results.

Table 2.2 shows the measured slopes of the cumulative luminosity func-

tions shown in Figure 2.10 and those immediately following. As can be

seen from the Table, the principal determining factor for this quantity is the

elapsed time since the end of star formation. This is because the luminosity

function becomes dramatically steeper as the population ages and luminous

X-ray sources die off. In principle, one could use this value to estimate the

age of a stellar population. In practice, this would require a great deal of

detailed information about the star formation history of the host galaxy, in

order to segregate individual stars by the particular star-formation episode

which spawned them.

Grimm et al. (2002) show a number of cumulative luminosity functions

based upon recent Chandra and ASCA observations of nearby starbursts.

The cummulative luminosity functions of twelve noted starbursts were fit to

a relation describing the fall off of the luminosity function at the high end.

They derive a best-fit power-law index of −0.6, which can be compared to

our results in Table 2.2. Grimm et al. (2002) does not discuss the variation

in this coefficient with time (as the stellar population evolves), and so it is

important to compare the value of the coefficient at the appropriate epoch.

As most of the objects in the study are still actively star-forming, we must

compare these results to our 10 Myr and 20 Myr calculations, as these

represent the model starburst when it is still active and the X-ray luminosity

is dominated by BH-HMXB systems. While still slightly steeper than that

of Grimm et al. (2002), the results at 10 Myr, especially for the Miller-

Scalo IMF, are in reasonable agreement. It should also be noted that the

75

power-law indices measured for the individual galaxies have a substantial

spread to them. Similar measurements for smaller sets of galaxies (Eracleous

et al., 2002; Kilgard et al., 2002), are in closer agreement with our steeper

cummulative luminosity function. Our cummulative LFs are qualitatively

correct, as they become both steeper and fainter with increasing time. This

point is at the heart of the observed discrepancy between the luminosity

functions of spiral galaxies and ellipticals (Zezas et al., 2001).

2.4.5 Further applications of the simulation results

In addition to being a useful probe of long-term trends in a population’s

X-ray luminosity, the technique we employ can give insight into the evolu-

tionary trends of other observables. The Hα luminosity is a quantity strongly

correlated with ongoing star formation, and can be predicted from the out-

put of our population synthesis code. The Hα luminosity is driven by the

recombination of electrons liberated from hydrogen atoms by the ionising

radiation of O-stars,. Thus, coupled with the assumption of an IMF, the

Hα luminosity leads to an estimate of the instantaneous star fomation rate.

For calculation of the Hα luminosity, we made use of the stellar spectra

by models of Kurucz (1991), implemented in the photoionisation program

Cloudy (v. 96.0) (Ferland, 1996). All Kurucz models for stars with an

effective temperature between 25000 K and 50000 K, and surface gravity

between 103 and 105 cm s−2 were considered. For each of these models, an

emission rate for ionising photons was calculated, for a fiducial bolometric

magnitude of −10. The surrounding medium (i. e. the HII region) was

assumed to have an extremely large optical depth, so that all ionising pho-

tons would eventually lead to a recombination. From atomic physics, it is

well-established that roughly 30% of such recombinations will result in an

76

Table 2.2. Power-law index of model cummulative luminosity function atfive epochs

Model 10 Myr 20 Myr 50 Myr 100 Myr 200 Myr

M-S / flat q −0.8 to −1.25 −1.1 to −1.7 −0.7 to −1.25 −3.3 to −4.4 −2 to −3.6M-S / low q −0.8 to −1.1 −1.1 to −1.5 −1.1 to −1.8 −2.9 to −5.7 −2.9 to −5.7Sal / flat q −1.2 to −2.5 −1.3 to −1.9 −1.4 to −3.6 −2.9 to −5.7 −2.9 to −5.0Sal / low q −0.9 to −1.5 −1.1 to −1.5 −0.9 to −1.6 −2.9 to −4.4 −2.2 to −3.6

Note. — The measured ranges of the slope of the tail-end a series of model luminosityfunctions. The model column refers to the assumed IMF and whether the mass ratio distributionis flat, or skewed towards low-mass companions. “Sal” = Salpeter IMF, “M-S” is the Miller-Scalo IMF formulation.

77

Hα photon being produced (with a slight temperature dependence). From

this, the Hα luminosity for the model (with a bolometric magnitude of −10)

results directly.

For each star that falls within the limits calculated (which maps to spec-

tral types O and B), the population synthesis code calculates the bolometric

magnitude using the effective temperature derived from the stellar evolu-

tion track. This is just the basic relation between effective temperature

and bolometric luminosity: L = 4π R2 σ T 4. Recast in terms of bolometric

magnitudes (with the radius given in cm), this becomes:

Mbol = 42.36 − 10 log Teff − 5 logR (2.31)

Once we have a bolometric magnitude for the star, we find the Hα lumi-

nosity that Cloudy calculated for a star with the same effective temperature

and gravity (but with a bolometric magnitude of -10), and then scale the

result appropriately.

The results are shown in figure 2.14. Panels (a) and (c) show the case

of a Salpeter IMF with a low-skewed and flat q-distribution, respectively.

Similarly, panels (b) and (d) use the Miller-Scalo IMF. The first thing to

note is the significant difference (20–30%) between the two IMFs. This is

not surprising, as the Salpeter IMF will result in a larger fraction of massive

stars than the Miller-Scalo IMF; hence, a larger number of O-stars result,

with a corresponding increase in ionising photons. Interestingly, the mass

ratio distribution makes very little difference at all, probably because few

secondary stars would have enough mass to be O- or B-stars, irrespective of

the mass ratio distribution used.

The unusual behaviour of LHα at large times (past ∼ 30 Myr), results

78

from a breakdown in a critical assumption in the calculation of the Hα

luminosity. In particular, after the rapid decay of Hα due to the decline in

the O-star population, the luminosity rebounds due to the contributions of a

larger population of relatively hot post-AGB stars of lower mass. However,

the HII region is generally dissipated by the strong winds and supernova

activity of the previous population of O-stars and so the assumption of an

infinite optical depth breaks down, so that one recombination requires many

ionising photons. The bottom line is that the plots in Figure 2.14 are not

valid beyond 30 Myr or so. The right axis of the plot, however, shows the

rate of ionising photons, and is independent of the surrounding medium.

This rate remains relatively constant over the remainder of the simulation,

but is not effective in producing Hα photons.

79

Figure 2.14 These four plots show the time evolution of the ionising photonrate for the first 2 Gyr after a star formation episode. SFR = 10M� yr−1,with a duration of 20 Myr. Panels (a) and (c) use the Salpeter IMF, whereas(b) and (d) make use of the Miller-Scalo IMF. The top plots have a low-skewed q-distribution, and the bottom plots have a flat one. Note that choiceof IMF is the biggest factor, whereas a change in the mass ratio distributionmatters very little. This is due to the fact that few secondaries would havesufficient mass to be O- or B-stars with either distribution. For large opticaldepths (early times), the Hα luminosity is almost exactly 1011 times smallerthan Qion. Beyond 30 Myr or so, the assumption of large optical depth toionising photons breaks down, and the Hα luminosity deviates from what ispredicted above.

80

The relationship between LHα and the star formation rate developed in

Figures 2.14 and 2.15 has a direct application to LINERs, including those in

a Chandra snapshot survey of nearby galaxies, further detailed in Chapter

3 and Ho et al. (2001). Ho et al. note that when plotting the log Hα

luminosity of known, luminous active galactic nuclei (AGN) such as Seyfert

galaxies and quasars, versus the log of their X-ray luminosity, the result is

that most objects fall close to a well-defined line. Similarly, nuclei identified

as LINERs and so-called “transition” or HII objects fall close to the same

line, though at much lower luminosities. The implication, they claim, is

that these objects are powered in precisely the same fashion as the more

energetic quasars and Seyfert galaxies; namely, through accretion onto a

supermassive black hole, and they simply occupy the low-power regime of

this mechanism.

One can ask, however, if there are different physical processes that could

give a similar result. In other words, if this test for AGN membership could

have an inherent degeneracy. XRBs resulting from vigorous star formation

pose an interesting alternative explanation for the observed LX–LHα rela-

tionship. By simulating a star formation episode, and then asking where on

the LX–LHα plot the results appear, we can evaluate the relation shown by

Ho et al. (2001).

Figure 2.15 shows a plot of LX versus LHα for a starburst with an SFR

of 10M�yr−1, lasting 20 Myr, from a Salpeter IMF and a flat mass ratio

distribution. The values from the first 40 Myr are plotted, with each point

representing 1 Myr. The values rise rapidly to the left when the starburst

begins, as massive O-stars turn on and begin ionising their HII regions. So

starbursts will remain essentially on the right-most vertical line indicated for

at least 40 Myr (at which point much of the ionised material has dispersed,

81

and our assumption of large optical depth is no longer valid). But this

constant Hα scales with the SFR just as LX does (i. e., linearly). We can

then ask what values of the SFR would bring the population into proximity

of the line discussed in Ho et al. (2001). The expected locus of points

for two smaller SFRs, 1M� and 0.2M� yr−1 are shown for comparison.

Interestingly, star formation rates similar to that of our own galaxy result

in values of LX and Hα that are not greatly out of line with the low-energy

region that Ho et al. show is populated by LINERs and transition objects.

As shown previously, LX from a burst of star formation may remain high

long after the burst ends, as LHα declines with the death of the last O-

stars. A weak starburst could potentially cross the AGN locus of points at

low LX as it evolves, directly after the end of star formation. This suggests

that low-luminosity AGN are not automatically distinguishable from actively

star-forming populations, and that the diagnostic put forward by Ho et al.

does not give a complete picture.

82

Figure 2.15 The figure shows the X-ray and Hα luminosity evolution fora population undergoing star formation at 10 M� yr−1for 20 Myr, with aSalpeter IMF and flat mass ratio distribution. The diagonal dashed lineshows the region that Ho et al. (2001) suggest implies a central AGN. Thetwo vertical lines on the left show where results at lower star formation rateswould fall. Note that for low SFRs, there is substantial confusion betweena population of X-ray emitting binaries and the AGNs from the Ho et al.sample.

83

Chapter 3

A snapshot survey of nearbymildly-active galaxies withChandra

3.1 Introduction

Among the most startling discoveries made by the Chandra X-ray Obser-

vatory was the presence of large populations of luminous X-ray binaries

in otherwise normal galaxies with inactive or mildly-active nuclei. Many

of these galaxies are actively star-forming, such as the Antennae and M82

(Zezas et al., 2001), or had a recent bout of star formation, like NGC 4736

(Eracleous et al., 2002). Even normal elliptical galaxies sport significant

XRB populations, albeit with a lower maximum luminosity than those seen

in many spirals. NGC 4697, for instance (Sarazin et al., 2000, 2001), con-

tains over 80 such sources.

The natural question to ask, then, is how the XRB population relates

to overall galactic properties such as Hubble type and nuclear activity. We

can attempt to understand these differences from population synthesis tech-

niques as described in Chapter 2. However, our imperfect understanding of

84

stellar evolution means that this approach must be informed by a compre-

hensive observational program.

To study the variation in these populations with different host galaxy

properties, there are two attacks one may consider. The first is to choose a

small number of canonical targets as archetypes and perform long observa-

tions on these. A second approach requires a broad but shallow survey of

host galaxies that are close enough for individual X-ray sources to be dis-

tinguished given the resolution limits of the telescope. This does have the

limitation of a higher minimum luminosity for sources to be catalogued, so

that the completeness limit will vary dramatically with the distance to the

host. Both approaches are being used with the Chandra observatory, and

we describe in Section 3.2 the results from a comprehensive survey of the

latter type.

3.2 Data analysis

A survey following the broad but shallow approach mentioned above was,

in fact, undertaken by the Penn State ACIS team through guaranteed time

observations in Cycles 1 and 2 (late 1999 through early 2001). The sample

consists of 41 targets, drawn from the Palomar optical spectroscopic survey

of nearby galaxies (Ho et al., 1997a,b), comprising a nearly complete subset

of 486 northern galaxies with BT ≤ 12.5 mag. The 41 targets were consid-

ered to be AGN candidates from optical studies and were chosen on that ba-

sis. They range from Seyfert nuclei, to low-ionisation nuclear emission-line

regions (LINERs; Heckman, 1980), and so-called LINER/HII “transition

nuclei” (Ho et al., 1997b). All but six comprise a complete, volume-limited

sample out to 13 Mpc. The remaining six were included because they were

85

archetypes of different classes.

The original purpose of this survey program was, foremost, to resolve the

issue of the power source in nearby emission-line nuclei. Detection of a single

nuclear hard X-ray source, in the absence of a significant number of ancillary

sources (XRBs) was to be construed as confirmation of a low-luminosity

AGN (LLAGN). Spectral information from the brighter sources could be

used to help further constrain the emission mechanism. Interestingly, of

the 41 target galaxies, eight do not display an X-ray source within several

arcseconds of the nucleus, and yet each of these was optically selected as a

potential LLAGN. While the initial focus of the survey was on the nuclear

sources, the benefits of Chandra’s spatial resolution apply equally well to

the study of the X-ray sources associated with the host galaxy.

The survey was carried out in snapshot mode, by the AXAF CCD Imag-

ing Spectrometer (ACIS) with exposure time ranging from 1–3 kiloseconds.

The standard 3.2 s readout time was used for all but six of the observa-

tions. The remaining targets possessed a luminous nuclear source that had

been noted in previous ROSAT and ASCA observations. To avoid the phe-

nomenon of pile-up (where multiple photon events occur in a given pixel

before a readout can be performed), a special subarray mode was used for

these exposures that allowed a fraction of the chip to be read out much more

frequently. The 12 -chip subarray mode (half the chip is read every 1.6 s) was

used for exposures of NGC 4278 (M98), NGC 4374 (M84), NGC 4639 and

NGC 5033. NGC 4579 and NGC 4594 both required 18 -chip mode to prevent

pileup. For these targets, studies of the off-nuclear sources are impeded by

the resulting smaller field of view.

Table 3.1 summarises the major properties of each of the 41 fields. The

morphological type and position (J2000.0 epoch) for each galaxy are given,

86

along with the distance in Mpc. These were mostly obtained from Cepheid

measurements (Ferrarese et al., 2000) and surface brightness variability tech-

niques (Tonry et al., 2001). All other distances come from Tully (1988), with

the assumption that H0 = 75km s−1Mpc−1. The error in nuclear position is

also shown, with references to the relevant astrometric survey. The last two

table columns give the mean background for the field in counts per square

arc-minute, and the minimum detectable source threshold in total counts.

This last quantity is quite low because the short exposure times result in

almost no background signal at all, allowing even five or six photon events

to become statistically significant.

Data reduction began with the level 1 event files supplied by the Chan-

dra X-ray Observatory Center (CXC). These events have undergone a bare

minimum of processing prior to delivery, as opposed to the level 2 event files

(also supplied for most of the observations), which have gone through the

complete CXC reduction pipeline. The choice to begin with the raw event

files was made because the reduction process in use at Penn State includes a

thorough correction for Charge Transfer Inefficiency (CTI) , an effect with a

strong temperature dependence that is discussed in Townsley et al. (2000),

and references therein. This approach also grants greater flexibility, as some

assumptions made in producing the supplied level 2 files (for example, the

introduced software position randomisation) are not necessary or appropri-

ate for our situation. As well, starting with the low-level event files gives

us better control over aspect glitches, and the effect they have on the final

events list.

The first correction applied removed the software dithering mentioned

previously. We then inspected the events for the so-called “Bev grades”—

flight grades 24,66,107,214 and 255. These events should be removed by the

87

ACIS camera itself, and should never appear in any event list; their presence

strongly indicates a processing error.

Next came the correction for CTI effects. By design, each of the chips

in the ACIS array have one of two energy responses, depending on whether

the chip is back- or front-illuminiated. This refers to the penetration depth

which electrons liberated by the impacting X-ray must attain to be registered

as a count by the detector. Back-illuminated chips have a much better

response at lower energies than front-illuminated chips, due to the smaller

required penetration depth. As differences in response exist even between

chips of the same type, the CTI correction is unique for each of the ten

chips in the array. All of our targets were centered on the fourth chip in the

spectral array, S3, which is back-illuminated. However, several targets had

significant source populations on neighbouring chips, so an accurate CTI

correction was needed on these chips as well.

The CTI effect is essentially a charge “stickiness” which prevents all

of the charge contents of a register from moving from row to row during

readout. As a result, events that occur further from a readout row appear

fainter, because a larger fraction of the generated charge is lost before it

can be read out. As CTI is strongly temperature-dependent, it follows that

colder chips show less of an effect than warmer ones. During Chandra’s

first observing cycle, the temperature of the ACIS array was lowered from

−110◦C to around −120◦C. This dramatically reduced the CTI problem for

later observations. Given the short observation lengths, and correspondingly

low count totals, CTI for these later observations was judged to be of little

significance to the overall result. Therefore, the CTI correction was only

performed on those observations taken at the higher chip temperature.

Following this, the event list was scanned for any flaring events that could

88

be seen. Flares are caused by cosmic ray impacts, that create a large amount

of charge in pixels in the vicinity of the event. This charge is dissipated over

the next several readings of the chip, and could be incorrectly interpreted

as a rapidly-decaying X-ray source. These events were flagged and then

removed after all other filtering had taken place. ACIS flight grades 0,2,3,4

and 6 were retained as good events, and the rest were discarded as probable

cosmic ray events. Filtering on the 32-bit status flags provided for each

event was limited to excluding events with bits 16–19 inclusive, as these are

set when the event is flagged as a flare.

The “flight timeline” distributed by the CXC for every observation de-

tails the so-called Good Time Intervals (GTIs), during which the aspect

solution of the satellite is well-known, and events can be counted. Outside

of these GTIs, event positions may be suspect, and should be excluded from

the final event lists. In addition, it is important to shorten the given expo-

sure time to account for these glitches, to ensure that count rates remain

accurate.

Lastly, the S4 chip in ACIS exhibits a considerable amount of horizontal

streaking (at constant CHIPY). This is a manifestation of readout noise and

must be compensated for before a source search can begin. Fortunately, the

CIAO tool destreak performs just this function. Streaking events have a

status bit set which can be filtered against later.

The resulting cleaned events file is now suitable for use by the source-

detection algorithm wavdetect, detailed extensively in Freeman et al. (2002).

The events are filtered for energies between 0.5 keV and 8 keV for front-

illuminated chips, and 0.2 keV to 8 keV for the low-energy sensitive back-

illuminated chips. From these events, four image files were constructed by

changing the binning applied to the array. The first 1024 × 1024 image was

89

just the S3 chip, “binned” by a factor of unity. The next two 1024 × 1024

images were binned by factors of 2 and 4, and show an increasing fraction

of the total field of view. The last image was a large 2048 × 2048 image

showing the entire array binned by a factor of 4.

The wavdetect algorithm makes use of wavelets—sinusoidal functions

with an average value of zero, and with a zero value outside of a very lim-

ited region of space. This property allows them to be used as filters in both

space and frequency. By choosing wavelets with appropriate size scales and

correlating with an image, one will get large correlation coefficients only in

the vicinity of a rapid change in the underlying data. The specific formu-

lation for wavelets in wavdetect is the Marr, or “Mexican Hat” function,

derived from the two-dimensional Gaussian. As a function of x and y, and

the input gaussian parameters σx and σy, the Marr function is defined as

W

(

x

σx,y

σy

)

=1

2πσxσy

(

2 − x2

σ2x

− y2

σ2y

)

× e−(x2/2σ2x)−(y2/σ2

y) (3.1)

There are a number of advantages to using this formulation. The for-

mula is easily manipulated analytically, allowing a number of operations (for

example, Fourier transforms) to be applied without computation, speeding

execution time dramatically. As well, the correlation of this function with

both linear and constant functions is zero, so that a flat or linear background

will not affect source detection in any way. We chose five spatial scales for

source detection: 1, 2, 4, 8 and 16 pixels.

For each of these four images, the wavdetect algorithm was run with a

sensitivity parameter of 10−6. The four resulting catalogues were merged so

as to remove multiple detections of the same source. At this point, the results

of wavdetectwere confirmed by inspection, to ensure that no obvious source

90

was skipped, and so that an obviously spurious source could be removed.

Source extraction was then performed on the resulting region list. Estimates

of source counts made by wavdetect were not used directly, only the source

positions.

The decision of whether a source was, in fact, associated with the target

galaxy, and not merely a foreground dMe star (or a luminous background

AGN) was made by comparing the source’s off-nuclear distance to the pub-

lished D25 diameter for each galaxy. Sources outside this distance were

excluded, and the rest were deemed to be associated with the host galaxy.

Finally, it should be noted that the source search was performed on

a full-band (0.2–8 keV) image, rather than two separate searches in each

band. The resulting background was correspondingly much higher than

an image confined to a 0.2–2 keV range. However, the source count rate

is only moderately larger in the full-band image, with the result that our

source detection threshold is somewhat conservative, even given the very

low background level seen on the full-band images.

91

Table 3.1. Observed sample of nearby LLAGN galaxies

Galaxy Nucleus ACIS observation

NGC Messier D Morph RA Dec δ Nucl. Obs. texp Bk Thresh.(Mpc) (J2000) (′′) Type Date (ks) (cts/′2) (cts)

253 · · · 2.4 SABc 00 47 33.10 −25 17 18.0 · · · · · · · · · 2000-08-16 2.160 106 6404 · · · 2.4 SA0 01 09 26.90 +35 43 03.0 · · · · · · L2 2000-08-30 1.760 72 6660 · · · 11.8 SBap 01 43 01.60 +13 38 23.1 0.40 T2/H 2001-01-28 1.940 75 4

1052 · · · 17.8 E4 02 41 04.80 −08 15 21.0 0.07 L1.9 2000-08-29 2.400 150 61055 · · · 12.6 SBb 02 41 45.20 +00 26 30.0 0.30 T2/L2 2000-01-29 1.150 338 101058 · · · 9.1 SAc 02 43 29.90 +37 20 27.0 · · · · · · S2 2000-03-20 2.440 107 62541 · · · 10.6 SAcd 08 14 40.40 +49 03 51.0 · · · · · · T2/H 2000-10-26 1.950 50 42683 · · · 5.7 SAb 08 52 41.20 +33 25 09.4 0.03 L2/S2 2000-10-26 1.760 67 52787 · · · 13.0 SB0 09 19 18.90 +69 12 10.5 0.05 L1.9 2000-01-07 1.160 49 42841 · · · 12.0 SAb 09 22 02.70 +50 58 35.0 · · · · · · L2 1999-12-20 1.770 20 53031 M81 1.4 SAab 09 55 33.20 +69 03 55.0 0.10 S1.5 2000-03-21 2.410 113 63368 M96 8.1 SABab 10 46 45.80 +11 49 11.0 0.30 L2 2000-11-20 2.010 57 63486 · · · 7.4 SABc 11 00 23.90 +28 58 30.0 · · · · · · S2 1999-11-03 1.780 17 63489 · · · 6.4 SAB0 11 00 18.10 +13 54 08.0 · · · · · · T2/S2 1999-11-03 1.780 142 53623 M65 7.3 SABa 11 18 55.60 +13 05 28.9 · · · · · · L2: 2000-11-03 1.760 77 53627 M66 6.6 SABb 11 20 14.90 +12 59 21.0 0.30 T2/S2 1999-11-03 1.780 257 43628 · · · 7.7 SAbp 11 20 16.20 +13 35 22.0 0.20 T2 1999-11-03 1.780 222 53675 · · · 12.8 SAb 11 26 08.00 +43 34 58.0 0.80 T2 1999-11-03 1.770 257 64150 · · · 9.7 SA0? 12 10 33.20 +30 24 12.8 · · · · · · T2 2000-10-29 1.760 86 54203 · · · 9.7 SAB0 12 15 05.00 +33 11 49.0 0.10 L1.9 1999-11-04 1.780 91 54278 · · · 9.7 E1 12 20 06.80 +29 16 50.0 0.10 L1.9 2000-04-20 1.430 33 44314 · · · 9.7 SBa 12 22 31.90 +29 53 43.0 · · · · · · L2 2000-07-07 1.960 70 64321 M100 16.8 SABbc 12 22 54.80 +15 49 20.0 0.60 T2 1999-11-06 2.530 884 44374 M84 16.8 E1 12 25 04.00 +12 53 14.0 0.30 L2 2000-04-20 1.110 · · · 4

92

Table 3.1 (cont’d)

Galaxy Nucleus ACIS observation

NGC Messier D Morph RA Dec δ Nucl. Obs. texp Bk Thresh.(Mpc) (J2000) (′′) Type Date (ks) (cts/′2) (cts)

4395 · · · 3.6 SAm 12 25 48.90 +33 32 48.0 0.10 S1.8 2000-04-17 1.260 · · · 54414 · · · 9.7 SAc? 12 26 26.30 +31 13 18.0 · · · · · · T2: 2000-10-29 1.760 70 64494 · · · 9.7 E1 12 31 24.30 +25 46 24.0 · · · · · · L2: 1999-12-20 1.780 · · · 54565 · · · 9.7 SAb? 12 36 20.70 +25 59 16.0 0.10 S1.9 2000-06-30 2.900 · · · 54569 M90 16.8 SABab 12 36 50.00 +13 09 46.0 0.30 T2 2000-02-17 1.710 · · · 44579 M58 16.8 SABb 12 37 43.50 +11 49 05.0 0.10 S1.9/L1.9 2000-02-23 2.950 · · · 54594 M104 20.0 SAa 12 39 58.80 −11 37 28.0 0.10 L2 1999-12-20 1.950 · · · 54639 · · · 16.8 SABbc 12 42 52.35 +13 15 26.4 0.10 S1.0 2000-02-05 1.470 · · · 44725 · · · 12.4 SABabp 12 50 26.60 +25 30 06.0 · · · · · · S2: 1999-12-20 1.780 · · · 64736 M94 4.3 SAab 12 50 53.00 +41 07 12.0 0.10 L2 2000-06-24 2.430 · · · 44826 M64 4.1 SAab 12 56 44.20 +21 41 05.0 0.80 T2 2000-03-27 1.820 · · · 55033 · · · 18.7 SAc 13 13 27.60 +36 35 39.7 0.10 S1.5 2000-04-28 2.970 · · · 55055 M63 7.2 SAbc 13 15 49.30 +42 01 45.0 · · · · · · T2 2000-04-15 2.450 · · · 65195 M51b 9.3 IA0p 13 29 58.70 +47 16 04.0 · · · · · · L2: 2000-01-23 1.150 · · · 45273 · · · 21.3 SA0 13 42 08.30 +35 39 15.0 0.10 S1.5 2000-09-03 1.760 · · · 56500 · · · 39.7 SAab 17 55 59.70 +18 20 18.3 0.10 L2 2000-08-01 2.130 · · · 46503 · · · 6.1 SAcd 17 49 27.00 +70 08 45.0 · · · · · · T2/S2 2000-10-27 2.040 145 4

93

3.3 Results

Table 3.2 shows the summary information for all 427 sources. The ID and

position columns are self-explanatory; dnuc gives the distance in arc-seconds

from the published position for the center of the host galaxy. Sources are

sorted in order of increasing nuclear distance, with the prefix X for all non-

nuclear sources. Nuclear sources are indicated by an N when confidently

identified as such, with a question mark following if the source is only posited

to be nuclear. Next, the count rate per kilosecond is given. Here, an impor-

tant distinction must be made between exposure time (time on target) and

the effective observation length. Because of the presence of aspect glitches

and similar telemetric problems listed in the GTI file, the actual useful inte-

gration time includes only those frames that are not flagged for this reason.

The count rate column is the total number of source counts divided by this

shorter, effective time.

Next is the error in the count rate from Poissonian statistics. Because

many of the sources in these shallow exposures are detected with only a

few counts, the standard Gaussian approximation for determining the count

rate error is no longer valid. Instead, we make use of the prescription of

Gehrels (1986), who derives accurate analytic approximations for the up-

per and lower error bounds in the low-count regime. Unlike the Gaussian

approximation, the errors are not symmetric about the quoted rate, as the

Poissonian distribution is skewed and one obviously cannot observe fewer

than zero counts. The confidence level represented by the calculated errors

must then be chosen; we chose an 84.13% confidence level, as this corre-

sponds to the confidence of a 1-σ Gaussian error. At this confidence level,

the upper bound on the number of counts (the measured number of counts

94

plus the positive error) is given by the expression

NU = N + (δN)U = N +

√

N +3

4+ 1 (3.2)

The above returns an error accurate to better than 1.4%, for any number

of counts N (Gehrels, 1986). Similarly, the formula for the lower count limit

is

NL = N − (δN)L = N

(

1 − 1

9N− 1

3√N

)3

(3.3)

The total number of counts is broken down by energy into two groups, a

soft band of 0.2–2 keV, and a hard band of 2–8 keV. This distinction allows

for a hardness ratio to be calculated via the relation

HR =F (2 − 8 keV) − F (0.2 − 2 keV)

F (2 − 8 keV) + F (0.2 − 2 keV)(3.4)

HR = f (H,S) =H − S

H + S(3.5)

Several sources show a hardness ratio of −1, meaning that they were not

detected at all in the hard band. The error in the hardness ratio resulting

from counting statistics in each bin is shown in the next column. As in

the above discussion, the small number of counts means that the standard

determination of error, σ2 =∑n

i=0(∂f∂xi

)2σ2i , is not reliable. We invoke the

more general procedure detailed in Lyons (1991), to estimate the error in

the hardness ratio. First, the hardness ratio is calculated for the measured

values of hard and soft counts. The extent of the errors in both directions

is estimated by calculating the hardness ratio with the extrema of both the

hard and soft counts, and summing the square of the differences. In other

words, letting δNU and δNL be the difference between the measured counts

95

N and the upper and lower count limits, respectively, the uncertainty σHR

in the hardness ratio function can be expressed as

σ2HR(+) = [f (H + δHU , S) − f (H,S)]2 + [f (H,S + δSU ) − f (H,S)]2

(3.6)

σ2HR(−) = [f (H − δHL, S) − f (H,S)]2 + [f (H,S − δSL) − f (H,S)]2

(3.7)

The penultimate column gives the full 0.2–8 keV X-ray luminosity. This

luminosity is derived indirectly, as most sources are too weak to provide

an adequate spectrum to integrate. The technique we use involves forward

modeling an X-ray spectrum for the column density to the target galaxy

of interest. Power-law spectra with a wide variety of photon indices are

adjusted for absorption through the column density for that Galactic lati-

tude and longitude (Dickey & Lockman, 1990). The hardness ratio of each

resulting artificial spectrum can then be computed, building a lookup table

between hardness ratio and the power-law index for a specific column den-

sity nH. This spectrum is easily integrated, and yields the full-band X-ray

luminosity once normalised to the appropriate number of observed counts.

A critical assumption for the above, of course, is that the column den-

sity remains relatively constant for all sources in the target galaxy. Even

assuming that variations in the intrinsic column are always comparable to

the variation in our own galaxy, it should be remembered that many of the

target galaxies are at a high Galactic latitude. This means that the absorp-

tion from the Galactic column density is likely to be much smaller than the

intrinsic absorption of the host galaxy, and may even be small compared

96

to the variation in the column density from one source to another. Un-

fortunately, there is little more that can be done without invoking shaky

assumptions about the properties of each individual source.

3.3.1 Target descriptions and notable trends

Ho et al. (2001) employ a simple scheme to broadly classify the observed

source population cum nucleus, if any. The four broad classes are defined

as follows. Class I galaxies have a clearly dominant nucleus, accompanied

by a number of fainter sources. In class II objects, the luminosity of the

nucleus is comparable to the brightest off-nulear sources. Class III objects

have a nucleus embedded in an extended diffuse emission, possibly with a

few fainter off-nuclear sources. Lastly, class IV targets have no discernible

nucleus at the nuclear position. There is some overlap between classes II and

IV, as the nucleus may not be easily discernible from a dense population of

equally-bright sources in close proximity. Conversely, if such a population

exists, it is not always possible to show that none of the sources is the

nucleus (i. e., that the nucleus is truly undetected).

Of the 41 galaxies, 33 have sources coincident with the published nuclear

positions. While some galaxies had as few as three or four sources associated

with them, still others had thirty sources or more, with 6 to 12 source being

most common. Most sources were distributed approximately evenly around

the host galaxy, with typical distances of 1 to 3 arcminutes. There were

some notable exceptions, most obviously NGC 4736, where a large number

of luminous sources exist in close proximity to the galaxy nucleus. Also,

this measure is susceptible to source confusion, an increasing problem as

the distance to the host galaxy increases. If two or more sources exist

in close proximity (within tens of parsecs of each other), they could not be

97

spatially discerned by Chandra beyond a few Mpc. With multiple exposures

at different epochs, variability information could be used to show that some

sources are distinct. Unfortunately, the exposures in this snapshot survey

cover each target only once, for a short duration.

Figure 3.1 shows a comparison of the 0.2–8 keV luminosity of the entire

sample of galaxies versus their respective BT (photographic) magnitudes

(upper panel) and (B − V )T colours (lower panel). One might anticipate

a correlation between these quantities, arguing that bluer and/or brighter

galaxies exhibit more rapid star formation, and hence should also show a

marked increase in X-rays produced by high mass X-ray binaries (HMXBs),

whose formation rate is closely tied to the local star formation rate (see

Chapter 2). However, as can be seen from Figure 3.1, this correlation, if it

indeed exists, is quite weak.

Diffuse emission was significant in one-fourth of the total sample, though

not enough to typically merit a Class III designation. Interestingly, this

fraction is a function of Hubble type: one-third of the Elliptical and early-

Spiral galaxies exhibit some diffuse nuclear emission, compared to only about

one-sixth of later Spirals (and 1 Irregular). This suggests that the diffuse

emission is not tied to current stellar formation.

Of considerable interest are the numerous high luminosity off-nuclear

sources, so-called Ultraluminous X-ray binaries (ULX, or UXB). These are

generally taken to have 0.5–8 keV luminosities above 1039 erg s−1. Fourteen

are seen in the current sample, though a few are sufficiently far from the

nucleus of the host galaxy to raise questions about their association. With

one exception, these sources are seen in spiral galaxies. Since the advent of

Chandra, significant numbers of these objects have been found, most notably

in actively star-forming galaxies like the Antennae (Zezas et al., 2001).

98

Figures 3.14–3.24 show each of the 41 targets, in an 18′ × 18′ region

centered on the nominal aim point. The following describes the environs of

each host galaxy, whether a nucleus is identified, and the luminosity range of

any other point sources. This is summarised by a class designation from the

Ho et al. scheme detailed above. Any other interesting or unusual features

are similarly noted.

NGC 253 Class III source, with a luminous nucleus embedded in a sub-

stantial diffuse emission region approximately 1 kpc in extent. Nearly

three dozen sources are detected, and are scattered liberally through-

out the disk of the galaxy. There is no clear correlation between source

distance from nucleus and the source luminosity. 0.2–8 keV lumi-

nosities range from the detection threshold at around 1037 erg s−1to

∼ 3× 1038 erg s−1. It should also be noted that the nucleus is not the

brightest source in the frame.

NGC 404 Class I. Three moderately-luminous sources (LX ∼ 1038 erg s−1).

NGC 660 Class II/IV. Several sources are detected, but it is unclear if the

nucleus is among them. A luminous source with LX ∼ 5×1038 erg s−1

is seen about 50 pixles (25 arcseconds) from the published position of

the nucleus. A luminous source exceeding 1039 erg s−1also occupies

the frame, but is just barely inside the D25 radius of the galaxy, and

so any association with NGC 660 is somewhat tenuous.

NGC 1052 Class III. Nucleus clearly detected (LX ∼ 1040 erg s−1). Sig-

nificant diffuse nuclear emission.

NGC 1055 Class IV. Only four sources detected, none near the published

nuclear position. One very luminous source (LX ∼ 4 × 1039 erg s−1)

99

is seen 4 arcminutes from the putative nuclear position.

NGC 1058 Class I. Several off-nuclear sources; none significant.

NGC 2541 Class IV. A handful of sources, none within an arcminute of

the published nuclear position. One luminous (LX ∼ 2×1039 erg s−1)

source was found an arcminute away. Source are well-scattered through-

out the galaxy disk.

NGC 2683 Class II/IV. Ten sources, all at or below 1038 erg s−1. Two

sources are found within 10 arcseconds of the nuclear position, with

the rest scattered evenly within the surrounding 4 arcminutes.

NGC 2787 Class I. No interesting sources.

NGC 2841 Class II. Clearly detected nucleus surrounded by several com-

parably bright sources. Less-luminous sources are scattered through-

out the disk.

NGC 3031 Class I. This is Messier 81, with a brilliant, easily segregated

nucleus with a luminosity of around LX ∼ 3×1040 erg s−1. This source

is, of course, heavily piled-up, and the count rate was estimated from

the counts present in the readout trail. Nearly three dozen sources

found throughout the galaxy, all with luminosities below 1038 erg s−1.

Source X-15 is actually the remnant of supernova SN1993J, which was

the second-brightest supernova known.

NGC 3368 Class II. This is Messier 96, with a clearly-detected nucleus.

It is surrounded by a dozen dispersed sources, many of which are as

bright as the nuclear source (LX ∼ 1038 erg s−1).

100

NGC 3486 Class IV. Three sources, two faint and one 1038 erg s−1 source

one-half arcminute from the published nuclear position.

NGC 3489 Class II. Three sources, each of which have LX ∼ 2 × 1038

erg s−1. One of these is clearly the galactic nucleus. The other two

are found along the rim of the galaxy (not close to each other). Two

fainter sources were also detected, but lie well outside the galaxy’s D25

radius.

NGC 3623 Class II/IV. Messier 65. Nine sources, with two sources at 8

and 15 arcseconds from the published nuclear position. Source lumi-

nosities range between about 1038 and 7×1038 erg s−1, with a relatively

flat distribution.

NGC 3627 Class II. A dozen sources, several with luminosities comparable

to that of the nucleus (LX ∼ 2 × 1038 erg s−1).

NGC 3628 Class II/IV. Ten sources, with one about 5 arcseconds from the

established position. This source is faint (LX ∼ 7× 1037 erg s−1), but

there is another source that is twice as bright only ten arcseconds from

the putative center. In addition, there is a much more luminous source

(LX ∼ 2 × 1039 erg s−1) only thirty arcseconds from the published

nuclear coordinates. It is likely that one of these is the nucleus, but it

is unclear which of the three holds that distinction.

NGC 3675 Class IV. Two sources of modest luminosity (LX ∼ 6 × 1038

erg s−1). Neither is close to the nuclear position.

NGC 4150 Class II/IV. About five sources, all with a luminosity in the

range between 1038 and 5 × 1038 erg s−1. One of these is twelve arc-

101

seconds from the nuclear position, and another is 17 arcseconds away.

Neither is particularly likely to be the nucleus. Another seven sources

are seen in the frame, but are outside the D25 radius. Two of these

sources are quite luminous, with LX of about 6.6×1039 and 2.7×1039

erg s−1.

NGC 4203 Class I. Brilliant nuclear source, with an LX ∼ 1040 erg s−1.

Two other sources with LX ∼ 1039 erg s−1are seen; one is just inside

the D25 radius, and the other is about 1.5 arcmin outside it.

NGC 4278 Class I. Messier 98. Clear nuclear source with LX ∼ 1040

erg s−1. Another source of comparable luminosity is found less than

two arcminutes away. What appears to be a telescope aspect anomaly

makes a precise luminosity comparison difficult.

NGC 4314 Class III. Eight faint sources (all less than ∼ 1038 erg s−1). One

is within 6 arcseconds of the nuclear coordinates, with the next nearest

being 1.5 arcminutes away. Nucleus is embedded in a considerable

amount of diffuse emission and may be substantially obscured.

NGC 4321 Class I. Clear nucleus with a luminous source (LX ∼ 3 × 1038

erg s−1) less than fifteen arcseconds away.

NGC 4374 Class I. Weak but distinct nucleus with two faint sources.

NGC 4395 Class I. Nucleus with LX ∼ 4 × 1038 erg s−1, attended by

another eight sources. One of these has a luminosity comparable to

the nucleus, and is less than two arcminutes away.

NGC 4414 Class II/IV. A possible nuclear source is heavily obscured by

diffuse emission. A number of moderately-luminous sources spread

102

through the galactic disk. One particularly luminous source (LX ∼4 × 1039 erg s−1) can be found in the frame, but it is about seven

arcminutes from the nucleus. As well, the object looks somewhat

extended, though it is difficult to tell so far off axis. The distance

from the nucleus, at any rate, makes an association with NGC 4414

unlikely.

NGC 4494 Class I. Nucleus detected with LX ∼ 7 × 1038 erg s−1. Some

diffuse emission noted in proximity to the nucleus. Two sources are

detected on the outer edge of the galaxy, with luminosities only slightly

less than that of the nucleus. Several other unremarkable sources also

in the disk.

NGC 4565 Class II. Bright nucleus with a rich group of luminous sources

distributed throughout the galaxy disk. One source is particular stands

out, with a luminosity approaching 1040 erg s−1. This source is less

than an arcminute away from the nucleus, and is located at the edge of

the central bulge. At least four other sources appear to be moderately

luminous (LX ∼ afew × 1038) halo sources.

NGC 4569 Class II. Messier 90. Nuclear luminosity of about 2 × 1039

erg s−1. Some diffuse emission noted. Surrounded by a dozen luminous

sources, evenly distributed. Two of these sources have luminosities in

excess of 1039 erg s−1.

NGC 4579 Class I. Messier 58. Brilliant nucleus with luminosity ∼ 1041

erg s−1. This observation utilised a 1/8 chip subarray to minimise the

effects of pileup. A few other uninteresting sources.

NGC 4594 Class I. Messier 104. This observation also made use of a 1/8

103

chip subarray to reduce pileup. Nucleus has a luminosity of around

1040 erg s−1. A few luminous sources in the disk, with one exceeding

1039 erg s−1.

NGC 4639 Class I. Clear nucleus, with no other interesting sources. A

small amount of diffuse emission is present.

NGC 4725 Class I. Distinct nucleus with seven other sources with ∼ 1

kpc.

NGC 4736 Class II. Messier 94. Ten sources seen, with several of the most

luminous contained within half a kiloparsec of the nucleus. One source

has a luminosity approaching 1039 erg s−1, with a projected distance

of only a few hundred parsecs from the nucleus.

NGC 4826 Class II/IV. Messier 64. Several 1038 erg s−1sources noted

throughout the frame. Considerable diffuse emission from the nuclear

region.

NGC 5033 Class I. 1/2-subarray mode used to reduce pileup. Nucleus has

LX ∼ 6 × 1040 erg s−1. One source near the nucleus with luminosity

greater than 1039 erg s−1.

NGC 5055 Class III. Messier 63. Considerable diffuse nuclear emission.

Several dozen faint sources.

NGC 5195 Class IV. Messier 51b. Several luminous sources (LX ∼ several×1038 erg s−1). No clear nucleus. Some diffuse nuclear emission.

NGC 5273 Class I. Bright nuclear source with LX ∼ 1040 erg s−1. Several

uninteresting sources in the disk.

104

NGC 6500 Class I. Nucleus detected. Little else of interest.

NGC 6503 Class IV. Four sources inside the D25 diameter.

3.4 Epilogue

The most obvious direction to take to improve upon the results here is to

obtain deeper observations of the entire 41 galaxy sample. Shallow 2–3 ks

exposures mean that only the brightest tip of the X-ray binary luminos-

ity function can be explored. Even slightly deeper 5 ks exposures would

permit many more detections, and would make this work more valuable in

comparing against theoretical results as above.

While it is something of a common joke among astronomers that what is

needed is always “better data”, it is clear that a 2 ks snapshot survey, while

well-suited to the task of studying relatively luminous LLAGN (or demon-

strating a non-detection of the central source), is not sufficient to effectively

characterise the luminosity function of the ancillary X-ray sources of the

host galaxy. Longer exposures, or, better still, multiple exposures at several

epochs would not only yield more and fainter sources, it would also permit

a limited study of source variability. As noted above, this could be helpful

in ruling out multiple unresolved sources in some instances. With the im-

position of a 1.5 ks per-target overhead begun in Chandra Cycle 2 however,

broad surveys building on this program may no longer be pragmatic. Data

mining of the growing Chandra archive may ultimately be the best way to

achieve this breadth of coverage with sufficient depth.

105

Figure 3.1 The upper frame shows the relation between the 0.2–8 keV X-rayluminosity of each galaxy and its BT magnitude. The lower frame showshow the (B − V )T colour changes with LX . To a first approximation, onewould expect bluer galaxies to have a higher X-ray luminosity, due to agreater incidence of star formation. This anticipated correlation appears tobe quite weak, if it exists.

106

Figure 3.2 The four diagrams above show the relative frequency of sourceswith varying luminosity, in four broad classes of galaxy represented in thesample.

107

Table 3.2. Summary of source properties

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ(J2000) (′′) (10−3

s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

NGC 253 N 00 47 33.19 -25 17 19.2 1.8 6.019+2.415−1.622 −0.23+0.31

−0.22 0.1785 0.707X-1 00 47 33.54 -25 17 21.3 7.4 3.704+2.079

−1.250 −0.25+0.40−0.26 0.1115 0.739

X-2 00 47 34.30 -25 17 03.3 23.2 3.241+1.997−1.162 −0.43+0.44

−0.26 0.1105 1.053X-3 00 47 33.01 -25 17 48.8 30.8 2.778+1.919

−1.066 0.33+0.47−0.29 0.0734 0.500

X-4 00 47 33.57 -25 18 16.0 58.5 2.315+1.823−0.963 −0.60+0.53

−0.25 0.0848 1.404X-5 00 47 36.40 -25 16 38.7 63.2 15.741+3.347

−2.671 −0.88+0.14−0.07 0.5047 2.352

X-6 00 47 33.01 -25 18 46.4 88.4 3.241+1.983−1.164 −0.71+0.44

−0.19 0.1196 1.694X-7 00 47 28.03 -25 18 20.0 98.1 3.241+1.953

−1.193 −1.00+0.42−0.00 0.0127 5.000

X-8 00 47 25.44 -25 16 42.9 120.2 3.241+1.983−1.164 −0.71+0.44

−0.19 0.1196 1.694X-9 00 47 35.29 -25 15 11.5 130.7 3.704+2.026

−1.279 −1.00+0.38−0.00 0.0146 5.000

X-10 00 47 31.70 -25 15 05.7 134.0 5.093+2.225−1.510 −1.00+0.29

−0.00 0.0200 5.000X-11 00 47 26.48 -25 19 13.4 152.2 3.241+1.983

−1.164 −0.71+0.44−0.19 0.1196 1.694

X-12 00 47 28.94 -25 14 58.5 152.8 10.185+2.891−2.135 −0.36+0.23

−0.17 0.3338 0.935X-13 00 47 23.55 -25 19 05.6 179.2 2.778+1.906

−1.068 −0.67+0.48−0.22 0.1027 1.565

X-14 00 47 43.11 -25 15 29.3 185.4 40.741+5.035−4.325 0.00+0.11

−0.10 1.0765 0.500X-15 00 47 25.20 -25 19 44.7 188.6 3.241+1.997

−1.162 −0.43+0.44−0.26 0.1105 1.053

X-16 00 47 24.51 -25 14 50.1 196.2 4.167+2.150−1.333 −0.33+0.38

−0.25 0.1338 0.882X-17 00 47 42.82 -25 15 01.8 199.5 124.537+8.267

−7.583 −0.17+0.06−0.06 3.5004 0.604

X-18 00 47 40.73 -25 14 12.0 218.4 3.241+1.983−1.164 −0.71+0.44

−0.19 0.1196 1.694X-19 00 47 44.90 -25 14 56.5 226.6 16.667+3.464

−2.749 −0.61+0.16−0.12 0.6119 1.429

X-20 00 47 45.60 -25 19 40.8 235.7 29.167+4.347−3.653 −0.59+0.12

−0.09 1.0646 1.375X-21 00 47 17.61 -25 18 11.9 238.5 2.778+1.906

−1.068 0.67+0.48−0.22 0.0734 0.500

X-22 00 47 17.68 -25 18 26.2 241.1 3.704+2.026−1.279 −1.00+0.38

−0.00 0.0146 5.000X-23 00 47 49.14 -25 16 28.4 245.7 5.093+2.282

−1.485 −0.45+0.34−0.22 0.1762 1.102

108



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-24 00 47 18.54 -25 19 14.3 247.5 13.426+3.208−2.461 −0.24+0.20

−0.16 0.4015 0.724X-25 00 47 22.64 -25 20 50.8 264.4 1.852+1.707

−0.884 −1.00+0.64−0.00 0.0073 5.000

X-26 00 47 48.57 -25 15 02.9 268.5 73.611+6.481−5.824 −0.67+0.07

−0.06 2.7228 1.581X-27 00 47 44.82 -25 20 46.0 272.4 2.315+1.823

−0.963 −0.60+0.53−0.25 0.0848 1.404

X-28 00 47 43.10 -25 13 22.6 279.0 7.870+2.630−1.868 −0.53+0.26

−0.17 0.2818 1.250X-29 00 47 18.39 -25 21 37.7 340.8 4.630+2.225

−1.410 0.00+0.36−0.25 0.1223 0.500

X-30 00 47 23.30 -25 10 52.3 412.7 1.389+1.634−0.708 −0.33+0.66

−0.35 0.0446 0.882X-31 00 47 43.14 -25 09 58.5 464.6 33.333+4.601

−3.908 −0.56+0.11−0.09 1.2049 1.305

X-32 00 48 00.95 -25 23 51.8 574.1 42.130+5.092−4.398 −0.45+0.10

−0.09 1.4542 1.095X-33 00 47 50.56 -25 08 42.1 578.6 3.241+1.983

−1.164 −0.71+0.44−0.19 0.1196 1.694

X-34 00 47 52.99 -25 07 34.9 655.0 19.444+3.685−2.974 0.57+0.15

−0.11 0.5138 0.500NGC 404 N 01 09 26.97 35 43 05.7 2.9 2.000+1.843

−0.954 −1.00+0.64−0.00 0.3003 5.000

X-1 01 09 24.73 35 46 01.6 181.6 4.500+2.312−1.440 −0.56+0.38

−0.22 0.9566 1.824X-2 01 09 21.32 35 46 19.1 213.3 3.000+2.076

−1.151 0.00+0.46−0.30 0.3503 0.724

X-3 01 09 11.16 35 42 16.5 240.7 7.500+2.732−1.889 −0.33+0.29

−0.20 1.3014 1.336X-4 01 09 05.93 35 42 46.4 315.0 9.000+2.824

−2.100 −1.00+0.19−0.00 1.3515 5.000

X-5 01 09 16.37 35 47 54.6 331.6 2.000+1.872−0.912 −0.50+0.59

−0.29 0.4059 1.690X-6 01 09 01.47 35 46 18.5 428.7 2.000+1.872

−0.912 0.50+0.59−0.29 0.1940 0.500

X-7 01 08 52.28 35 46 19.6 555.3 2.000+1.872−0.912 0.50+0.59

−0.29 0.1940 0.500X-8 01 08 42.69 35 47 36.7 717.4 +

−0.00+0.00

−0.00

NGC 660 X-1 01 43 02.38 13 38 44.3 24.3 3.333+1.850−1.127 −0.75+0.40

−0.17 0.4596 2.009X-2 01 43 03.87 13 39 55.2 98.2 2.083+1.650

−0.865 −0.20+0.51−0.31 0.2136 0.806

X-3 01 43 01.20 13 40 03.4 100.5 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0479 5.000X-4 01 42 51.17 13 34 25.1 284.8 1.667+1.566

−0.759 0.00+0.56−0.34 0.1409 0.500

109



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-5 01 42 51.71 13 33 52.3 308.7 11.667+2.811−2.176 −0.79+0.17

−0.10 1.5948 2.136X-6 01 43 14.72 13 31 43.5 445.4 1.250+1.450

−0.678 −1.00+0.77−0.00 0.0359 5.000

X-7 01 43 13.70 13 30 10.5 525.0 2.500+1.727−0.959 −0.33+0.47

−0.29 0.2875 1.040NGC 1052 N 02 41 04.84 -08 15 20.2 1.0 115.833+7.552

−6.938 0.23+0.06−0.06 9.5919 0.500

X-1 02 41 01.46 -08 14 30.1 71.4 2.500+1.689−0.989 −1.00+0.47

−0.00 0.0488 5.000X-2 02 41 10.16 -08 17 13.0 137.9 2.083+1.650

−0.865 −0.20+0.51−0.31 0.2006 0.749

X-3 02 41 07.02 -08 18 16.5 178.6 1.667+1.560−0.760 −0.50+0.59

−0.29 0.1989 1.293X-4 02 41 06.08 -08 12 20.2 181.8 4.583+2.053

−1.336 −0.45+0.34−0.22 0.5339 1.203

NGC 1055 X-1 02 41 41.00 00 26 44.8 64.8 4.583+2.029−1.338 −0.82+0.32

−0.13 0.6999 2.176X-2 02 41 32.38 00 26 15.1 192.9 5.417+2.162

−1.460 −0.54+0.31−0.19 0.8216 1.372

X-3 02 41 45.26 00 30 28.4 238.4 12.500+2.893−2.254 −0.73+0.17

−0.11 1.9739 1.869X-4 02 41 40.43 00 30 50.0 269.7 1.250+1.471

−0.637 0.33+0.66−0.35 0.1293 0.500

NGC 1058 X-1 02 43 28.43 37 20 22.6 22.5 2.500+1.981−1.037 −0.20+0.51

−0.31 0.2749 0.822X-2 02 43 27.40 37 20 58.9 49.2 2.000+1.880

−0.910 0.00+0.56−0.34 0.1789 0.500

X-3 02 43 23.28 37 20 42.1 100.4 12.000+3.230−2.412 −0.17+0.23

−0.17 1.2741 0.763X-4 02 43 38.11 37 21 44.5 145.5 3.000+2.076

−1.151 0.00+0.46−0.30 0.2683 0.500

X-5 02 44 06.81 37 16 31.8 601.6 2.000+1.843−0.954 −1.00+0.64

−0.00 0.0793 5.000X-6 02 43 45.33 37 10 39.9 631.1 12.000+3.209

−2.412 −0.58+0.21−0.15 1.7555 1.583

X-7 02 44 02.15 37 13 22.3 643.7 1.500+1.765−0.765 −0.33+0.66

−0.35 0.1860 1.061NGC 2541 X-1 08 14 37.03 49 03 26.6 56.2 21.250+3.587

−2.954 −0.57+0.14−0.11 2.8081 1.509

X-2 08 14 42.42 49 05 51.1 123.9 2.917+1.758−1.073 −1.00+0.42

−0.00 0.0805 5.000X-3 08 14 51.36 49 04 57.7 177.4 2.083+1.641

−0.867 −0.60+0.53−0.25 0.2787 1.583

X-4 08 14 33.54 48 59 15.5 294.1 7.500+2.413−1.732 −0.56+0.25

−0.17 0.9855 1.480X-5 08 14 32.03 49 12 58.7 561.9 2.083+1.615

−0.898 −1.00+0.54−0.00 0.0575 5.000

110



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-6 08 15 24.41 49 02 50.5 662.9 2.500+1.727−0.959 0.33+0.47

−0.29 0.2105 0.500NGC 2683 X-1 08 52 41.32 33 25 18.2 9.0 2.083+1.615

−0.898 −1.00+0.54−0.00 0.0407 5.000

X-2 08 52 41.76 33 25 04.2 9.9 2.083+1.650−0.865 0.20+0.51

−0.31 0.1719 0.500X-3 08 52 37.22 33 25 13.4 59.8 3.750+1.885

−1.224 −1.00+0.34−0.00 0.0732 5.000

X-4 08 52 45.57 33 26 05.0 85.9 4.167+1.996−1.270 −0.40+0.36

−0.23 0.4728 1.116X-5 08 52 40.67 33 27 05.0 115.9 5.833+2.187

−1.520 0.86+0.27−0.11 0.4813 0.500

X-6 08 52 42.47 33 27 43.4 155.2 1.667+1.560−0.760 0.50+0.59

−0.29 0.1375 0.500X-7 08 52 33.31 33 22 38.0 192.2 2.500+1.715

−0.961 −0.67+0.48−0.22 0.3170 1.691

X-8 08 52 40.37 33 21 05.5 244.2 4.167+1.987−1.270 −0.60+0.35

−0.20 0.5210 1.526X-9 08 52 34.07 33 21 13.1 259.4 2.500+1.730

−0.959 0.00+0.46−0.30 0.2063 0.500

X-10 08 52 58.70 33 25 22.5 262.9 2.083+1.641−0.867 0.60+0.53

−0.25 0.1719 0.500NGC 2841 N 09 22 02.73 50 58 35.1 0.5 2.500+1.730

−0.959 0.00+0.46−0.30 0.2009 0.500

X-1 09 22 02.52 50 58 18.9 16.4 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2398 1.459X-2 09 22 02.21 50 58 53.9 20.2 4.583+2.053

−1.336 −0.45+0.34−0.22 0.4998 1.162

X-3 09 21 59.37 50 57 31.4 80.9 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0210 5.000X-4 09 21 58.12 50 59 58.4 108.0 1.250+1.450

−0.678 −1.00+0.77−0.00 0.0158 5.000

X-5 09 21 58.69 50 56 11.5 155.6 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0210 5.000X-6 09 22 02.34 51 02 02.7 207.8 1.667+1.536

−0.795 −1.00+0.64−0.00 0.0210 5.000

X-7 09 21 49.67 50 57 04.9 215.2 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0210 5.000X-8 09 21 44.22 50 56 47.7 297.3 4.583+2.029

−1.338 −0.82+0.32−0.13 0.5038 2.092

X-9 09 21 49.06 51 02 13.5 299.3 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0210 5.000X-10 09 21 53.88 50 53 22.1 339.7 5.417+2.162

−1.460 −0.54+0.31−0.19 0.6126 1.326

X-11 09 21 36.35 51 00 46.8 416.7 2.917+1.798−1.046 −0.43+0.44

−0.26 0.3138 1.113X-12 09 22 51.13 51 07 52.6 915.8 2.083+1.641

−0.867 −0.60+0.53−0.25 0.2398 1.459

111



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

NGC 3031 N! 09 55 33.26 69 03 55.9 1.3 5.833+2.226−1.518 −0.29+0.30

−0.21 1000.6262 0.918X-1 09 55 34.86 69 03 42.1 28.1 80.000+6.296

−5.762 −0.93+0.04−0.03 8.5509 2.887

X-2 09 55 35.41 69 03 52.8 33.3 2.917+1.758−1.073 −1.00+0.42

−0.00 0.0727 5.000X-3 09 55 31.23 69 04 19.1 38.1 4.167+1.972

−1.272 −0.80+0.34−0.14 0.5444 2.147

X-4 09 55 35.19 69 03 15.7 49.3 2.500+1.715−0.961 −0.67+0.48

−0.22 0.3313 1.716X-5 09 55 34.60 69 04 53.9 62.5 11.667+2.845

−2.176 −0.36+0.20−0.15 1.3246 1.046

X-6 09 55 27.91 69 04 08.3 80.4 2.500+1.689−0.989 −1.00+0.47

−0.00 0.0623 5.000X-7 09 55 27.70 69 04 00.2 82.6 8.750+2.544

−1.876 −0.62+0.23−0.15 1.1461 1.593

X-8 09 55 27.03 69 04 14.9 94.6 5.833+2.162−1.538 −1.00+0.24

−0.00 0.1453 5.000X-9 09 55 27.16 69 02 47.7 112.8 56.667+5.369

−4.846 −0.97+0.04−0.02 4.5057 3.479

X-10 09 55 42.11 69 03 36.2 134.9 3.333+1.823−1.151 −1.00+0.38

−0.00 0.0830 5.000X-11 09 55 34.38 69 06 21.6 147.6 2.083+1.650

−0.865 −0.20+0.51−0.31 0.2072 0.769

X-12 09 55 22.07 69 05 10.5 183.2 7.083+2.332−1.683 −0.88+0.23

−0.09 0.8509 2.550X-13 09 55 21.82 69 05 22.0 191.6 3.333+1.823

−1.151 −1.00+0.38−0.00 0.0830 5.000

X-14 09 55 32.90 69 00 33.2 201.9 17.917+3.367−2.709 −0.16+0.16

−0.13 1.7202 0.707X-15 09 55 24.72 69 01 13.2 205.8 3.750+1.935

−1.199 −0.33+0.38−0.25 0.4182 1.003

X-16 09 55 21.83 69 06 38.0 235.9 5.833+2.214−1.519 −0.57+0.29

−0.18 0.7511 1.480X-17 09 55 47.01 69 05 49.4 236.6 2.083+1.650

−0.865 −0.20+0.51−0.31 0.2072 0.769

X-18 09 55 49.79 69 05 31.9 267.1 40.833+4.726−4.109 −0.53+0.10

−0.08 5.1615 1.389X-19 09 55 52.98 69 05 20.3 308.7 2.083+1.615

−0.898 −1.00+0.54−0.00 0.0519 5.000

X-20 09 55 53.19 69 02 06.4 319.0 0.417+1.241−0.344 −1.00+1.30

−0.00 0.0104 5.000X-21 09 55 53.12 69 01 13.0 339.9 67.083+5.890

−5.275 −0.39+0.08−0.07 7.8051 1.110

X-22 09 55 10.24 69 05 02.2 350.9 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0415 5.000X-23 09 55 49.32 69 08 11.7 352.7 2.917+1.784

−1.048 −0.71+0.44−0.19 0.3883 1.852

112



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-24 09 55 58.47 69 05 25.6 389.8 3.333+1.850−1.127 −0.75+0.40

−0.17 0.4426 1.965X-25 09 55 09.72 69 07 01.6 398.6 5.417+2.152

−1.461 −0.69+0.30−0.16 0.7203 1.787

X-26 09 55 59.20 69 06 17.8 415.3 2.500+1.730−0.959 0.00+0.46

−0.30 0.2106 0.500X-27 09 55 57.73 69 00 36.6 418.1 4.583+2.002

−1.359 −1.00+0.29−0.00 0.1142 5.000

X-28 09 54 57.54 69 02 40.8 540.0 7.500+2.394−1.733 −0.78+0.23

−0.13 0.9891 2.063X-29 09 56 08.87 69 01 05.4 561.4 1.667+1.536

−0.795 −1.00+0.64−0.00 0.0415 5.000

X-30 09 54 50.38 69 04 18.8 642.7 0.833+1.353−0.536 −1.00+0.97

−0.00 0.0208 5.000X-31 09 54 45.08 68 56 58.1 833.5 12.083+2.870

−2.215 −0.59+0.19−0.13 1.5649 1.514

X-32 09 54 06.17 69 08 43.7 1337.0 262.917+11.065−10.460 −0.21+0.04

−0.04 26.5105 0.794NGC 3368 N 10 46 45.71 11 49 11.3 1.3 2.917+1.803

−1.045 −0.14+0.43−0.28 0.2662 0.658

X-1 10 46 49.00 11 49 35.9 54.0 3.750+1.935−1.199 −0.33+0.38

−0.25 0.4003 0.976X-2 10 46 42.95 11 51 11.2 127.5 3.750+1.885

−1.224 −1.00+0.34−0.00 0.0692 5.000

X-3 10 46 53.18 11 50 22.8 132.0 4.167+1.972−1.272 −0.80+0.34

−0.14 0.5066 2.089X-4 10 46 53.21 11 50 27.0 134.7 1.667+1.536

−0.795 −1.00+0.64−0.00 0.0308 5.000

X-5 10 46 53.49 11 51 16.1 170.1 2.500+1.715−0.961 −0.67+0.48

−0.22 0.3118 1.670X-6 10 46 44.64 11 52 06.8 176.6 1.667+1.566

−0.759 0.00+0.56−0.34 0.1373 0.500

X-7 10 46 57.96 11 49 38.1 184.4 2.500+1.715−0.961 −0.67+0.48

−0.22 0.3118 1.670X-8 10 46 38.89 11 45 53.8 222.8 1.667+1.560

−0.760 −0.50+0.59−0.29 0.1971 1.289

X-9 10 46 36.17 11 45 25.6 267.7 2.917+1.784−1.048 −0.71+0.44

−0.19 0.3642 1.802X-10 10 46 36.98 11 44 59.2 284.5 6.250+2.211

−1.594 −1.00+0.22−0.00 0.1154 5.000

X-11 10 46 41.93 11 54 01.2 295.9 2.083+1.615−0.898 −1.00+0.54

−0.00 0.0385 5.000X-12 10 46 24.66 11 47 58.7 325.3 +

−0.00+0.00

−0.00

NGC 3486 X-1 11 00 22.23 28 58 16.2 28.6 3.333+1.850−1.127 −0.75+0.40

−0.17 0.3978 1.877X-2 11 00 22.41 28 59 23.4 57.9 2.500+1.689

−0.989 −1.00+0.47−0.00 0.0366 5.000

113



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-3 11 00 30.22 28 56 32.4 151.1 3.750+1.885−1.224 −1.00+0.34

−0.00 0.0549 5.000NGC 3489 X-1 11 00 18.54 13 54 02.8 8.4 5.833+2.214

−1.519 −0.57+0.29−0.18 0.6852 1.406

X-2 11 00 05.17 13 55 26.2 209.2 7.083+2.332−1.683 −0.88+0.23

−0.09 0.7388 2.421X-3 11 00 32.67 13 53 44.8 219.8 5.000+2.099

−1.400 −0.67+0.31−0.18 0.5983 1.631

X-4 11 00 53.57 13 53 27.3 533.7 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2467 1.470X-5 11 00 48.26 13 48 45.6 555.5 3.750+1.939

−1.199 0.11+0.38−0.26 0.3064 0.500

NGC 3623 X-1 11 18 56.00 13 05 33.4 7.5 5.000+2.099−1.400 −0.67+0.31

−0.18 1.0406 2.054X-2 11 18 55.03 13 05 41.6 15.4 2.917+1.784

−1.048 −0.71+0.44−0.19 0.6229 2.206

X-3 11 18 52.85 13 05 42.0 43.3 2.500+1.689−0.989 −1.00+0.47

−0.00 0.3034 5.000X-4 11 18 58.54 13 05 30.9 44.2 11.667+2.850

−2.176 −0.21+0.21−0.16 1.6413 1.055

X-5 11 19 00.59 13 05 37.4 75.4 3.750+1.927−1.200 −0.56+0.38

−0.22 0.7238 1.754X-6 11 18 52.44 13 03 35.9 122.6 6.667+2.285

−1.631 −0.88+0.24−0.10 1.4553 2.954

X-7 11 19 01.70 13 09 45.3 272.2 1.667+1.560−0.760 −0.50+0.59

−0.29 0.3079 1.623X-8 11 19 09.36 13 09 50.6 333.2 5.000+2.109

−1.400 −0.50+0.32−0.20 0.9238 1.623

X-9 11 19 28.43 13 02 51.1 517.1 7.917+2.423−1.783 −0.89+0.21

−0.08 1.7050 3.099NGC 3627 X-1 11 20 15.12 12 59 27.8 7.5 12.500+3.263

−2.463 −0.52+0.21−0.15 1.4703 1.325

X-2 11 20 14.25 12 59 27.0 11.4 4.000+2.220−1.353 −0.75+0.40

−0.17 0.4866 1.900X-3 11 20 14.56 12 59 46.0 25.5 13.000+3.270

−2.514 −0.85+0.17−0.09 1.4825 2.269

X-4 11 20 18.30 12 59 00.3 55.1 6.500+2.564−1.755 −0.85+0.28

−0.11 0.7413 2.269X-5 11 20 13.57 13 00 16.1 58.6 2.000+1.843

−0.954 −1.00+0.64−0.00 0.0333 5.000

X-6 11 20 18.20 12 59 58.9 62.3 19.000+3.796−3.053 −0.79+0.14

−0.09 2.2738 2.035X-7 11 20 16.64 12 58 20.1 66.2 2.000+1.880

−0.910 0.00+0.56−0.34 0.1633 0.500

X-8 11 20 13.46 13 00 26.0 68.4 10.500+3.043−2.252 −0.71+0.22

−0.13 1.2858 1.792X-9 11 20 20.89 12 58 45.9 96.5 4.500+2.312

−1.440 −0.56+0.38−0.22 0.5369 1.400

114



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-10 11 20 17.60 13 01 40.0 144.8 18.500+3.786−3.011 −0.57+0.16

−0.12 2.2166 1.426X-11 11 20 19.01 13 01 35.2 147.6 3.500+2.109

−1.288 −1.00+0.42−0.00 0.0584 5.000

X-12 11 19 59.98 12 59 26.8 223.9 8.000+2.761−1.955 −0.75+0.26

−0.14 0.9731 1.900X-13 11 20 21.66 12 55 13.6 267.4 5.000+2.395

−1.524 −0.40+0.36−0.23 0.5517 1.093

X-14 11 20 34.96 13 05 44.5 487.5 3.500+2.141−1.257 −0.71+0.44

−0.19 0.4286 1.792X-15 11 20 37.10 13 05 44.3 507.7 +

−0.00+0.00

−0.00

X-16 11 20 46.56 12 54 28.3 557.8 3.500+2.109−1.288 −1.00+0.42

−0.00 0.0584 5.000NGC 3628 N? 11 20 16.23 13 35 27.0 5.0 2.917+1.803

−1.045 0.14+0.43−0.28 0.2380 0.500

X-1 11 20 15.75 13 35 13.1 11.1 2.917+1.798−1.046 −0.43+0.44

−0.26 0.3247 1.136X-2 11 20 14.30 13 35 09.8 31.0 55.833+5.438

−4.810 −0.15+0.09−0.08 5.0460 0.660

X-3 11 20 06.89 13 34 53.7 142.5 3.333+1.864−1.125 −0.50+0.41

−0.24 0.3852 1.274X-4 11 20 05.55 13 34 49.9 163.0 4.167+1.987

−1.270 −0.60+0.35−0.20 0.4995 1.488

X-5 11 20 14.69 13 32 27.6 175.9 7.917+2.423−1.783 −0.89+0.21

−0.08 0.8180 2.522X-6 11 20 11.75 13 31 23.1 248.0 5.417+2.169

−1.460 −0.38+0.31−0.21 0.5872 1.055

X-7 11 20 10.45 13 39 34.8 267.1 23.333+3.749−3.097 −0.04+0.14

−0.12 1.9043 0.500X-8 11 20 08.97 13 39 30.4 271.0 8.750+2.544

−1.876 −0.62+0.23−0.15 1.0536 1.532

X-9 11 19 57.05 13 34 56.4 288.4 3.750+1.927−1.200 −0.56+0.38

−0.22 0.4434 1.390NGC 3675 X-1 11 26 07.32 43 34 06.2 52.8 4.167+1.987

−1.270 −0.60+0.35−0.20 0.5367 1.465

X-2 11 25 48.11 43 32 11.1 341.9 6.667+2.332−1.628 −0.12+0.28

−0.21 0.6249 0.587NGC 4150 X-1 12 10 32.81 30 24 24.2 12.8 1.667+1.560

−0.760 −0.50+0.59−0.29 0.2986 1.613

X-2 12 10 33.75 30 23 58.0 17.0 1.667+1.560−0.760 0.50+0.59

−0.29 0.1528 0.500X-3 12 10 34.77 30 23 58.3 27.7 2.083+1.650

−0.865 −0.20+0.51−0.31 0.2804 1.022

X-4 12 10 34.80 30 23 21.4 56.8 1.250+1.450−0.678 −1.00+0.77

−0.00 0.1446 5.000X-5 12 10 32.37 30 21 20.9 172.3 2.500+1.689

−0.989 −1.00+0.47−0.00 0.2892 5.000

115



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-6 12 10 17.84 30 25 49.7 249.9 1.667+1.560−0.760 −0.50+0.59

−0.29 0.2986 1.613X-7 12 10 16.04 30 23 59.5 257.7 45.000+4.914

−4.315 −0.69+0.08−0.07 9.1624 2.099

X-8 12 10 49.88 30 26 13.1 277.7 4.167+1.996−1.270 −0.40+0.36

−0.23 0.6851 1.400X-9 12 10 15.08 30 21 28.7 317.5 22.500+3.683

−3.041 −0.41+0.14−0.11 3.7244 1.415

X-10 12 10 11.59 30 24 29.5 324.6 4.167+2.001−1.269 −0.20+0.36

−0.25 0.5607 1.022X-11 12 10 52.35 30 30 03.7 453.5 2.083+1.641

−0.867 −0.60+0.53−0.25 0.4023 1.856

X-12 12 11 05.73 30 26 12.3 502.3 2.917+1.784−1.048 −0.71+0.44

−0.19 0.6028 2.194X-13 12 10 51.94 30 31 27.3 517.5 2.083+1.641

−0.867 −0.60+0.53−0.25 0.4023 1.856

X-14 12 11 07.13 30 26 33.4 528.0 2.917+1.798−1.046 −0.43+0.44

−0.26 0.4919 1.459NGC 4203 N 12 15 05.02 33 11 49.9 1.0 2.917+1.758

−1.073 −1.00+0.42−0.00 0.0351 5.000

X-1 12 15 09.89 33 11 28.8 76.1 5.000+2.099−1.400 0.67+0.31

−0.18 0.4172 0.500X-2 12 15 07.19 33 13 44.0 119.6 0.833+1.353

−0.536 −1.00+0.97−0.00 0.0100 5.000

X-3 12 15 09.20 33 09 54.6 130.6 7.500+2.394−1.733 −0.78+0.23

−0.13 0.8596 1.905X-4 12 15 14.33 33 11 04.5 146.8 0.833+1.353

−0.536 −1.00+0.97−0.00 0.0100 5.000

X-5 12 15 15.61 33 10 12.4 186.2 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2429 1.420X-6 12 15 15.32 33 13 54.3 199.2 2.500+1.730

−0.959 0.00+0.46−0.30 0.2086 0.500

X-7 12 15 19.69 33 11 11.5 223.5 146.667+8.376−7.809 −0.74+0.04

−0.03 17.0590 1.796X-8 12 15 19.82 33 10 12.4 242.4 7.500+2.378

−1.734 −0.89+0.22−0.09 0.7481 2.397

X-9 12 14 46.34 33 13 23.6 295.5 2.500+1.715−0.961 −0.67+0.48

−0.22 0.2939 1.580X-10 12 15 06.20 33 16 53.9 305.4 141.667+8.276

−7.675 −0.42+0.05−0.05 15.3883 1.064

X-11 12 15 33.66 33 05 42.5 565.0 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2429 1.420NGC 4278 X-1 12 19 46.80 29 15 50.3 305.8 1.667+1.536

−0.795 −1.00+0.64−0.00 0.2715 5.000

X-2 12 19 45.32 29 11 34.4 451.0 2.083+1.650−0.865 −0.20+0.51

−0.31 0.3509 1.028X-3 12 19 39.44 29 11 41.1 513.6 4.167+1.987

−1.270 −0.60+0.35−0.20 1.0284 1.891

116



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-4 12 19 35.70 29 13 00.2 520.1 4.167+1.996−1.270 −0.40+0.36

−0.23 0.8658 1.419X-5 12 19 37.62 29 11 54.3 528.2 5.000+2.115

−1.399 −0.33+0.32−0.22 0.9726 1.283

X-6 12 19 31.90 29 14 11.3 547.0 2.083+1.650−0.865 −0.20+0.51

−0.31 0.3509 1.028X-7 12 19 31.99 29 13 51.9 551.7 2.083+1.650

−0.865 0.20+0.51−0.31 0.2383 0.500

X-8 12 19 30.48 29 20 20.8 584.2 4.583+2.044−1.337 −0.64+0.33

−0.19 1.1613 1.993X-9 12 19 28.15 29 11 40.7 657.1 13.750+2.964

−2.369 −0.94+0.13−0.05 3.5049 3.615

X-10 12 19 24.00 29 19 26.3 660.7 3.333+1.864−1.125 0.50+0.41

−0.24 0.3813 0.500X-11 12 19 22.30 29 20 17.9 699.1 6.667+2.301

−1.629 −0.75+0.26−0.14 1.8076 2.372

X-12 12 19 20.62 29 18 59.8 704.8 37.917+4.491−3.960 −0.98+0.05

−0.02 7.7829 4.407X-13 12 19 19.38 29 19 53.7 734.7 4.167+1.996

−1.270 −0.40+0.36−0.23 0.8658 1.419

X-14 12 19 18.71 29 19 47.0 742.8 5.000+2.083−1.402 0.83+0.30

−0.12 0.5720 0.500X-15 12 19 22.42 29 10 09.2 777.0 10.833+2.736

−2.095 −0.77+0.18−0.11 2.9616 2.449

X-16 12 19 15.86 29 19 23.9 779.4 6.250+2.264−1.575 −0.60+0.28

−0.17 1.5426 1.891X-17 12 19 14.62 29 19 13.6 795.7 3.750+1.939

−1.199 0.11+0.38−0.26 0.4290 0.500

X-18 12 19 17.49 29 11 17.8 810.8 2.917+1.784−1.048 0.71+0.44

−0.19 0.3337 0.500X-19 12 19 11.61 29 20 23.0 854.8 5.000+2.083

−1.402 −0.83+0.30−0.12 1.3880 2.751

X-20 12 19 11.29 29 22 07.8 891.2 2.917+1.784−1.048 −0.71+0.44

−0.19 0.7764 2.240X-21 12 19 06.25 29 10 15.7 990.1 40.000+4.597

−4.068 −0.98+0.05−0.02 8.0965 4.447

X-22 12 19 06.16 29 10 18.6 990.3 60.417+5.515−5.005 −0.99+0.03

−0.01 10.8845 4.756X-23 12 19 06.19 29 10 09.7 993.4 64.583+5.705

−5.175 −0.95+0.04−0.02 16.0211 3.745

X-24 12 19 05.88 29 10 09.4 997.8 30.417+4.087−3.543 −0.97+0.06

−0.02 6.5988 4.240NGC 4314 N? 12 22 31.78 29 53 48.3 5.6 2.500+1.689

−0.989 −1.00+0.47−0.00 0.0354 5.000

X-1 12 22 27.00 29 54 05.9 77.0 2.917+1.803−1.045 −0.14+0.43

−0.28 0.2616 0.643X-2 12 22 34.39 29 54 50.9 77.5 1.250+1.471

−0.637 −0.33+0.66−0.35 0.1303 0.955

117



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-3 12 22 28.90 29 54 49.7 80.4 1.667+1.566−0.759 0.00+0.56

−0.34 0.1363 0.500X-4 12 22 27.21 29 52 37.2 96.3 2.917+1.758

−1.073 −1.00+0.42−0.00 0.0412 5.000

X-5 12 22 23.90 29 53 11.5 124.1 1.250+1.471−0.637 −0.33+0.66

−0.35 0.1303 0.955X-6 12 22 40.55 29 57 20.8 253.5 3.333+1.823

−1.151 −1.00+0.38−0.00 0.0471 5.000

X-7 12 22 18.26 29 49 17.8 335.0 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2474 1.474NGC 4395 N 12 25 48.86 33 32 48.7 0.9 5.417+2.136

−1.462 −0.85+0.28−0.11 0.5656 2.200

X-1 12 25 49.07 33 32 01.8 46.3 5.833+2.214−1.519 −0.57+0.29

−0.18 0.6554 1.386X-2 12 25 47.30 33 34 47.9 122.3 45.833+4.986

−4.355 0.20+0.10−0.09 3.6490 0.500

X-3 12 25 39.55 33 32 04.1 146.9 1.667+1.566−0.759 0.00+0.56

−0.34 0.1327 0.500X-4 12 25 59.90 33 33 21.2 168.3 1.250+1.471

−0.637 0.33+0.66−0.35 0.0995 0.500

X-5 12 25 55.18 33 30 16.1 178.8 6.250+2.237−1.577 −0.87+0.25

−0.10 0.6322 2.299X-6 12 25 43.89 33 29 60.0 184.1 1.667+1.536

−0.795 −1.00+0.64−0.00 0.0199 5.000

X-7 12 26 01.46 33 31 30.7 203.6 60.000+5.507−4.988 −0.97+0.04

−0.02 3.5848 3.274X-8 12 25 43.77 33 28 54.2 246.2 2.917+1.803

−1.045 −0.14+0.43−0.28 0.2508 0.621

X-9 12 25 42.67 33 40 00.4 442.3 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0199 5.000NGC 4414 X-1 12 26 27.19 31 13 23.7 14.5 1.250+1.450

−0.678 −1.00+0.77−0.00 0.1590 5.000

X-2 12 26 25.40 31 13 40.6 26.3 6.667+2.260−1.647 −1.00+0.21

−0.00 0.8482 5.000X-3 12 26 19.52 31 13 02.8 102.8 1.667+1.566

−0.759 0.00+0.56−0.34 0.1965 0.657

X-4 12 26 15.95 31 13 10.8 155.4 2.500+1.727−0.959 −0.33+0.47

−0.29 0.4288 1.251X-5 12 26 24.62 31 10 33.2 166.8 2.083+1.641

−0.867 −0.60+0.53−0.25 0.4469 1.841

X-6 12 26 37.48 31 15 14.4 204.1 1.250+1.450−0.678 −1.00+0.77

−0.00 0.1590 5.000X-7 12 26 24.74 31 17 12.2 235.3 2.917+1.784

−1.048 −0.71+0.44−0.19 0.6696 2.180

X-8 12 26 35.00 31 09 51.0 244.7 2.917+1.758−1.073 −1.00+0.42

−0.00 0.3711 5.000X-9 12 26 10.16 31 15 41.4 281.4 4.167+1.972

−1.272 −0.80+0.34−0.14 0.9847 2.513

118



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-10 12 26 01.88 31 12 07.2 373.1 3.333+1.871−1.125 0.25+0.40

−0.26 0.3449 0.500X-11 12 26 49.63 31 17 36.5 435.1 32.917+4.326

−3.686 −0.16+0.12−0.10 4.7248 0.940

X-12 12 26 43.19 31 20 18.2 490.6 3.750+1.912−1.202 −0.78+0.37

−0.16 0.8820 2.417X-13 12 27 11.42 31 15 12.8 686.5 1.250+1.471

−0.637 −0.33+0.66−0.35 0.2144 1.251

NGC 4494 N? 12 31 24.06 25 46 30.1 7.1 8.750+2.524−1.877 −0.81+0.21

−0.11 0.9808 2.050X-2 12 31 23.49 25 45 58.2 28.5 1.667+1.566

−0.759 0.00+0.56−0.34 0.1359 0.500

X-3 12 31 29.57 25 46 21.3 79.1 4.167+1.972−1.272 −0.80+0.34

−0.14 0.4704 2.014X-4 12 31 25.95 25 44 52.8 94.5 1.250+1.471

−0.637 −0.33+0.66−0.35 0.1277 0.931

X-5 12 31 28.55 25 44 57.0 107.8 10.000+2.658−2.010 −0.75+0.20

−0.12 1.1589 1.843X-6 12 31 34.16 25 45 16.6 162.6 2.917+1.803

−1.045 0.14+0.43−0.28 0.2378 0.500

X-7 12 31 07.83 25 47 34.0 256.7 7.917+2.449−1.782 −0.68+0.24

−0.14 0.9283 1.654NGC 4565 N 12 36 20.78 25 59 15.7 1.3 1.667+1.560

−0.760 −0.50+0.59−0.29 0.1833 1.237

X-1 12 36 20.91 25 59 26.8 11.3 1.667+1.566−0.759 0.00+0.56

−0.34 0.1334 0.500X-2 12 36 19.01 25 59 31.3 29.6 1.667+1.566

−0.759 0.00+0.56−0.34 0.1334 0.500

X-3 12 36 18.65 25 59 34.8 36.0 2.083+1.650−0.865 0.20+0.51

−0.31 0.1667 0.500X-4 12 36 19.46 25 58 45.1 36.1 3.333+1.864

−1.125 −0.50+0.41−0.24 0.3666 1.237

X-5 12 36 23.83 25 58 59.6 49.8 54.583+5.370−4.756 −0.47+0.08

−0.07 5.9100 1.170X-6 12 36 17.40 25 58 55.5 53.6 7.083+2.348

−1.682 −0.76+0.24−0.13 0.7959 1.886

X-7 12 36 19.02 26 00 27.2 75.6 2.500+1.727−0.959 0.33+0.47

−0.29 0.2001 0.500X-8 12 36 25.95 25 59 31.9 80.4 2.500+1.715

−0.961 −0.67+0.48−0.22 0.2863 1.605

X-9 12 36 28.12 26 00 00.9 120.1 7.083+2.377−1.681 −0.29+0.27

−0.20 0.6907 0.865X-10 12 36 14.60 26 00 53.0 133.3 6.667+2.285

−1.631 −0.88+0.24−0.10 0.6670 2.341

X-11 12 36 27.39 25 57 32.8 143.9 2.500+1.727−0.959 −0.33+0.47

−0.29 0.2505 0.932X-12 12 36 31.27 25 59 37.4 159.9 7.917+2.423

−1.783 −0.89+0.21−0.08 0.7573 2.456

119



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-13 12 36 08.05 25 55 25.3 298.7 9.583+2.607−1.967 −0.83+0.19

−0.10 1.0297 2.110X-14 12 36 14.22 25 50 25.2 539.6 3.333+1.864

−1.125 −0.50+0.41−0.24 0.3666 1.237

X-15 12 35 42.76 25 56 54.3 586.5 121.250+7.689−7.099 −0.59+0.05

−0.05 13.7370 1.419NGC 4569 N 12 36 49.82 13 09 46.2 2.8 5.833+2.187

−1.520 −0.86+0.27−0.11 0.6625 2.324

X-1 12 36 49.83 13 09 57.4 11.6 2.083+1.650−0.865 −0.20+0.51

−0.31 0.1987 0.742X-2 12 36 47.69 13 08 40.2 74.3 19.583+3.462

−2.834 −0.66+0.14−0.10 2.4194 1.641

X-3 12 36 46.36 13 10 55.2 88.1 1.250+1.471−0.637 −0.33+0.66

−0.35 0.1329 0.970X-4 12 36 52.64 13 11 40.9 121.6 2.917+1.758

−1.073 −1.00+0.42−0.00 0.0496 5.000

X-5 12 36 53.05 13 11 40.0 122.8 2.500+1.730−0.959 0.00+0.46

−0.30 0.2061 0.500X-6 12 36 53.67 13 11 54.0 139.3 4.583+2.053

−1.336 −0.45+0.34−0.22 0.5263 1.192

X-7 12 36 40.11 13 10 08.8 150.0 4.583+2.053−1.336 −0.45+0.34

−0.22 0.5263 1.192X-8 12 36 37.98 13 10 51.1 191.6 5.833+2.226

−1.518 −0.29+0.30−0.21 0.5985 0.888

X-9 12 36 39.62 13 11 38.2 192.0 7.917+2.449−1.782 −0.68+0.24

−0.14 0.9797 1.706X-10 12 36 38.84 13 12 34.2 237.2 1.250+1.471

−0.637 −0.33+0.66−0.35 0.1329 0.970

X-11 12 36 34.55 13 08 42.2 240.4 2.500+1.730−0.959 0.00+0.46

−0.30 0.2061 0.500X-12 12 36 43.41 13 15 13.1 341.7 2.917+1.803

−1.045 0.14+0.43−0.28 0.2404 0.500

NGC 4579 N 12 37 43.52 11 49 05.4 0.5 1.250+1.471−0.637 −0.33+0.66

−0.35 0.1323 0.970X-1 12 37 43.61 11 49 07.4 2.9 1626.9+25.847

−25.274 −0.55+0.01−0.01 183.2740 1.384

X-2 12 37 44.41 11 49 10.1 14.5 1635.0+25.898−25.325 −0.55+0.01

−0.01 184.1871 1.390X-3 12 37 45.40 11 49 07.2 28.5 2.500+1.689

−0.989 −1.00+0.47−0.00 0.0422 5.000

X-4 12 37 41.48 11 49 05.5 30.3 0.833+1.369−0.487 0.00+0.76

−0.41 0.0684 0.500X-5 12 37 43.85 11 48 27.2 38.2 1.667+1.566

−0.759 0.00+0.56−0.34 0.1369 0.500

X-6 12 37 45.74 11 49 31.3 42.7 0.833+1.369−0.487 0.00+0.76

−0.41 0.0684 0.500X-7 12 37 41.50 11 49 54.6 58.0 0.833+1.353

−0.536 −1.00+0.97−0.00 0.0141 5.000

120



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-8 12 37 42.20 11 48 09.0 59.3 2.917+1.798−1.046 −0.43+0.44

−0.26 0.3286 1.143X-9 12 37 45.10 11 51 20.2 137.3 0.833+1.353

−0.536 −1.00+0.97−0.00 0.0141 5.000

X-10 12 37 43.71 11 46 44.2 140.8 1.250+1.450−0.678 −1.00+0.77

−0.00 0.0211 5.000X-11 12 37 41.87 11 51 30.1 147.1 0.833+1.353

−0.536 −1.00+0.97−0.00 0.0141 5.000

X-12 12 37 41.68 11 46 11.3 175.9 2.500+1.689−0.989 −1.00+0.47

−0.00 0.0422 5.000X-13 12 37 45.37 11 44 38.8 267.7 1.250+1.450

−0.678 −1.00+0.77−0.00 0.0211 5.000

NGC 4594 X-1 12 39 59.43 -11 37 23.5 10.5 3.333+1.864−1.125 −0.50+0.41

−0.24 0.4101 1.322X-2 12 39 57.36 -11 37 20.6 22.8 151.250+8.533

−7.930 −0.40+0.05−0.05 17.5225 1.125

X-3 12 40 00.32 -11 37 24.0 23.2 11.250+2.725−2.150 −1.00+0.13

−0.00 0.2596 5.000X-4 12 40 00.05 -11 37 09.2 26.6 2.917+1.784

−1.048 −0.71+0.44−0.19 0.3822 1.844

X-5 12 40 01.03 -11 37 24.6 33.6 3.333+1.864−1.125 −0.50+0.41

−0.24 0.4101 1.322X-6 12 40 00.95 -11 37 02.7 41.1 5.417+2.136

−1.462 −0.85+0.28−0.11 0.6704 2.337

X-7 12 39 59.30 -11 38 29.1 61.5 7.500+2.405−1.732 −0.67+0.24

−0.15 0.9794 1.709X-8 12 39 59.86 -11 36 23.5 66.4 11.667+2.850

−2.176 −0.21+0.21−0.16 1.1682 0.797

X-9 12 39 59.66 -11 35 25.4 123.3 3.750+1.912−1.202 −0.78+0.37

−0.16 0.4860 2.052X-10 12 40 00.67 -11 35 20.1 130.9 2.917+1.798

−1.046 −0.43+0.44−0.26 0.3443 1.180

X-11 12 40 05.34 -11 35 00.5 177.1 2.083+1.650−0.865 −0.20+0.51

−0.31 0.2058 0.772NGC 4639 N 12 42 52.38 13 15 26.6 0.5 159.583+8.745

−8.146 −0.45+0.05−0.04 18.1161 1.183

X-1 12 42 51.19 13 14 39.9 49.7 3.333+1.823−1.151 −1.00+0.38

−0.00 0.0545 5.000X-2 12 42 53.41 13 13 46.1 101.6 2.917+1.784

−1.048 −0.71+0.44−0.19 0.3563 1.785

X-3 12 42 54.38 13 23 56.2 510.7 1.667+1.560−0.760 −0.50+0.59

−0.29 0.1939 1.278NGC 4736 N 12 50 53.03 41 07 12.4 0.6 12.500+2.893

−2.254 −0.73+0.17−0.11 1.4413 1.794

X-1 12 50 53.32 41 07 14.1 5.3 0.833+1.369−0.487 0.00+0.76

−0.41 0.0673 0.500X-2 12 50 52.71 41 07 19.2 8.4 1.250+1.471

−0.637 0.33+0.66−0.35 0.1009 0.500

121



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-3 12 50 52.56 41 07 02.1 11.9 80.417+6.373−5.777 −0.61+0.06

−0.05 9.2720 1.465X-4 12 50 53.70 41 07 18.5 12.3 4.583+2.029

−1.338 −0.82+0.32−0.13 0.5042 2.085

X-5 12 50 53.31 41 07 00.0 12.8 5.417+2.162−1.460 −0.54+0.31

−0.19 0.6126 1.319X-6 12 50 52.10 41 06 54.9 21.8 30.000+4.084

−3.518 −0.92+0.08−0.04 2.7308 2.617

X-7 12 50 50.31 41 07 12.3 40.4 5.000+2.083−1.402 −0.83+0.30

−0.12 0.5413 2.148X-8 12 50 47.60 41 05 12.4 144.5 18.750+3.398

−2.772 −0.69+0.14−0.10 2.1769 1.668

X-9 12 50 04.00 41 05 16.0 744.1 4.583+2.059−1.336 −0.27+0.34

−0.23 0.4451 0.833NGC 4826 X-1 12 56 43.67 21 40 57.1 11.2 2.083+1.641

−0.867 −0.60+0.53−0.25 0.2603 1.495

X-2 12 56 45.81 21 41 03.2 24.2 4.167+2.001−1.269 0.20+0.36

−0.25 0.3518 0.500X-3 12 56 41.60 21 41 03.5 39.1 4.583+2.053

−1.336 0.45+0.34−0.22 0.3870 0.500

X-4 12 56 42.05 21 41 34.6 43.8 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2603 1.495X-5 12 56 43.95 21 39 57.2 67.9 1.667+1.560

−0.760 0.50+0.59−0.29 0.1407 0.500

X-6 12 56 32.88 21 40 58.4 170.0 2.083+1.615−0.898 −1.00+0.54

−0.00 0.0368 5.000X-7 12 56 32.67 21 40 23.9 177.7 2.500+1.730

−0.959 0.00+0.46−0.30 0.2111 0.500

X-8 12 56 45.59 21 38 05.5 180.7 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2603 1.495X-9 12 56 14.01 21 39 23.9 464.1 4.167+1.945

−1.293 −1.00+0.31−0.00 0.0736 5.000

X-10 12 56 58.70 21 50 04.2 581.4 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0295 5.000NGC 5033 N 13 13 27.48 36 35 38.1 2.4 3.333+1.871

−1.125 −0.25+0.40−0.26 0.3104 0.783

X-1 13 13 29.65 36 35 23.0 35.0 20.000+3.514−2.865 −0.33+0.15

−0.12 1.9788 0.923X-2 13 13 29.45 36 35 17.3 35.7 1.250+1.450

−0.678 −1.00+0.77−0.00 0.0136 5.000

X-3 13 13 25.18 36 35 43.5 36.4 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0181 5.000X-4 13 13 24.78 36 35 03.7 55.6 2.083+1.650

−0.865 −0.20+0.51−0.31 0.1864 0.702

X-5 13 13 24.89 36 36 56.2 86.6 1.667+1.560−0.760 0.50+0.59

−0.29 0.1326 0.500X-6 13 13 35.55 36 34 04.4 152.6 469.167+14.574

−13.977 −0.29+0.03−0.03 45.1615 0.855

122



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-7 13 13 39.39 36 37 17.6 202.1 15.000+3.090−2.475 −0.83+0.14

−0.08 1.5628 2.121X-8 13 13 14.26 36 34 16.9 216.5 2.917+1.803

−1.045 −0.14+0.43−0.28 0.2489 0.612

X-9 13 13 15.60 36 32 56.2 243.1 7.083+2.367−1.681 −0.53+0.26

−0.17 0.7761 1.284X-10 13 13 51.28 36 36 20.4 357.5 3.333+1.850

−1.127 −0.75+0.40−0.17 0.3694 1.822

X-11 13 12 58.16 36 34 26.7 447.6 1.250+1.471−0.637 −0.33+0.66

−0.35 0.1237 0.923X-12 13 13 17.13 36 42 43.7 452.1 2.500+1.727

−0.959 −0.33+0.47−0.29 0.2474 0.923

NGC 5055 N 13 15 49.28 42 01 46.6 1.6 2.500+1.689−0.989 −1.00+0.47

−0.00 0.0297 5.000X-1 13 15 49.57 42 01 27.1 18.4 3.333+1.871

−1.125 −0.25+0.40−0.26 0.3127 0.785

X-2 13 15 50.95 42 01 59.9 28.9 1.250+1.471−0.637 0.33+0.66

−0.35 0.1000 0.500X-3 13 15 51.39 42 01 40.8 31.6 2.083+1.650

−0.865 −0.20+0.51−0.31 0.1875 0.703

X-4 13 15 46.64 42 02 01.3 43.1 20.000+3.416−2.876 −1.00+0.07

−0.00 0.2379 5.000X-5 13 15 53.25 42 02 15.2 66.4 5.833+2.203

−1.519 −0.71+0.28−0.15 0.6633 1.729

X-6 13 15 53.89 42 01 04.7 79.7 2.917+1.758−1.073 −1.00+0.42

−0.00 0.0347 5.000X-7 13 15 43.36 42 01 50.7 89.3 2.917+1.784

−1.048 −0.71+0.44−0.19 0.3317 1.729

X-8 13 15 49.46 41 59 51.9 113.1 11.667+2.838−2.176 −0.50+0.20

−0.14 1.2779 1.232X-9 13 15 40.83 42 01 49.6 127.1 4.167+1.996

−1.270 −0.40+0.36−0.23 0.4337 1.044

X-10 13 15 58.82 42 02 03.9 144.0 2.500+1.689−0.989 −1.00+0.47

−0.00 0.0297 5.000X-11 13 15 39.31 42 01 54.0 150.1 2.083+1.641

−0.867 −0.60+0.53−0.25 0.2358 1.442

X-12 13 15 39.49 42 02 27.0 153.1 6.250+2.280−1.574 0.20+0.29

−0.21 0.4998 0.500X-13 13 15 39.25 42 00 30.7 168.1 3.333+1.823

−1.151 −1.00+0.38−0.00 0.0397 5.000

X-14 13 15 48.52 42 04 32.7 168.2 2.500+1.730−0.959 0.00+0.46

−0.30 0.1999 0.500X-15 13 15 43.85 41 59 10.4 174.9 117.917+7.594

−7.000 −0.55+0.05−0.05 13.1847 1.344

X-16 13 15 37.62 42 02 13.4 177.5 11.250+2.801−2.136 −0.48+0.20

−0.15 1.2222 1.196X-17 13 16 02.26 42 01 53.7 194.6 14.583+3.032

−2.441 −0.94+0.12−0.05 1.1481 2.841

123



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-18 13 15 36.34 42 01 24.7 195.5 2.500+1.730−0.959 0.00+0.46

−0.30 0.1999 0.500X-19 13 15 37.31 42 03 32.0 209.2 6.250+2.211

−1.594 −1.00+0.22−0.00 0.0743 5.000

X-20 13 16 05.68 42 01 15.0 247.6 7.500+2.413−1.732 −0.56+0.25

−0.17 0.8388 1.345X-21 13 15 30.17 42 03 13.6 300.3 7.917+2.449

−1.782 −0.68+0.24−0.14 0.9031 1.647

X-22 13 15 19.50 42 03 02.2 453.7 3.333+1.823−1.151 −1.00+0.38

−0.00 0.0397 5.000X-23 13 15 18.12 42 04 04.5 488.0 3.750+1.927

−1.200 0.56+0.38−0.22 0.2999 0.500

X-24 13 15 08.57 42 01 12.8 611.9 1.667+1.536−0.795 −1.00+0.64

−0.00 0.0198 5.000X-25 13 14 59.15 41 58 38.4 775.1 40.833+4.690

−4.109 −0.82+0.08−0.06 4.4129 2.067

X-26 13 14 54.74 42 02 39.6 820.2 4.167+1.972−1.272 −0.80+0.34

−0.14 0.4567 2.005NGC 5195 X-1 13 29 58.37 47 16 12.6 9.9 0.833+1.369

−0.487 0.00+0.76−0.41 0.0691 0.500

X-2 13 30 00.40 47 15 58.4 26.1 5.833+2.226−1.518 −0.29+0.30

−0.21 0.5763 0.824X-3 13 29 53.68 47 16 45.2 85.8 2.083+1.641

−0.867 −0.60+0.53−0.25 0.2429 1.426

X-4 13 30 02.96 47 15 06.6 85.9 4.167+1.996−1.270 −0.40+0.36

−0.23 0.4450 1.024X-5 13 29 54.60 47 14 36.7 106.8 2.917+1.784

−1.048 −0.71+0.44−0.19 0.3428 1.716

X-6 13 30 06.90 47 15 43.4 124.8 4.583+2.059−1.336 −0.27+0.34

−0.23 0.4481 0.802X-7 13 29 59.18 47 13 21.9 162.3 1.250+1.471

−0.637 −0.33+0.66−0.35 0.1278 0.906

X-8 13 29 59.82 47 12 12.4 232.2 7.500+2.378−1.734 −0.89+0.22

−0.09 0.7560 2.413X-9 13 29 51.60 47 11 55.3 270.6 6.667+2.285

−1.631 −0.88+0.24−0.10 0.6918 2.332

X-10 13 30 16.65 47 15 17.6 273.2 1.667+1.560−0.760 −0.50+0.59

−0.29 0.1877 1.214X-11 13 29 53.68 47 11 40.9 273.7 20.417+3.514

−2.895 −0.71+0.13−0.09 2.3996 1.716

X-12 13 29 38.81 47 16 15.1 298.6 8.333+2.466−1.831 −0.90+0.20

−0.08 0.8167 2.483X-13 13 30 08.42 47 11 07.0 330.9 42.917+4.751

−4.214 −0.96+0.05−0.02 3.0775 3.077

X-14 13 29 39.46 47 18 55.5 335.7 2.500+1.715−0.961 −0.67+0.48

−0.22 0.2944 1.587X-15 13 29 40.87 47 12 38.0 337.5 4.583+2.053

−1.336 0.45+0.34−0.22 0.3798 0.500

124



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-16 13 30 18.32 47 13 17.6 338.1 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2429 1.426X-17 13 29 44.30 47 11 35.4 344.7 4.583+2.053

−1.336 −0.45+0.34−0.22 0.5047 1.125

NGC 5273 N 13 42 08.35 35 39 14.6 0.8 42.917+4.844−4.214 0.26+0.10

−0.09 3.4126 0.500X-1 13 42 08.99 35 39 28.7 17.1 3.333+1.823

−1.151 −1.00+0.38−0.00 0.0356 5.000

X-2 13 42 08.43 35 43 33.5 258.5 2.083+1.641−0.867 −0.60+0.53

−0.25 0.2322 1.431X-3 13 41 54.06 35 36 07.6 284.1 3.333+1.823

−1.151 −1.00+0.38−0.00 0.0356 5.000

X-4 13 41 48.49 35 40 04.6 301.3 1.667+1.566−0.759 0.00+0.56

−0.34 0.1325 0.500X-5 13 42 31.00 35 35 16.1 416.0 2.083+1.615

−0.898 −1.00+0.54−0.00 0.0222 5.000

X-6 13 41 33.74 35 36 36.8 541.9 5.000+2.099−1.400 −0.67+0.31

−0.18 0.5610 1.588X-7 13 41 50.27 35 30 05.0 612.9 2.500+1.715

−0.961 −0.67+0.48−0.22 0.2805 1.588

X-8 13 41 33.06 35 32 52.5 652.5 25.833+3.890−3.261 −0.55+0.12

−0.10 2.8422 1.320NGC 6500 N 17 55 59.78 18 20 17.9 1.3 15.000+3.065

−2.476 −0.94+0.12−0.04 1.8469 3.275

X-1 17 56 01.58 18 20 22.8 28.6 2.917+1.798−1.046 −0.43+0.44

−0.26 0.3991 1.293X-2 17 55 56.44 18 19 10.5 83.6 2.083+1.650

−0.865 −0.20+0.51−0.31 0.2347 0.869

X-3 17 55 52.78 18 20 35.6 105.3 2.083+1.641−0.867 −0.60+0.53

−0.25 0.3155 1.673X-4 17 56 03.76 18 22 23.4 139.1 2.083+1.641

−0.867 −0.60+0.53−0.25 0.3155 1.673

NGC 6503 X-1 17 49 28.96 70 08 43.1 29.5 10.000+2.647−2.011 −0.83+0.19

−0.10 1.3018 2.304X-2 17 49 31.59 70 08 19.4 73.5 5.000+2.099

−1.400 −0.67+0.31−0.18 0.6771 1.735

X-3 17 49 26.58 70 06 51.1 114.0 2.500+1.715−0.961 −0.67+0.48

−0.22 0.3385 1.735X-4 17 49 12.43 70 09 30.3 223.2 8.750+2.524

−1.877 −0.81+0.21−0.11 1.1593 2.201

X-5 17 48 51.64 70 07 48.6 533.5 4.167+2.002−1.269 0.00+0.36

−0.25 0.3542 0.500X-6 17 50 12.46 70 04 54.4 719.9 2.917+1.803

−1.045 0.14+0.43−0.28 0.2479 0.500

X-7 17 48 31.79 70 08 10.7 828.8 4.167+1.945−1.293 −1.00+0.31

−0.00 0.1051 5.000X-8 17 50 25.17 70 00 57.6 989.9 2.917+1.798

−1.046 −0.43+0.44−0.26 0.3567 1.204

125



s−1) (1038 erg s−1)

(1) (2) (3) (4) (5) (6) (7)

X-9 17 50 56.12 69 58 56.8 1460.4 8.333+2.521−1.829 0.00+0.25

−0.19 0.7084 0.500

Note. — (1) Gives the source identifier, ordered by increasing distance from the nucleus. An exclamation pointindicates a source with heavy pileup. (2) J2000 coordinates for the source. (3) Source distance from nucleus. (4)Observed count rate per ks. and the Poissonian error in count rate (5) Hardness ratio, defined between 0.2–2 keVand 2–8 keV. and the error in hardness ratio from counting statistics. (6) Inferred source luminosity (see text), inunits of 1038 erg s−1. (7) The photon power law index that is inferred from the hardness ratio.

126

Figure 3.3 “Colour magnitude” diagram, luminosity function and cumula-tive luminosity function for the targets NGC 253, NGC 404, NGC 660 andNGC 1052. The top panel plots source hardness ratio against luminosity,analogous to a colour-magnitude diagram from optical astronomy. For mea-suring the hardness ratio, a hard band (2–8 keV) and a soft band (0.2–2 keV)were used. Sources along the −1 hardness ratio line were not detected at allin the hard band. The middle plot shows the distribution of sources withthe 0.2–8 keV X-ray luminosity. The lower panel is a cumulative luminos-ity function derived from the middle panel. This plot shows the fractionof sources brighter than the corresponding luminosity (again using the fullband, 0.2–8 keV).

127

Figure 3.4 Identical to 3.3, but for the galaxies NGC 1055, NGC 1058,NGC 2541 and NGC 2683.

128


129


130


131


132


133


134


135


136

Figure 3.13 Identical to 3.3, but for the galaxy NGC 6503.

137

Figure 3.14 18′×18′ images of NGC 253, NGC 404, NGC 660 and NGC 1052.

138


139


140


141


142


143


144


145


146


147

Figure 3.24 Identical to 3.14, but for the galaxy NGC 6503.

148

Chapter 4

Nova Sco and coalescing lowmass black hole binariesas LIGO sources

Abstract

Double neutron star (NS-NS ) binaries, analogous to the well known Hulse–

Taylor pulsar PSR 1913+16 (Hulse & Taylor, 1975b), are guaranteed-to-

exist sources of high frequency gravitational radiation detectable by LIGO.

There is considerable uncertainty in the estimated rate of coalescence of

such systems (Phinney, 1991; Narayan et al., 1991; Kalogera et al., 2001),

with conservative estimates of ∼ 1 per million years per galaxy, and opti-

mistic theoretical estimates one or more magnitude larger. Formation rates

of low-mass black hole-neutron star binaries may be higher than those of

NS-NS binaries, and may dominate the detectable LIGO signal rate. Rate

estimates for such binaries are plagued by severe model uncertainties. Re-

cent estimates suggest that BH-BH binaries do not coalesce at significant

rates despite being formed at high rates (Portegies Zwart & Yungelson, 1998;

de Donder & Vanbeveren, 1998).

149

We estimate the enhanced coalescence rate for BH-BH binaries due to

weak asymmetric kicks during the formation of low mass black holes like

Nova Sco (Brandt et al., 1995), and find they may contribute significantly

to the LIGO signal rate, possibly dominating the phase I detectable signals

if the range of BH masses for which there is significant kick is broad enough.

For a standard Salpeter IMF, assuming mild natal kicks, we project that the

R6 merger rate (the rate of mergers per million years in a Milky Way-like

galaxy) of BH-BH systems is ∼ 0.5, smaller than that of NS-NS systems.

However, the higher chirp mass of these systems produces a signal nearly

four times greater, on average, with a commensurate increase in search vol-

ume. Hence, our claim that BH-BH mergers (and, to a lesser extent, BH-

NS coalescence) should comprise a significant fraction of the signal seen by

LIGO.

The BH-BH coalescence channel considered here also predicts that a

substantial fraction of BH-BH systems should have at least one component

with near-maximal spin (a/M ∼ 1). This is from the spin-up provided by the

fallback material after a supernova. If no mass transfer occurs between the

two supernovae, both components could be spinning rapidly. The waveforms

produced by the coalescence of such a system should produce a clear spin

signature, so this hypothesis could be directly tested by LIGO.

4.1 Introduction

With the arrival of LIGO, and other planned gravitational radiation ob-

servatories, the nascent field of gravitational radiation astronomy is set to

prosper, if there are detectable sources in the local universe. A consider-

able amount of effort has been directed towards identifying potential grav-

150

itational radiation sources, and the relative rate of contribution of these

sources to the anticipated signals. The canonical scenario envisioned is the

final coalescence of a binary neutron star system (NS-NS), where the pair’s

orbital energy has been radiated away by gravitational waves.

NS-NS merger can produce a copious signal for LIGO, if they occur at

high enough a rate locally — current estimates for LIGO phase I place the

maximum detection radius for such an event at ∼20 Mpc or less (Kalogera

et al., 2001). The merger rate of NS-NS binaries can be estimated from

observed systems (Phinney, 1991; Narayan et al., 1991), such estimates are

plagued by small number statistics and possible observer biases (Kalogera,

1998; Kalogera et al., 2001). Alternatively, the rate can be estimated from ab

initio theoretical models (see review by Grishchuk et al. 2000, also Portegies

Zwart & Yungelson 1998; Belczynski et al. 2002; Fryer 1999; Bloom et al.

1999).

A number of authors have explored binary population synthesis models,

making a number of assumptions about the input physics, leading to rates

consistent with observational constraints, but uncertain by 1–2 orders of

magnitude (Portegies Zwart & Yungelson, 1998; Kalogera, 1998; Kalogera

& Lorimer, 2000; Bloom et al., 1999; de Donder & Vanbeveren, 1998; Bel-

czynski & Bulik, 1999; Lipunov et al., 1997; Brandt & Podsiadlowski, 1995;

Belczynski et al., 2002; Fryer, 1999) . Conventionally, the rates are expressed

in terms of R6, the merger rate per million years per Milky Way-like galaxy,

assuming normal rates of star formation. Then the rate in the local universe

is the integrated rate over the number density of galaxies, the rate per galaxy,

scaled to the Milky Way rate, per detection volume. Kalogera et al. (2001)

find a LIGO I event rate of 3× 10−4 y−1 for NS-NS mergers within 20 Mpc,

assuming R6 = 1. For a given detector sensitivity, higher mass coalescences

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are detectable to larger volumes, with the detection distance, dL ∝ M5/6chirp,

where Mchirp = (m1m2)3/5/(m1 +m2)

1/5 (Thorne, 1994). Since black holes

are expected to have masses several times larger than neutron stars, and the

event rate scales as d3L (for dL small compared to the size of the universe),

a black hole coalescence rate of order R6 implies event rates 2–3 orders of

magnitude higher.

The problem of accurately estimating the coalescence rate of compact

binaries can be appreciated by noting that the type II supernovae rate in the

Milky Way is 1–2 per century, implying that the rate of type II supernova

in binaries is about 10−2 y−1, given a 50% binarity rate. Estimates of the

coalescence rate are canonically close to R6 = 10−6 y−1 per Milky Way. So

the branching ratio for type II supernovae to form merging systems is of

the order 10−4. Calculating the mean rate, averaged over all scenarios for

coalescence, in the local universe, is hard, with small errors of assumption

about the physics of stellar evolution leading to large fractional changes in

the branching ratios of particular channels for mergers.

Theoretical models require a series of assumptions, about the mass func-

tion of high mass stars, the cut-off points for which zero age masses lead to

NS or BH formation, the binary fraction and mass ratio distribution, the

amount of mass loss during (binary) stellar evolution, and the amplitude

and distribution of natal kicks. Secondary assumptions, that are usually

not explored in detail, include the dependence of all of the above on metal-

licity and environment in which the massive stars form; and the possibility

that the NS/BH cut-off, and the natal kick, may depend on stellar rota-

tion and magnetic fields. In fact, it is not implausible that the NS/BH

formation boundary is “fuzzy”, that there is not a sharp border in zero-age

152

mass between stars that form neutron stars and those which form black

holes. A further potential confounding effect, is that natal kicks are gener-

ally assumed to be random, but may in principle be correlated with some

macroscopic property of the progenitor star, such as rotation (e.g. Spruit &

Phinney 1998; Pfahl et al. 2002).

There are two arguments against a high rate of coalescence of compact

binaries: most high mass binaries become unbound during the near instan-

taneous mass-loss at supernova; the second problem is that of the ‘kicks’

believed to be inflicted upon the NS from an asymmetrical supernova blast.

While the range of energies imparted by the kick is a subject of intense de-

bate (Lyne & Lorimer, 1994; Hansen & Phinney, 1997; Tauris & Savonije,

1999; Cordes & Chernoff, 1998; Fryer et al., 1998; Arzoumanian et al., 2002),

the resulting velocity change is believed to be of the order 250 km sec−1 for

a 1.4 M� neutron star. A properly aligned kick can allow the system to

remain bound, albeit with dramatically altered orbital parameters, but a

random kick is unlikely to be directed so fortuitously, with the extra energy

making a bound final state even less likely.

An alternative to the NS-NS scenario is one in which both stars are

of sufficient mass to end up as black holes. The minimum mass required

for black hole formation is not well known, and is heavily influenced by

the evolutionary history of the black hole candidate (see Fryer 1999; Fryer

& Kalogera 2001). Accretion induced spin-up of the star prior to collapse

could result in a higher minimum mass threshold, while the presence of

strong winds could drop the progenitor mass below the required minimum.

Finally, unless an unusually flat IMF is assumed (as apparently seen in

certain starburst galaxies, see, for example, Doane & Mathews 1993), few

of these objects will be produced in the first place.

153

Nevertheless, precursors to black hole binary systems are more likely to

survive both supernovae due to the smaller fractional mass loss during the

event. Depending upon the mass of the star, a significant amount of material

can fall back upon it just after the blast. Indeed, a sufficiently massive

progenitor may not undergo a supernova at all, reaching a point where

nearly all of the material is quickly reabsorbed (Fryer, 1999). After losing a

significant fraction of mass to stellar winds and (possibly) two supernovae,

a typical bound binary system will have expanded considerably, with most

Porb > 10days. Long-period systems do not decay in less than a Hubble time

from gravitational radiation, and hence will never reach a frequency range

useful to LIGO. However, including asymmetric supernova kicks changes

the picture significantly. Assuming that the total momentum change is

approximately the same for all supernovae, the velocity imparted to the

nascent black hole will be scaled to its mass, via ∆vBH = ∆vNSMNS/MBH

(see Grishchuk et al 2001 for review). For a typical 7M� hole, this gives

a kick of the order ∼ 50 km s−1, comparable to or larger than the orbital

speed, but not so large as to always rip the system apart. Systems that

remain bound are generally in highly eccentric orbits, which expedites their

merger through emission of gravitational radiation.

Ultimately, the point is this: the trace of the metric perturbation from

gravitational waves, varies as h ∝M5/6chirp. As the maximum detection radius

scales linearly with h, the maximum search volume scales as V ∝ M5/2chirp.

The implied several hundred-fold increase in search volume means that, even

if only a small fraction of these systems can merge in τ < 1/H0, they may

dominate the detected signal.

Our approach is to concentrate on estimating the event rate from one

particular coalescence channel. The total branching ratio for coalescence is

154

of course the sum of all possible channels, and it is possible that other chan-

nels contribute significantly to the event rate, possibly dominating the total

rate; for example, dynamical evolution of cluster binaries may create new

channels for merger with high coalescence rates (Sigurdsson & Hernquist,

1993; Portegies Zwart & McMillan, 2000), or accretion induced collapse of

neutron stars with soft cores may lead to enhanced rates (Bethe & Brown,

1998). Here, rather than trying to estimate the total event rate, we make an

observationally motivated estimate of the rate for one particular channel.

4.2 Example of Nova Sco

Nova Sco 1994 (GRO J1655-40) is a strong candidate for being a black hole

binary (Bailyn et al., 1995; Orosz & Bailyn, 1997), with the primary being a

6.3 ± 0.5M� black hole (Greene et al., 2001; Shahbaz et al., 1999). Perhaps

its most remarkable feature is an unusually high space velocity, whose lower

limit of 106 km s−1was, until recently, several times greater than any other

known black hole transient (Shahbaz et al., 1999; Brandt et al., 1995). The

likely true space velocity is greater by a factor of√

3, adjusting for mean

projection effects.

A number of scenarios have been put forward to explain the unusual

speed of Nova Sco. Brandt et al. (1995) point out that the momentum

component of Nova Sco along the line of sight is comparable to that of a

single 1.4M� neutron star, having received a natal kick in the range 300–700

km s−1. This is not an unreasonable value for a neutron star kick (Lyne &

Lorimer, 1994; Cordes & Chernoff, 1998; Fryer et al., 1998), and so lends

strength to the possibility that Nova Sco can be explained by the primary

experiencing a natal kick prior to formation of the black hole. Invoking

155

Blaauw-Boersma kicks (Blaauw, 1961) as the sole acceleration mechanism

invites difficulty, as the low mass of the secondary means that most Blaauw-

Boersma kicks strong enough to give the observed speed would also disrupt

the binary system completely (Brandt et al., 1995). This is not to say

that such a scenario is impossible (see, for example, Nelemans et al., 1999).

However, the space velocity measurement of the X-ray nova XTE J1118+480

has provided a further example of a black hole binary with a high-velocity

Galactic-halo orbit. Mirabel et al. (2001) used the VLBA to obtain a precise

proper motion for the system, calculating a speed of 145±35 km s−1, with

respect to the local standard of rest. The system primary has a mass function

of 6.0±0.4M� (McClintock et al., 2001), with a faint (∼ 19mag) optical

counterpart. To accelerate this system to the observed peculiar velocity

using Blaauw-Boersma kicks alone, roughly 40 M� of material would have

to be expelled during stellar collapse, an implausibly large amount of matter.

This issue remains contentious, however, as calculations in Nelemans et al.

(1999) show that the velocity of Nova Sco, at least, might be explained by

a symmetric supernova where the black hole progenitor lost more than half

of its mass. This is marginally possible, but becomes much more tenuous if

Nova Sco turns out to have a significant transverse velocity.

One principal difficulty with the natal kick premise is arranging for suffi-

cient neutrinos to drive a supernova explosion prior to being trapped by the

formation of an event horizon, ejecting neutrinos or other material asymmet-

rically. Few neutrinos escape if the horizon forms over the dynamical time

of the collapsing core (Gourgoulhon & Haensel, 1993b). The drop in the

resulting neutrino heating of the envelope allows most or all of the envelope

to fall back onto the nascent black hole (see, for example, the hydrodynam-

ical simulations of Janka & Mueller 1996), hence preventing the supernova.

156

However, there is now strong evidence that a supernova must have taken

place in the Nova Sco system, from estimates of metal abundances in the

atmosphere of the secondary star. Israelian et al. (1999b) show that the sec-

ondary, an F3–F8 IV/III star, possesses a dramatic enhancement (factors

of six to ten) in α elements such as oxygen, magnesium, silicon and sulfur

(and see also the discussion in Podsiadlowski et al. 2002). Interestingly, no

significant enhancement in iron was found. The implication is that the pro-

genitor of the black hole did experience a supernova during its formation,

and a significant amount of the former atmosphere was captured by its com-

panion. As most of the iron core went on to collapse to a singularity, no

enhancement of this particular element is seen. The question is then how

long after the supernova it took for the black hole to form. One possibil-

ity is that the star, at the instant of the supernova, experienced sufficient

rotational support to avoid collapse for an extended period of time, until

spin-down allowed the system to collapse to a black hole some time later.

Another possible scenario has some of the material cast off in the supernova

explosion recaptured by the newly-formed neutron star, elevating its mass

above the threshold for collapse. In either case, a supernova is seen, with a

corresponding asymmetric natal kick. More massive progenitors would form

a horizon directly, with no possibility for a kick. We discuss limits for this

behaviour in the next section. Nova Sco 1994 and XTE J1118+480 provide

strong evidence that black holes do, in fact, experience natal asymmetric

kicks, at least under some conditions. The resulting orbital eccentricities

tend to accelerate binary coalescence from the enhanced radiation emitted

at every periastron passage.

157

4.3 Population synthesis

We make use of a binary evolution code developed by Pols & Marinus (1994),

and modified for use in NS-NS systems by Bloom et al. (1999). Our extension

of the code allows for evolution to the black hole state, with assumptions

about the mass function of such objects at the time of collapse.

Initially, the code chooses the mass of the primary from a given mass

function. For this work, we have chosen two power law IMFs, with indices

α of −2.0 and −2.35 (the latter, of course, being the Salpeter IMF). In

both cases, we established a lower cutoff of 4 M�, confining the code to

an interesting range of initial masses; i. e., where at least one supernova

is possible. Our primary stellar models are taken from Maeder & Meynet

(1989). The helium star models used are a mix of models from Habets

(1986) and Paczynski (1971). We assume that the mass ratio distribution

between the two components is flat. After choosing an initial separation

a and eccentricity e after Pols & Marinus (1994), the code evolves each

binary system until both components have reached their final degenerate

form, accounting for mass-transfer-induced stellar regeneration and stellar

winds. During the common-envelope phase, the orbit is circularised, and the

orbital energy is reduced by the binding energy of the envelope divided by

the common-envelope efficiency parameter, which we take to be 0.5. In other

words, the orbital energy is reduced by twice the envelope binding energy.

Neutron stars are formed from progenitors with ZAMS masses of between 8

and 20 M�, inclusive, and are always given a mass of 1.4 M�. More massive

stars end up as black holes. As noted in the Introduction, this boundary is

likely to be “fuzzy”, i.e., not a monotonic function of the progenitor mass, as

it is strongly coupled to the spin state of the star prior to collapse, a quantity

158

which our code simply does not track. Even assuming this was known to

perfect accuracy, it is far from trivial to estimate the effects of magnetic

field and rotational support vis-a-vis the compact object’s end state.

The black hole mass function (i. e., the post-collapse mass of a BH, given

its mass just prior to the explosion) is highly speculative at this point, and

is almost certainly not merely a function of initial mass, but also of angular

momentum, to the extent that this determines the fraction of material falling

back onto the collapsing star. In order to experience a kick, the black holes

formation must be delayed somewhat, either from rotational support, or

because event horizon formation occurs only after delayed fallback of mass

initially ejected from the core. Fryer (1999) has performed core-collapse

simulations in order to explore the critical mass for black hole formation,

and their final masses. As a best working guess, we have constructed a

mass relation from a quadratic fit to the limited data set found in Fryer

(1999). The mass of the black hole at formation (MBH) is related to the

ZAMS mass of the progenitor (M0) by MBH = (M0/25)2 × 5.2M�. We

have also chosen a simple criterion for whether a black hole will receive an

asymmetric neutrino kick during collapse; namely, all objects below 40 M�

(referring to the ZAMS mass) experience a random kick. Above this limit,

objects collapse directly to a black hole, with no kick. We explore the effect

of ignoring black hole kicks in the next section.

As a last step, the results of the code are normalised to the supernova

rate of the Milky Way, 0.01 yr−1. Here, the code produces some arbitrarily

large number of complete evolutionary sequences, including a large number

of supernova events. Scaling all these events to the Milky Way SNR allows

us to generate event rates out of data not previously ordered in time. This

effectively simulates a constant star-formation rate, where the population of

159

merger candidates has reached a dynamic equilibrium.

4.4 Results

Tables 4.1 and 4.2 summarize the investigation. For each IMF, six simula-

tions (generating 106 binary systems each) were run, varying two parame-

ters: Kmax, the upper limit of the imparted kick speed (acting on a 1.4M�

NS), and σ, the dispersion in the Maxwellian distribution of the kick speed.

Maximum kick values were chosen at 500 km s−1(for σ = 90 km s−1and σ

= 190 km s−1), and 1000 km s−1(for σ = 450 km s−1). The inclusion of

the 90 km s−1kick intensity is based upon recent observational work on the

velocity distribution of pulsars by Pfahl et al. (2002), which suggests a bi-

modal kick distribution centered around ∼ 100 and ∼ 500 km s−1. Further

discussions concerning this bi-modality can be found in Arzoumanian et al.

(2002); Cordes & Chernoff (1998); Fryer et al. (1998). This range has been

touched on in previous work (Grishchuk et al., 2000), but we have looked at

it specifically as a new observationally-motivated choice in kick magnitude.

The following columns show the R6 rate of BH-BH , BH-NS , NS-NS and

BH-PSR pairs generated in the sample. R6 is a rate of 1 event per Myr

per Milky Way galaxy, found by scaling event rates to the estimated local

supernova rate of 0.01 yr−1. One must take into account that not all stars

(and hence not all supernovae) occur in binaries; hence a binarity fraction

must be assumed, and we take that value to be 0.5 throughout (i. e. roughly

two-thirds of supernovae occur in a binary system). The alternating columns

show the R6 of such pairs expected to coalesce through emission of gravita-

tional radiation in less than the Hubble time (here, taken as 10 Gyr). Table

4.1 details the formation and merger rates when black holes and neutron

160

stars are given kicks as described above. Table 4.2 gives the relevant rates

when black holes are not allowed to have asymmetric kicks of any kind (even

if below 40 M�).

Figure 4.1 show examples of the generated data sets. Here, the separa-

tions of the BH-BH and BH-NS systems after the second supernova (i. e.,

stellar evolution has ended) are plotted against the post-mortem orbital

eccentricity. Dots represent systems stable against orbital decay, whilst tri-

angles represent those systems which will undergo coalescence in less than

a Hubble time. Figure 4.2 shows the distribution of masses in surviving

BH-BH binaries, irrespective of whether the system is unstable to orbital

decay.. A clear bifurcation in mass is seen, with the vast majority at around

5–6 M�, and another, smaller concentration at roughly 35 M�. The low end

is comprised of black holes with 20–40 M� ZAMS progenitors, which lose

much of their mass through a supernova (and hence experience a natal kick).

The higher mass group are from more massive progenitors, and collapsed

to a black hole without a supernova or the resulting kick. The histogram

in figure 4.3 shows the ”chirp” mass distribution for all BH-BH systems

that eventually merge from gravitational radiation. As the wave amplitude

scales like M5/6chirp, this plot, coupled with the sensitivity of the LIGO detec-

tor, allows us to estimate a detection rate for BH-BH binaries. By way of

comparison, two 1.4 M� objects produce a chirp mass of 1.22 M�.

As can be seen from column 8 in tables 4.1 and 4.2, most NS-NS pairs

that remain intact coalesce in τ < 1/H0, irrespective of IMF and kick

strength. This is perhaps not surprising, since NS-NS systems must gen-

erally be tightly bound to remain intact through the second supernova. For

NS-NS systems, we estimate the Galactic merger rate to range from ∼0.04–8

Myr−1, with a strong dependence on the severity of the natal kick. Given

161

a likely LIGO I detection radius of ∼ 20 Mpc for such systems, this would

imply a conservative detection rate of 0.01–3 ×10−3yr−1 (Phinney, 1991;

Kalogera & Lorimer, 2000), with a likely mean rate of ∼10−3 yr−1. These

estimates are an order of magnitude lower than those stated in Grishchuk

et al. (2000).

A more unexpected result was the relative frequency of BH-NS pairs

relative to bound NS systems. While far fewer BH-NS systems are formed,

their mass allows them to weather two supernovae more frequently than two

neutron stars. From an estimate of the BH-NS formation rate, we can say

something about the expected frequency of BH-PSR systems. For purposes

of discussion, we divide these systems into three categories, based on for-

mation mechanism. The first type results from the standard scenario: a

massive black hole forms first, with a regular short-lived pulsar at a later

epoch. The second possibility is that the black hole progenitor transfers

a substantial amount of matter on to the neutron star progenitor early in

the evolution of the system. This results in the neutron star forming first,

and allows the black hole progenitor to continue to spill matter through its

Roche lobe on to the slowing pulsar, thereby recycling it. The last possi-

bility is that the system from scenario two is disrupted by the black hole

formation, resulting in a (possibly recycled) pulsar and single black hole.

This channel is not relevant for our purposes, as it ceases to be a potential

LIGO source. The R6 rates for the remaining formation channels are shown

in tables 4.1 and 4.2. The BH-NS column covers all formation channels for

a BH-NS system, whereas the BH–PSR2 column considers only that sub-

set of BH-NS systems where a recycled pulsar is formed first, via channel

two, as described above. Surprisingly, of the systems that go on to form

a BH-NS pair, around 40% experience the reversal described in case two

162

above, where the initially more massive star forms a compact object last.

Only 0.5% of the BH-BH progenitor systems experience a similar reversal.

In the first case, an ordinary, short-lived (∼ 106 yr) pulsar is created. In

the latter, a fast, long-lived (∼ 109 yr) millisecond pulsar should often be

the result. It is likely that type II BH-PSR systems with recycled pulsars

would be observable as radio objects. The small predicted formation rate

of such objects, however, is consistent with having not yet been seen among

known pulsars. However, their formation rate, while 30–60 times smaller

than that of “type 1” BH-NS systems, should mean that they are consider-

ably more common than black holes with normal pulsar companions, being

longer-lived. Also, we note that the formation rate of “type 2” BH-PSR sys-

tems is more severely affected by kick intensity, as strong kicks may widen

the system enough to prevent mass transfer on to the neutron star, leaving

an ordinary BH-PSR system. We conclude that the galactic scale height

for such systems should be substantially smaller than that of ordinary BH-

NS and BH-PSR systems. Further details of the BH-PSR systems (including

a prediction of orbital distributions) will be deferred to a future work (Sipior

& Sigurdsson, in prep). Note finally that the chirp mass of a typical coa-

lescing BH-PSR system is roughly twice as large as a NS-NS binary. As dL

scales with M5/6chirp, this implies at least a five-fold increase in search volume.

Adjusting the estimated R6 rates for this implies that BH-NS coalescence

should be seen with substantially greater frequency than NS-NS binaries at

all kick intensities, with a conservative maximum of 7 × 10−3 LIGO I de-

tections per year for low kick strengths. A more likely “best bet” rate is on

the order of 2–3×10−3 yr−1, with a mix of high (σ = 450 km s−1) and low

(σ = 90 km s−1) kick velocities, with 60% of kicks drawn from the former,

the balance from the latter (as suggested by Arzoumanian et al., 2002; Pfahl

163

et al., 2002).

BH-BH systems are shown here to be far more common than either NS-

NS or BH-NS hybrids. Only a small fraction of these will merge in a Hubble

time, as the larger mass permits the system to remain bound at higher

separations. As well, the greater mass of BH-BH systems implies a more

gradual response to an increasing kick parameter. Indeed, the R6 rate for

bound BH-BH system formation remains high (more than thirty per Myr

in the Milky Way), even when kicks are permitted to reach 103 km s−1on

a 1.4 M� object. Figure 4.3 shows the distribution of chirp masses for all

BH-BH systems that coalesce in less than 10 Gyr. As can be seen, there is

a concentration of chirp masses around 4 M�, implying a twentyfive-fold in-

crease in search volume. Allowing for this, we anticipate a LIGO I detection

rate of 0.3–12×10−3 yr−1, with a likely rate of 3–4×10−3 yr−1, given the

two-component kick speed distribution described above. Figure 4.4 shows

the strong correlation between the final system velocity (a function of the

kick magnitude and component masses), and the time required for the sys-

tem to coalesce due to emitted gravitational wave energy. A clear dynamic

criterion for coalescence emerges, with slower systems rarely merging in a

Hubble time. This is essentially a selection effect, as the kick speed must be

of a magnitude comparable to the orbital speed of the system to have a dra-

matic effect on the merger rate. Relative to the orbital speed, a weak kick

will have no appreciable effect, while a strong kick will disrupt the system.

So, the kick speeds that bring about more rapid mergers are necessarily

tuned to the orbital speed of the system at the second supernova.

164

4.5 Discussion

We claim a “best guess” LIGO I detection rate of 3–4 ×10−3yr−1 for BH-

BH coalescence events, 2–3×10−3 yr−1 for BH-NS events, and ∼10−3 NS-

NS coalescence per year. LIGO II, with an anticipated order of magnitude

increase in sensitivity, should encompass roughly 103 times the search vol-

ume, with a proportional increase in event detection rates. Unless LIGO I is

quite lucky, it seems unlikely that mergers from this channel will be detected

until the advent of LIGO II in a few years. With LIGO II, we can antici-

pate an event rate of many per year. These are essentially consistent with

the most pessimistic detection rates calculated by Grishchuk et al. (2000).

There are significant differences between our results and those in Portegies

Zwart & Yungelson (1998), primarily regarding BH-BH coalescence, where

a negligible merger rate was found. This discrepancy is likely due to our

lower cutoff for black hole formation, where we adopt a value of 20 M�,

against the 40 M� cutoff adopted by the latter. While recent models of

Fryer (1999) have established a lower black hole mass cutoff, more work is

needed to resolve this area of contention. LIGO-measured coalescence rates

should provide a clearer resolution on this point.

It is instructive to compare our results with those obtained in two recent

population synthesis studies. Fryer et al. (1999) performed detailed synthesis

calculations in the context of black hole-accretion driven gamma ray bursts.

As a result, BH-BH binaries are not considered; however, BH-NS and NS-

NS systems are. For the Salpeter IMF, and a Gaussian kick distribution

peaked at 100 km s−1, FWHM of 50 km s−1(roughly corresponding to our

σ = 90 km s−1kicks), the R6 rate of BH-NS formation is identical (R6 =

16). We predict many more NS-NS (R6 of 11, as opposed to 4.2). This

165

discrepancy arises from the inclusion of hypercritical accretion in Fryer et al.

scenario I for NS-NS formation. The result is that all neutron stars that

pass through a common envelope phase become black holes, removing a

significant channel of NS-NS pair formation. At higher kick intensities, the

BH-NS formation rates remain in good agreement, whilst the NS-NS rates

become more disparate. This is likely because the two high speed kick

distributions are not the same, and the discrepancy affects BH-NS systems

less dramatically because of the larger mass involved.

Very recently, the paper of Belczynski et al. (2002) performed a simi-

lar comprehensive study, considering a wide variety of kick paradigms and

population synthesis models. Our anticipated LIGO I detection rates are

consistently an order of magnitude lower than those reported by the au-

thors for their “standard model”. Though the kick distribution chosen for

this standard model is more intense than in our own work (two Maxwellian

distributions, with σ = 175 km s−1and σ = 700 km s−1, with 80% of kicks

drawn from the former, and the balance from the latter distribution), the

mean neutron star mass is allowed to be much higher (up to 3 M�, allow-

ing more systems to remain bound, and shed gravitational radiation more

quickly. Thus, the overall effect is to enhance the anticipated NS-NS and

BH-NS merger rates. It should be noted that our calculated merger rates

fall within the range of merger rates calculated by Belczynski et al. when

all posited model assumptions are considered. The difference between our

results and the standard model of the authors for BH-BH systems is larger,

by roughly two orders of magnitude (though our results still fall within the

wider range resulting from considering all the models presented). Our model

assumptions are greatly discrepant at one point in particular; namely, the

assumed mass function of newly-formed black holes as a function of ZAMS

166

mass. Where we take a rough interpolation between model results presented

in Fryer (1999), the authors use a much more sophisticated relationship be-

tween the ZAMS mass and the initial mass of the resulting black hole. This

mass function tends to produce substantially more massive holes than those

generated from our interpolation, and we believe this to be the principal

cause of the discrepancy in merger rates for BH-BH binaries.

After the neutron star/black hole mass cutoff, the second pivotal assump-

tion concerns the distribution of natal kick speeds, and indeed, whether black

holes can receive kicks under any circumstances. The cases of Nova Sco 1994

and XTE J1118+480 show that our natal kick assumptions are plausible.

However, we suffer from a paucity of data concerning the frequency and

scaling (with respect to mass) of black hole kicks. There is mounting evi-

dence that neutron star kick distributions are bi-modal (Arzoumanian et al.,

2002), allowing many more NS-NS systems to survive and merge after the

second supernova. The greater mass of black holes means that uncertain-

ties in these distributions have less effect on the coalescence of BH-NS and

BH-BH systems, as can be seen in table 4.1. Coupling this fact with the

“residual” merger rate one gets when black holes are not allowed natal kicks

at all (cf. table 4.2), we argue that the effects of uncertainty in the natal kick

models will not affect the predicted R6 rates of BH-BH and BH-NS mergers

by more than factors of a few. Interestingly, the large number of BH-BH bi-

naries which remain bound suggests that another merger channel; namely,

a merger due to hardening resulting from external dynamical perturbations

(Sigurdsson & Hernquist, 1993). We do not quantify this effect here, but

note that the extent and duration of a star-formation episode could have a

notable effect on the rate at which such interactions occur.

Black holes experience natal kicks only when formation of the event hori-

167

zon is delayed, from fallback material and/or initial spin support. Therefore

it is reasonable to posit a correlation between natal kicks and a high ini-

tial spin for the nascent black hole. In a BH-BH system, the first hole is

gradually spun down by interaction with the stellar wind of its companion,

and will likely be a slow rotator even if it began with maximal spin. The

second hole will not experience this, and should retain its high spin. We

therefore predict that, for BH systems that experience natal kicks, LIGO

will see a slow rotating primary, with a (generally less massive) black hole

companion with near maximal spin. If the components do not experience

natal kicks, we would anticipate low spins all around, with the coalescence

rate primarily determined by the wind mass loss rate and the boundary cri-

terion for black hole formation. This spin signature is a directly testable

hypothesis—LIGO II should provide a large array of high-quality sources

to verify this prediction, and allow for careful testing of gravitational wave

phenomenology.

A similar spin correlation may be found in BH-PSR systems, with the

two categories described above having different anticipated signatures. The

type I systems (black hole first, followed by standard pulsar) should have

two slow rotators, as no pulsar recycling is possible. Type II systems (neu-

tron star forms first, is spun up by black hole progenitor, black hole forms)

should have at least one rapid rotator, and possibly two, if the black hole

is spun up during its formation, as above. These spin correlations may be

demonstrated with high-S/N data from LIGO II. More will be said about

the spin signatures of BH-PSR systems in an upcoming paper (Sipior & Sig-

urdsson, in prep), in addition to a study of the orbital parameters of such

systems, and the ratio of BH-PSR to NS-PSR systems, which is relevant for

new tests of General Relativity, should these systems be detected.

168


α σ (km s−1) BH-BH τ < τh BH-NS τ < τh NS-NS τ < τh BH-PSR2 τ < τh

-2.0 90 80 1.6 26 8.2 11 8.4 0.62 0.44-2.0 190 68 0.59 5.9 2.5 1.7 1.5 0.11 0.09-2.0 450 62 0.11 0.38 0.2 0.09 0.06 0.0 0.0-2.35 90 48 1.2 16 5.5 11 7.9 0.47 0.37-2.35 190 41 0.55 4.0 1.7 1.6 1.3 0.07 0.07-2.35 450 35 0.04 0.2 0.09 0.07 0.05 0.0 0.0

Note. — R6 formation and merger rates for BH-BH , BH-NS , NS-NS and BH-PSR systems. α is the index of the IMF power-law, σ provides the dispersion ofthe Maxwellian distribution of kick speeds, and the kick cutoff gives the maximumpermitted kick speed (acting on a 1.4 M� neutron star). Black hole kicks arepermitted below a ZAMS mass of 40 M�, and are scaled to the compact objectmass. The BH-PSR column refers to a subset of the BH-NS systems, where thepulsar is recycled by mass transfer from the black hole progenitor star. The masstransfer should in many cases spin-up the pulsar to millisecond-order periods.

Model uncertainties, especially involving the details of black hole forma-

tion, still dominate the estimates of coalescence rates to be seen by LIGO.

Nonetheless, it is becoming clear that BH-BH mergers form a significant

channel, comparable to the rates anticipated for NS-NS systems. While

LIGO I detection rates appear too small to catch any merger events from

this channel, we may still be lucky enough (at the level of a few percent) to

serendipitously catch events from this channel (especially given incremental

upgrades in the sensitivity of LIGO I throughout its operational lifetime).

LIGO II should easily see a large number of these events every year.

169


α σ (km s−1) BH-BH τ < τh BH-NS τ < τh NS-NS τ < τh BH-PSR2 τ < τh

-2.0 90 250 0.81 31 9.0 10 7.8 0.63 0.53-2.0 190 240 0.62 12 5.5 1.8 1.5 0.08 0.06-2.0 450 240 0.77 2.0 1.1 0.04 0.03 0.0 0.0-2.35 90 170 0.55 21 6.5 11 8.1 0.55 0.47-2.35 190 170 0.71 7.8 3.4 1.7 1.4 0.07 0.07-2.35 450 170 0.32 1.4 0.83 0.04 0.04 0.0 0.0

Note. — R6 formation and merger rates. Identical to table 4.1, save that blackhole kicks are not permitted under any circumstances. This clearly elevates thenumber of BH-BH and BH-NS systems seen. Interestingly, the application of natalkicks increases the fractional merger rate in BH-BH systems, though the largenumber of BH-BH systems which remain bound when kicks are not present meansthat the number of merging systems is still comparable, especially for the mostenergetic kick parameters.

170

Figure 4.1 A plot of the semi-major axis versus eccentricity for all BH-BH (left) and BH-NS (right) systems generated in a single run of 106 bi-naries. Triangles designate systems which will coalesce in less than 10 Gyr,whilst circles are systems stable against gravitational coalescence. For theBH-BH systems, a clear distinction between merging and stable binaries isevident. The bulk of those BH-NS binaries which remain bound after thesecond supernova also merge within a Hubble time. The IMF index used isα = 2.35, the Salpeter IMF. The dispersion in the Maxwellian kick appliedat each supernova is σ = 90 km s−1, with the kick maximum Kmax = 500km s−1. All kick speeds apply to a 1.4 M� neutron star; the actual ∆v isfound by scaling the kick linearly with the compact object mass.

171

Figure 4.2 Two histograms displaying mass distributions for BH-BH pairsthat remain bound after the second supernova. The parameters of the runshown are an IMF parameter α = 2.35, kick parameters σ = 90 km s−1andKmax = 500 km s−1. The left histogram shows that black hole masses clumpin two locations; one around 5 M�, and the other at 35 M�. We associatethe lower-mass BHs with 20–40 M� ZAMS progenitors, which lose much oftheir mass through a supernova (and hence experience a natal kick). Thehigh-mass set came from more massive progenitors, and collapsed to a blackhole without a supernova or the resulting kick.

172

Figure 4.3 Shows the distribution of chirp masses for all BH-BH systems that

will eventually merge. The gravitational wave amplitude scales as M5/6chirp,

so this parallels the distribution of signal strengths one could expect from aBH-BH population.

173

Figure 4.4 A plot of merger time versus the final velocity of the BH-BH bi-naries (left), and BH-NS binaries (right). The natal kick parameters wereσ = 90 km s−1, Kmax = 500 km s−1(upper panels), and σ = 190 km s−1,Kmax = 500 km s−1(lower panels). Of the systems that remained bound af-ter the second supernova, there is a clear correlation between increasing sys-tem speed and a shortening of the gravitational radiation merger timescale,from kick-induced high eccentricity orbits, with enhanced GW radiation atperiastron passage.

174

Acknowledgments: Both authors would like to profusely thank Onno

Pols and Joshua Bloom for access to the code base that we built upon here.

Steinn Sigurdsson would like to acknowledge the support of the Center for

Gravitational Wave Physics, and the hospitality of the Aspen Center for

Physics. The Center for Gravitational Wave Physics is supported by the

NSF under co-operative agreement PHY 01-14375. Michael Sipior is sup-

ported in part by NASA through grant GO01152 A,B from the Smithsonian

Astrophysical Observatory. He would like to acknowledge travel support

kindly provided by the Zaccheus Daniel Foundation.

175

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Michael Shawn Sipior

Refereed Publications

• Feigelson, E. D., Ho, L., Sipior, M. S., Ptak, A. 2002, “Chandra Surveyof Nearby Galaxies with Low-Luminosity Active Nuclei”, in prepara-tion

• Sipior, M. S., Sigurdsson, S., 2002, “Nova Sco and coalescing low massblack hole binaries as LIGO sources”, ApJ, accepted

• Ciardullo, R., Bond, H. E., Sipior, M. S., Fullton, L. K., Zhang, C.-Y.,Schaefer, K. G. 1999, “Hubble Space Telescope Survey for ResolvedCompanions of Planetary Nebula Nuclei”, A. J., 118, 488

• Andersson, N., Kokkotas, K. D., Laguna, P., Papadopoulos, P., Si-pior, M. S. 1999, “Construction of initial data for perturbations ofrelativistic stars”, Phys. Rev. D, 60, 124004

Presentations

• Sipior, M. S., Eracleous, M., Sigurdsson, S. “ ’Till never do us part:an XRBs fatal dance, from X-rays to gravitational waves”, AmericanAstronomical Society 199th Meeting, January 2002, Washington, D. C.(oral)

• Sipior, M. S., Feigelson, E., Ho, L., Ptak, A., Garmire, G. “X-rayproperties of low-luminosity AGN in nearby galaxies”, New Visions ofthe X-Ray Universe in the XMM-Newton and Chandra Era, November2001, Noordwijk, the Netherlands (poster)

• Sipior, M. S., Eracleous, M. “Simulating X-ray emission from starburstgalaxies”, HEAD 2000, November 2000, Honolulu, Hawaii (poster)

Documents

POPULATION SYNTHESIS AND ITS CONNECTION TO …