Binary population synthesis implications for gravitational wave

sources

Tomasz BulikCAMKwith

Dorota Gondek-Rosińska

Krzyś Belczyński

Bronek Rudak

Questions

What are the expected rates?

How uncertain the rates are?

What are the properties of the sources?

Are the methods credible?

Binary compact objects

Only few coalescing NSNS known:

Hulse-Taylor PSR1913+16, t=300 Myrs

B1534+12, t=2700 Myrs

B2127+11C, t=220 Myrs

Binary Pulsar J0737 – 3039, t=80 Myrs

BHNS? BHBH?

Rate estimate

Method I: observations

Use real data

Selection effects

Very low or even zero statistics

Large uncertainty

V

N1

RATES – METHOD 1

Find the galactic density of coalescing sources from the modelObtain galactic merger rateExtrapolate from the Galaxy further out:

Scale by: mass density? galaxy density? blue luminosity? Supernovae rate density?

The result is dominated by a single object:J0737-3039!!

Kalogera etal 2004

Rate estimate

Method II: binary population synthesis

Binary evolution

Formation of NS i BH binaries

Dependence on the parametrization

Unknowns in the stellar evolution

Population synthesis -single stars

● Numerical models● Helium stars● Evolutionary times● Radii● Internal structure: mass and radius of the core● Convection● Winds● NS i BH formation, supernovae

Binary evolution

Mass transfers

Rejuvenation

Supernovae and orbits

Masses of BH i NS

Orbit changes - circularization

Parameter study: many models

Simulations

Initial masses Mass ratios Orbits A chosen parameter set Typically we evolve binaries106

An example ofa binary leading to formation of a coalescing binary BH-BH:

Parameter study

Initial conditions: m, q, a ,e

Mass transfers: mass loss, ang momentum loss and mass transfer

Compact object masses

Supernovae explosions: kick velocities

Metallicity , winds

Standard model

Evolutionary times

Short lived NSNSare not observable as pulsars

Chirp mass distribution

Detection

Inspiral phase:

Amplitude and frequency depend on chirp mass:

Signal to noise:

5/121

5/321 )()( mmmmM chirp

RNS M chirp

1)/(

6/5

Sampling volume: 2/5

chirpMV

From simulations to rates

Requirements:

1. model of the detector, signal to noise, sampling volume

2. normalisation

Simulation to rates: normalisation

Galactic supernova rate, Galactic blue luminosity + blue luminosity density in the local Universe:

Coalescence rate ~ blue luminosity

Star formation rate history + initial mass function + evolutionary times:

Calculate the coalescence rate as a function of z

Star formation rate:

What was it at large z?

Does it correspond to the localSFR a few Gyrs ago?

Cosmological model (0.3, 0.7) and H=65 km/s/Mpc

Assumptions:

Initial mass function

sf

MM )(

avM Needed to convert from SFR mass to number of stars formed

We do not simulate all the stars only a small fraction that may produce compact object binaries

Results

is observed

chirpMz)1(

Uncertainty in rate

Star formation history

IMF – shape and range

Stellar evolution model

Non-stationary noise

Together a factor of at least 30

A factor of 10

A factor of 10

RATES – METHOD 1

Find the galactic density of coalescing sources from the modelObtain galactic merger rateExtrapolate from the Galaxy further out:

Scale by: mass density? galaxy density? blue luminosity? Supernovae rate density?

The result is dominated by a single object:J0737-3039!!

Kalogera etal 2004

METHOD 1+2

Population synthesis predicts ratios

What types of objects were used for Method 1?

Long lived NSNS binaries

Observed NSNS population dominated by the short lived objects

Observed objects dominated by BHBH

Number of “observed” binaries ________________________________ = 200 (from 10 to 1000) Number of “observed” long lived NSNS

● BHBH – have higher chirp mass

● BHBH have longer coalescing times

This brings the expected VIRGO rate to 1-60 per year!

Such an estimate leans on a single object.....

PSR J0737-3039

Seeing this :Imagine

THIS !

Expected object types

● NSNS● BHNS● BHBH

Population of observed objects in the mass vs mass ratio space

BHBH binaries

NSNS binaries

BHNS binaries

SHOULD YOU BELIEVE IN ANY OF

THIS?

Observed masses of pulsars

The initial-final mass relation depends on the estimate of the mass of the core, and on numerical simulations of supernovae explosions.

Some uncertainty may cancel out if one considers mass ratios not masses themselves

The intrinsic mass ratio distribution: burst star formation, all stars contained in a box.

T> 100 Myrs

Simulated radio pulsars:Observability proportional to lifetime.

Constant SFR.

Assume that one sees objects in avolume limited sample, eg. Galaxy.

Sample is dominated by long lived objects.

Typical mass ratio shifted upwards.

Gravitational waves:

Constant SFR.

A flux limited sample.

Low mass ratio objects

have larger chirp masses.

Long libed pulsars are a small fraction of all systems

Summary

Uncertainty of rates is huge

First object: BHBH with similar masses

NSNS binaries –less than 5-10%

Important to consider no equal mass neutron star binaries.

What next?

● Binaries in globular clusters, different formation channels, three body interactions

● Population 3 binaries● ?

Resonant detectors

Requirements: mass, ccooling, specified frequency bands, strongly directionalAURIGA, EXPLORER, NAUTILUS

First detection attempts

J. Weber – the 1960-ies

r 10 16cm

Sensitivity

Narrow bands corresponding to resonant frequencies of the bar

Interferometers

Michelsona-Morley design

Noise: seismic, therma, quantum (shot)

Czułość LIGO

Gravitational wave sources

Requirements:mass asymmetry, size

Frequencies: 10 to 1000Hz

Dh..

M

MsunHzf 2200

Gravitational waves

Predicted by the General Relativity Theory

Binary pulsars:

Indirect observations of gravitational waves Weak field approximation

PSR 1913+16

Present and future detectors

Resonant: bars and spheres

Typical frequencies:around 1kHz, but in a narrow band

Interferometric: LIGO, VIRGO, TAMA300, GEO600

Typical frequencies:50 – 5000 Hz – wide bands

LISA0.001 – 0.1 Hz

Astronomical objects

Pulsars

Supernovae

Binary coalescences

Interferometers

Parameter D

2

4

DN

Cosmological parametersOmega Hubble constant

A

A

BB

Non stationary noise

A

B

Stellar evolutionA: B:

Chirp mass versus evolutionary time

Three phases of coalescence

“inspiral” - until the marginally stable orbit “merger” - unitl formation of horizon “ringdown” - black hole rotation and oscillations

Detection

Star on ZAMS

A compact object binary is formed

Slow tightening

Coalescence

z1z2z3 0z

RateFormation at z3:

Coalescence rate at z1

Observed rate:

)()()(),,( ichirpi

chirpav

schirp ttMM

NM

fzSFRtzMF

)'),',(,('),( ttzzMFdtzMf fchirpchirp

z

dz

dz

dVzMfR

chirpMV

chirp 1

),(4)(

Rates are very uncertain.

Can observations in GW be useful for astronomy?

Consider not the rates but the ratios of the rates!

•BHBH to NSNS etc.

•Distribution of observed chirp masses

Weakly depends on normalisation.

Distribution of observed chirp mass

Simple toy model:

●Constant SFR

●Euclidean space

BHBH are dominant!

Dependence:

On cosmological model

On star formation rate

On stellar binary evolution

We can use the Kolmogorov-Smirnov test to comparedifferent distributionsParameter D – cumulative distribution distance.

Two example detectors: A: 100Mpc i B: 1Gpc for NSNS

Stellar evolution