Binary Neutron Star MergersBinary Neutron Star MergersGravitational-Wave SourcesGravitational-Wave Sources

andand

Gamma-Ray BurstsGamma-Ray Bursts

Vicky KalogeraDept. of Physics & Astronomy

Northwestern University

Binary Compact ObjectsBinary Compact Objects

• Double Neutron Stars: the sampleDouble Neutron Stars: the sample• Two new DNS binaries! Two new DNS binaries!

• Empirical DNS rates: updatesEmpirical DNS rates: updates

• Theoretical Merger RatesTheoretical Merger Rates• Constraining population synthesesConstraining population syntheses

• Expectations for LIGO - when???Expectations for LIGO - when???

• NS mergers and short GRBs?NS mergers and short GRBs?• Merger delays and redshift distributionsMerger delays and redshift distributions

In this talk:

DNS pulsars: Hulse-Taylor DNS pulsars: Hulse-Taylor

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pulsar as a`lighthouse'

GWorbitaldecay

PSR B1913+16

Weisberg &Taylor 03

Indirect evidence forIndirect evidence forGravitational WavesGravitational Waves

DirectDirect detection? detection?

LIGO GEO VirgoTAMA

AIGO

Coincidence: detection confidence source localization

signal polarizationGW Interferometers: global network

Double Neutron Star (DNS) SystemsDouble Neutron Star (DNS) Systems

one of the prime targets of large-scale GW detectors

(e.g. LIGO, VIRGO, GEO, TAMA)

Galactic merger rate of DNS systems

Event rate estimation

for DNS inspiral search

Strong sources of gravitational waves (waveforms are well understood)

Development and designing of GW detectors

Understanding of the astrophysics of compact objects

DNS merger rate calculationsDNS merger rate calculations

Empirical method: based on radio pulsar properties and observational

selection effects of pulsar surveys (Narayan et al. (1991), Phinney (1991), Curran & Lorimer (1993),

VK, Narayan et al. (2001), Kim, VK et al. (2003), VK, Kim et al. (2004))

Theoretical method:

based on our understanding of binary formation and

evolution (population synthesis models) (Portegies Zwart & Yungelson (1998), Nelemans et al. (2001),

Belczynski, VK, & Bulik (2002), O’Shaughnessy, VK et al. (2005)

and many more)

DNS pulsars: the observed sampleDNS pulsars: the observed sample

PSR name Ps (ms) Pb (hr) e life (Gyr)

B1913+16 59.03 7.752 0.617 0.365

B1534+12 37.90 10.1 0.274 2.7

J0737-3039A 22.70 2.45 0.088 0.185

J1756-2251 28.46 7.67 0.181 2.0

J1906+0748 144.07 3.98 0.085 0.083

Burgay et al. 2003 Parkes double pulsarFaulkner et al. 2004 Parkes MB survey, acceleration searchLorimer et al. 2005 Arecibo ALFA survey

Merger rate Merger rate RR

Q: How many pulsars “similar” to each of the known DNS binaries exist in our Galaxy?

Lifetime of a systemNumber of sources

x correction factorR =beaming

Goal : Calculate the probability

distribution of the Galactic DNS

merger rates P(R)

Method - Modeling & Simulation (Kim et al. 2003, ApJ,

584, 985 )

assume luminosity & spatial distribution functions

adapt spin & orbital periods from each observed PSR

1. Model pulsar sub-populations

Selection effects for faint pulsars are taken into account.

Method - Modeling & Simulation (Kim et al. 2003, ApJ,

584, 985 )

count the number of pulsars observed (Nobs)

populate a model galaxy with Npop PSRs (same Ps & Porb)

Nobs follows the Poisson distribution,P(Nobs; <Nobs>)

carefully model thresholds of PSR surveys

Earth

2. Simulate large-scale pulsar surveys

For an each observed system i,

Pi(R) = Ci2R exp(-CiR)

where Ci =

Combine the three individual PDFs and calculate P(Rgal)

Statistical Analysis

Individual probability density function (PDF)

<Nobs> life Npop fb i

Probability density function of Rgal

P(Rgal )

Lifetime ~ 185 Myr

NJ0737 ~ 1600 (most abundant)

Lifetime ~ 80 Myr (shortest)

NJ1906 ~ 300

The revised DNS merger rate

~83 +209

-66 ~13+40

-11

raterateper Myrper Myr

Reference model:

Rpeak (revised) Rpeak (previous)

~ 6-7

Increase rate factor due to PSR J0737-3039:

B1913+B1534+J0737 B1913+B1534

(at 95% CL)

Rpeak (revised) Rpeak (previous)

~1.5-1.7

Increase rate factor due to PSR J1906+0746:

B1913+B1534+J0737+J1906

~120

Detection rate of DNS inspirals for LIGO

Rdet (adv. LIGO) ~ 350 events per

yr

Rdet (ini. LIGO) ~ 1 event per 20 yr

The most probable DNS inspiral detection rates for LIGO

Rdet (adv. LIGO) ~ 15 – 850 events

per yr

Rdet (ini. LIGO) ~ 1 event per 5 – 250 yr

All models:

Reference model:

Implications of J1756-2251

Discovered by the Parkes Multibeam Pulsar Survey with

the acceleration search technique.

Standard Fourier techniques failed to detect J1756-2251.

Contribution of J1756-2251 to the Galactic DNS merger rate.

No significant change in the total rate.

Rpeak (4 PSRs + J1756) Rpeak (4 PSRs)

~ 1.04

J1756-2251: Another merging DNS in the Galactic disk

Similar to the Hulse-Taylor system

(Faulkner et al. 2005)

Global P(Rgal): motivation

f(L) L-p, where Lmin is a cut-off luminosity and p is a power index.

Lmin (mJy kpc2)

p

Rpeak (Myr-1)

Radio pulsar luminosity function

Global P(Rgal): motivation

, where Lmin is a cut-off luminosity and p is a power index.

Radio pulsar luminosity function

Global probability density function Pglobal(R)

Pglobal(R) P(R; Lmin,p) f(Lmin)

g(p)intrinsic functions for Lmin and p

P(R) P(R; Lmin,p)

Rpeak is strongly dependent on Lmin & p.

f(L) L-p

Global P(Rgal) and SNe rate constraints

Probability Density

Galactic DNS

merger rate (Myr-1)

SNU5

SNL5

SN Ib/c = 600-1600 Myr-1 (Cappellaro, Evans, &

Turatto 1999)

SNL5= SN (lower)x0.05 = 30 Myr-1

SNU5= SN (upper)x0.05 = 80 Myr -1

Suppose, ~5% of Ib/c SNe are

involved in the DNS formation.

The empirical SNe rate

Compact Binary Inspiral Rates: Compact Binary Inspiral Rates: What about Black Hole Binaries?What about Black Hole Binaries?

BH-NS binaries could in principle be detected as binary pulsars, BUT…

the majority of NS in BH-NS are expected to be young short-lived hard-to-detect harder to detect than NS-NS by >~10-100 !

So farSo far, inspiral rate predictionsrate predictions only from population calculations from population calculations with uncertainties of ~ 3 orders of mag

We can use NS-NS empirical rates as constraintson population synthesis models

Binary Compact Objects: FormationBinary Compact Objects: FormationMassive primordial binary

Mass-transfer #1: hydrostatically and thermally Stable,

but Non-Conservative: mass and A.M. loss

Supernova and NS Formation #1: Mass Loss and Natal Kick

High-mass X-ray Binary: NS Accretion from Massive Companion’s Stellar Wind

Mass-transfer #3: Dynamically Unstable

Mass-tranfer #4: Possible and Stable

Supernova and NS Formation #2: Mass Loss and Natal Kick

Double Neutron-Star Formed!

Population Synthesis Parameter StudyPopulation Synthesis Parameter Study

• Large parameter space

• Most important parameters: 7

• 7D parameter study: computationally demanding

• Acceleration of computations: • Use of Genetic Algorithms

Rate Fits vs. StarTrack calculations: 7DRate Fits vs. StarTrack calculations: 7D

BH-BH

NS-NS

O’Shaughnessy et al. 2004

Fit accuracy is comparableor usually smaller thanthe Poisson errors of StarTrack Monte Carlo rates

(Belczynski et al. 2005)

Black Hole Binary Inspiral: Event RatesBlack Hole Binary Inspiral: Event Rates

From Population Synthesis Modeling:

- 8 -7 -6 -5 -4 -3 -2

0.2

0.4

0.6

0.8

1

log ( events per yr )

PDF

BH-BH

BH-NS

NS-NS

Empirical Constraints imposed on population synthesis rate predictions

Merging NS-NS Wide NS-NS

O’Shaughnessy et al. 2006

log(rate) log(rate)

Four More Rate Constraints: O’Shaughnessy et al. 2006

SN Ib/c

SN II

mergingPSR-WD

eccentricPSR-WD

BH-BH BH-NS

NS-NS

Constrained vs. Unconstrained Rate Predictions from StarTrack:

O’Shaughnessy et al. 2006

BH-BHBH-NS

NS-NS

Short GRBs and NS-NS / BH-NS mergers

Short GRB afterglows reveal association with both elliptical and star-forming galaxies:

Progenitors must exist in both OLD and YOUNG stellar populations!

NS-NS and BH-NS mergers: prime candidates

What is the event (GRB and mergers) rate vs. redshift ?

What is the spatial distribution w/r to the host galaxies ?

What is the event (GRB and mergers) rate vs. redshift ?

Star-formation rate vs. redshift Porciani & Madau

Time-Delay between formation and mergers

Formation efficiency (# mergers / unit SF mass)

Relative Contribution of spirals and elliptical galaxies

GRB Luminosity function unknown …

We need to know:

Time-Delay between formation and mergers

NS-NS

SPIRAL GALAXIES

BH-NS

log(Merger Time / Myr)

BH-NS

ELLIPTICAL GALAXIES

log(Merger Time / Myr)

NS-NS

BH-NS

BelczynskiO’Shaughnessy

Compact Binary Formation efficiencies

What is the number of binaries formed per unit stellar mass?SPIRAL GALAXIES ELLIPTICAL GALAXIES

NS-NS NS-NS

BH-NS BH-NS

log(efficiency * Msun) log(efficiency * Msun)

BelczynskiO’Shaughnessy

Merger Rate vs. redshift

If ellipticals contributed 20% of the SF mass in the past until about redshift of 2

Comparison with observed redshift distribution requires a luminosity model … ?

Binary Center-of-mass velocities and Lifetimes: Where do they merge ?

SPIRAL GALAXIES ELLIPTICAL GALAXIES

NS-NS NS-NS

BH-NS BH-NS

1kpc 10 kpc

log(merger time / Myr)log(merger time / Myr)

log(Vcm / km/s)

log(Vcm / km/s)

BelczynskiO’Shaughnessy