Stellar Populations and Gravitational Wave Observations Vicky Kalogera Northwestern University

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Stellar Populations and Gravitational Wave
ObservationsVicky KalogeraNorthwestern
University

• Center for
• Gravitational Wave Physics
• Penn State University

November 6 8, 2003
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Stellar Populations andGravitational Wave
Observations
Physical constraints
Event Rates Compact Object Masses Space
distribution
Compact Object Spins NS EOS
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Stellar Populations andGravitational 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

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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

binary PSR modeling
population synthesis
constraints

• Strength of constraints
• depends on
• gt rate accuracy
• gt 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)
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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
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Radio Pulsars in NS-NS binaries
NS-NS Merger Rate Estimates
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
(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
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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
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Probability Distribution of NS-NS Inspiral Rate

• Choose PSR space luminosity distribution
• power-law constrained from radio
  pulsar obs.
• Populate Galaxy with Ntot 191316-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) --gt
  P(Ntot/t x fb)
• Ntot/t x
  fb rate
• Repeat for each of the other two known NS-NS
  binaries

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Current Rate Predictions
3 NS-NS a factor of 6-7 rate increase
Initial LIGO Adv. LIGO per
1000 yr per yr ref peak 75
400 95 15 - 275 80 -
1500 opt peak 200 1000 95
35 - 700 200 - 3700
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Dependence of predicted NS-NS rates on PSR
luminosity function f(L) L-p for L gt Lmin
Joint constraints on luminosity-function parameter
s Lmin and p can be derived
from VK, Kim, Lorimer, Burgay, et al. 2003
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Binary Compact Object Inspiral
Mass measurements

• gt measurement of relative inspiral rates
• gt mass distribution model fitting
• (even a few events could turn out important
  model exclusions)

In both cases constraints on compact object
formation models
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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

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Binary Compact Object Inspiral
Observational Biases

• detection efficiency depends on galaxy
• and mass distributions
• gt assumption of isotropicity is not
  appropriate
• for the nearby Universe, i.e., initial
  LIGO

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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
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Binary Compact Object Inspiral
Observational Biases

• detection efficiency depends on galaxy
• and mass distributions
• gt assumption of isotropicity is not
  appropriate
• for the nearby Universe, i.e., initial
  LIGO

• detection bias against massive binaries
• due to inspiral template uncertainties
• gt affects rates of BH-BH relative to NS-NS

• detection bias against precessing binaries,
• if precession modulation is not included in
  templates
• gt affects rates of high-mass ratio binaries
  (BH-NS)

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GW Source Locations
What can we learn from them ?

• For individual sources
• identification of EM counterparts
• or host stellar systems

• For large source samples
• gt space distributions of stellar pops
• (e.g. Galactic WD-WD pop)
• gt correlations between
• source and host types

key issue accuracy of distance and position
measurements
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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
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Learning about Stellar Populationsfrom
Gravitational Wave Observations
What ? How ?
Important elements
Understand selection effects and how they 'skew'
observations
Understand how model predictions depend on
physical uncertainties
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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 ?