1. Center for Gravitational Wave Physics Penn State University
Stellar Populations and Gravitational Wave Observations Vicky Kalogera Northwestern University
Center for
Gravitational Wave Physics
Penn State University
November 6 – 8, 2003

2. Stellar Populations and Gravitational Wave Observations
Stellar Sources
Binary Compact Objects
inspiral/burst signal
or continuous waves
single sources or background
Pulsar Populations
inspiral or continuous waves
binary or isolated
Compact Object Formation
burst or background signal
Stellar Compact Objects
Captured by SMBH
Physical constraints
Event Rates
Compact Object Masses
Space distribution
Compact Object Spins
NS EOS

3. Stellar Populations and Gravitational Wave Observations
Types of physical constraints and statistical methods
used for their derivation will depend on whether
GW observations provide us with:
upper limits on rates
detections of a few events
detection of large event samples
detection of confusion -limited foregrounds

4. Binary Compact Object Inspiral
Event Rates
Model Rate Predictions
GW Observations
Upper limits can help us
exclude models
Even just a few detections
can give us tighter constraints
population
synthesis
binary PSR
modeling
constraints
Strength of constraints
depends on
> rate accuracy
> sensitivity of predictions on
model uncertainties
(e.g., WD-WD will benefit the least)
stellar
evolution
(stellar winds,
mass transfer,
SN kicks)
PSR
properties
(luminosity
function)

5. Constraints on binary evolution models
For example:
Dependence of predicted rates on
NS kick magnitudes:
In practice need to
obtain constraints
in many dimensions
depending on the
sensitivity of models
on various input
assumptions
from Belczynski,
VK, & Bulik 2002

6. X Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates 3
Use of observed sample and models for PSR survey selection effects:
estimates of total NS- NS number combined with lifetime estimates
(Narayan et al. '91; Phinney '91)
Dominant sources of rate estimate uncertainties identified: X 3
(VK, Narayan, Spergel, Taylor '01)
small - number observed sample (2 NS - NS in Galactic field)
PSR population dominated by faint objects
Rates uncertain by more than ~100

7. It is possible to assign statistical significance
Radio Pulsars in
NS-NS binaries
NS-NS
Merger
Rate Estimates
(Kim, VK, Lorimer 2002)
It is possible to assign statistical significance
to NS-NS rate estimates
with Monte Carlo simulations
Bayesian analysis used to derive the
probability density of NS-NS inspiral rate

8. Probability Distribution of NS-NS Inspiral Rate
Choose PSR space & luminosity distribution
power-law constrained from radio pulsar obs.
Populate Galaxy with Ntot ‘‘ like’’ pulsars
same pulsar period,
pulse profile,
orbital period
Simulate PSR survey detection and produce lots of
observed samples for a given Ntot
Distribution of Nobs for a given Ntot : it is Poisson
Calculate P ( 1; Ntot )
Use Bayes’ theorem to calculate P(Ntot) --> P(Ntot/t x fb)
Ntot/t x fb = rate
Repeat for each of the other two known NS-NS binaries

9. Current Rate Predictions
Burgay et al. 2003
VK et al. 2003
(Nature embargo)
new relativistic NS-NS has been discovered!
3 NS-NS : a factor of 6-7 rate increase
Initial LIGO Adv. LIGO
per 1000 yr per yr
ref:
peak
95%
opt:
peak
95%

10. Dependence of predicted NS-NS rates on
PSR luminosity function: f(L) ~ L-p for L > Lmin
Joint constraints
on luminosity-function
parameters Lmin and p
can be derived
from VK, Kim, Lorimer,
Burgay, et al. 2003

11. Binary Compact Object Inspiral
Mass measurements
> measurement of relative inspiral rates
> mass distribution: model fitting
(even a few events could turn out important: model exclusions)
In both cases: constraints on compact object
formation models

12. Binary Compact Object Inspiral
Mass measurements
For example:
reference model
inefficient CE ejection
from Belczynski,
VK, & Bulik 2001
first SN
first SN
second SN
second SN
Constraints on models of binary compact object formation
and on specifics of stellar evolutionary phases

13. Binary Compact Object Inspiral
Observational Biases
detection efficiency depends on galaxy
and mass distributions
> assumption of isotropicity is not appropriate
for the nearby Universe, i.e., initial LIGO

14. The galaxy distribution in the nearby universe
Is NOT uniform and isotropic …
from Nutzman, VK, Finn, et al. 2003
Total number of
`Milky Way Equivalent Galaxies’
for which inspiral detection is
possible
as a function of distance
NS-NS detection rates have
been underestimated by
a factor of 2-3

15. Binary Compact Object Inspiral
Observational Biases
detection efficiency depends on galaxy
and mass distributions
> assumption of isotropicity is not appropriate
for the nearby Universe, i.e., initial LIGO
detection bias against massive binaries
due to inspiral template uncertainties
> affects rates of BH-BH relative to NS-NS
detection bias against precessing binaries,
if precession modulation is not included in templates
> affects rates of high-mass ratio binaries (BH-NS)

16. GW Source Locations For individual sources:
What can we learn from them ?
For individual sources:
identification of EM counterparts
or host stellar systems
For large source samples:
> space distributions of stellar pops
(e.g. Galactic WD-WD pop)
> correlations between
source and host types
key issue: accuracy of distance and position measurements

17. GW detections of inspirals will provide us with constraints on
In summary …
GW detections of inspirals will provide us with constraints on
binary evolution models and populations
pulsar luminosity characteristics
space distribution and possibly EM counterparts
BUT have we exhausted model constraints from EM observations ?
rate estimates and mass measurements from binary PSRs
can still constrain binary formation models and
BH binary inspiral rates

18. Learning about Stellar Populations from Gravitational Wave Observations
What ? How ?
Important elements:
Understand selection effects and
how they 'skew' observations
Understand how model predictions
depend on physical uncertainties

19. Side Interesting Questions
Have we exhausted model constraints from EM observations ?
rate estimates and mass measurements from binary PSRs
If source position is known, can we detect individual sources
burried in the LISA binary foreground ?
would allow us to measure orbital periods of close binaries
Can we constrain the compact-object/progenitor mass relation ?
Are there sources detectable by both LISA and LIGO ?
what are their properties ?
how are they formed ?
what's their relative formation frequency ?
If WD-WD mergers are SN Type Ia progenitors,
could we ever predict a SN Ia event ?