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

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

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

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)

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

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

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

Probability Distribution of NS-NS Inspiral Rate Choose PSR space & luminosity distribution power-law constrained from radio pulsar obs. Populate Galaxy with Ntot ‘‘1913+16-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

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 75 400 95% 15 - 275 80 - 1500 opt: peak 200 1000 95% 35 - 700 200 - 3700

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

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

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

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

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

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)

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

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

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

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 ?