Binary population synthesis implications for gravitational wave sources
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Transcript of Binary population synthesis implications for gravitational wave sources
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