Transcript Population synthesis view of gravitational waves - Astro-PF

Binary population synthesis
implications for gravitational wave
sources
with
Dorota Gondek-Rosińska
Krzyś Belczyński
Bronek Rudak
Tomasz Bulik
CAMK
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
1
N 
V
Use real data
Selection effects
Very low or even zero statistics
Large uncertainty
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
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
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 106 binaries
An example of
a 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 NSNS
are not observable as
pulsars
Chirp mass distribution
Detection
Inspiral phase:
Amplitude and frequency depend on chirp mass:
M
 (m1m2 ) (m1  m2 )
3/ 5
chirp
Signal to noise:
1
( S / N )  M chirp
R
5/ 6
Sampling volume:
V M
5/ 2
chirp
1/ 5
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
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 H=65 km/s/Mpc
Initial mass function
(M )  M
M av
fs

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
(1  z) M chirp
is observed
Uncertainty in rate
Star formation historyA factor of 10
IMF – shape and range
Together a factor of at least 30
Stellar evolution model
A factor of 10
Non-stationary noise
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
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
________________________________ =
Number of “observed” long lived NSNS
●
BHBH – have higher chirp mass
●
BHBH have longer coalescing times
200 (from 10 to 1000)
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 a
volume 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 directional
AURIGA, EXPLORER, NAUTILUS
First detection attempts
r 10
16
cm
J. Weber – the 1960-ies
Sensitivity
Narrow bands
corresponding to resonant
frequencies of the bar
Interferometers
Michelsona-Morley design
Noise: seismic, therma, quantum (shot)
Czułość LIGO
Gravitational wave sources
..
hD
Requirements:
mass asymmetry, size
Frequencies: 10 to 1000Hz
Msun
f  2200 Hz
M
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
LISA
0.001 – 0.1 Hz
Astronomical objects
Pulsars
Supernovae
Binary coalescences
Interferometers
Parameter D
4
N 2
D
Cosmological parameters
Hubble constant
Omega
B
B
A
A
Non stationary noise
A
B
Stellar evolution
A:
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
Slow
tightening
Star on
ZAMS
z3
z2
z 0
z1
Detection
A compact
object binary
is formed
Coalescence
Rate
Formation at z3:
fs
F ( M chirp , z , t )  SFR( z )
 ( M chirp  M i chirp ) (t  t i )
NM av
Coalescence rate at z1
f ( M chirp , z )   dt ' F (M chirp , z f ( z , t ' ), t ' )
Observed rate:
R  4

V ( M chirp )
dV dz
f ( M chirp , z )
dz 1  z
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 compare
different distributions
Parameter D – cumulative distribution distance.
Two example detectors: A: 100Mpc i B: 1Gpc for NSNS
Stellar
evolution