Binary population synthesis implications for gravitational wave sources

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Binary population synthesis implications for
gravitational wave sources

• Tomasz Bulik
• CAMK

with Dorota Gondek-Rosinska Krzys Belczynski
Bronek Rudak
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Questions

• What are the expected rates?
• How uncertain the rates are?
• What are the properties of the sources?
• Are the methods credible?

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Binary compact objects

• Only few coalescing NSNS known
• Hulse-Taylor PSR191316, t300 Myrs
• B153412, t2700 Myrs
• B212711C, t220 Myrs
• Binary Pulsar J0737 3039, t80 Myrs
• BHNS? BHBH?

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Rate estimate

• Method I observations
• Use real data
• Selection effects
• Very low or even zero statistics
• Large uncertainty

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RATES METHOD 1

• Find the galactic density of coalescing sources
  from the model
• Obtain galactic merger rate
• Extrapolate 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
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Rate estimate

• Method II binary population synthesis
• Binary evolution
• Formation of NS i BH binaries
• Dependence on the parametrization
• Unknowns in the stellar evolution

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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

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Binary evolution

• Mass transfers
• Rejuvenation
• Supernovae and orbits
• Masses of BH i NS
• Orbit changes - circularization
• Parameter study many models

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Simulations

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

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

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Evolutionary times
Short lived NSNS are not observable as pulsars
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Chirp mass distribution
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Detection

• Inspiral phase
• Amplitude and frequency depend on chirp mass

Signal to noise
Sampling volume
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From simulations to rates

• Requirements
• model of the detector, signal to noise, sampling
  volume
• normalisation

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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

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Assumptions
Star formation rate What was it at large
z? Does it correspond to the local SFR a few
Gyrs ago?
Cosmological model (0.3, 0.7) and H65 km/s/Mpc
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Initial mass function
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
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Results
is observed
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Uncertainty in rate

• Star formation history
• IMF shape and range
• Stellar evolution model
• Non-stationary noise

A factor of 10
Together a factor of at least 30
A factor of 10
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RATES METHOD 1

• Find the galactic density of coalescing sources
  from the model
• Obtain galactic merger rate
• Extrapolate 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
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METHOD 12

• 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

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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

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This brings the expected VIRGO rate to 1-60 per
year!
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Such an estimate leans on a single
object..... PSR J0737-3039
Seeing this
Imagine
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THIS !
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Expected object types

• NSNS
• BHNS
• BHBH

Population of observed objects in the mass vs
mass ratio space
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BHBH binaries
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NSNS binaries
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BHNS binaries
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SHOULD YOU BELIEVE IN ANY OF THIS?
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Observed masses of pulsars
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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
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The intrinsic mass ratio distribution burst
star formation, all stars contained in a box.
Tgt 100 Myrs
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Simulated radio pulsars Observability
proportional to lifetime. Constant SFR. Assume
that one sees objects in a volume limited sample,
eg. Galaxy. Sample is dominated by long lived
objects. Typical mass ratio shifted upwards.
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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
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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.

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What next?

• Binaries in globular clusters, different
  formation channels, three body interactions
• Population 3 binaries
• ?

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Resonant detectors
Requirements mass, ccooling, specified
frequency bands, strongly directional AURIGA,
EXPLORER, NAUTILUS
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First detection attempts
J. Weber the 1960-ies
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Sensitivity
Narrow bands corresponding to resonant
frequencies of the bar
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Interferometers
Michelsona-Morley design
Noise seismic, therma, quantum (shot)
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Czulosc LIGO
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Gravitational wave sources
Requirements mass asymmetry, size Frequencies
10 to 1000Hz
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Gravitational waves

• Predicted by the General Relativity Theory
• Binary pulsars
• Indirect observations of gravitational waves
• Weak field approximation

PSR 191316
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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 LISA 0.001 0.1 Hz
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Astronomical objects

• Pulsars
• Supernovae
• Binary coalescences

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Interferometers
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Parameter D
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Cosmological parameters
Hubble constant
Omega
B
B
A
A
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Non stationary noise
A
B
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Stellar evolution
A
B
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Chirp mass versus evolutionary time
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Three phases of coalescence

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

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Slow tightening
Star on ZAMS
Detection
Coalescence
A compact object binary is formed
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Rate
Formation at z3
Coalescence rate at z1
Observed rate
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Rates are very uncertain.Can observations in GW
be useful for astronomy?
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• Consider not the rates but the ratios of the
  rates!
• BHBH to NSNS etc.
• Distribution of observed chirp masses
• Weakly depends on normalisation.

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Distribution of observed chirp mass

• Simple toy model
• Constant SFR
• Euclidean space
• BHBH are dominant!

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Dependence

• On cosmological model
• On star formation rate
• On stellar binary evolution

We can use the Kolmogorov-Smirnov test to
compare different distributions Parameter D
cumulative distribution distance. Two example
detectors A 100Mpc i B 1Gpc for NSNS
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Stellar evolution