Binary Compact Object Inspiral: Rate Expectations Vicky Kalogera with Chunglee Kim Richard O’Shaughnessy Tassos Fragkos Physics & Astronomy Dept

In this talk : In this talk : Gravitational Waves and Double Neutron Stars Gravitational Waves and Double Neutron Stars PSR J the most relativistic binary pulsar: PSR J the most relativistic binary pulsar: NS-NS Inspiral Rates BH-NS, BH-BH Inspirals: BH-NS, BH-BH Inspirals: How PSRs can help in predictions … What to expect in the near future What to expect in the near future

Double Neutron Star Inspiral Do they exist ? YES! First known NS -NS: radio pulsar PSR B What kind of signal ? inspiral chirp GW emission causes orbital shrinkage leading to higher GW frequency and amplitude orbital decay PSR B Weisberg & Taylor 04

Sensitivity to coalescing binaries What is the expected detection rate out to D max ? Scaling up from the Galactic rate Inspiral Event Rates

Inspiral Rates for the Milky Way Theoretical Estimates Based on models of binary evolution until binary compact objects form. for NS -NS, BH -NS, and BH -BH Empirical Estimates Based on radio pulsar properties and survey selection effects. for NS -NS only

Properties of known coalescing DNS pulsars B x B x J x Galactic Disk pulsars P s (ms) (ss -1 ) PsPs. Burgay et al. 2003

Properties of known coalescing DNS pulsars Galactic Disk pulsars B x B x J x P s (ms) (ss -1 ) P orb (hr) PsPs. Burgay et al. 2003

Properties of known merging NS-NS pulsars Galactic Disk pulsars B x B x J x P s (ms) (ss -1 ) P orb (hr) e PsPs. Burgay et al. 2003

Properties of known coalescing DNS pulsars Galactic Disk pulsars B x (1.39) B x (1.35) J x (1.24) P s (ms) (ss -1 ) P orb (hr) e M tot ( ) PsPs. MoMo Burgay et al. 2003

Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates (Phinney ‘91; Narayan et al. ‘91; Lorimer & vdHeuvel ‘97; Arzoumanian et al. ‘99) Bayesian analysis developed to derive the probability density of NS-NS inspiral rate Small number bias and selection effects for faint pulsars are implicitly included in our method. It is possible to assign statistical significance to NS-NS rate estimates with Monte Carlo simulations Kim, VK, Lorimer 2002

Inspiral rate R Lifetime of a system = current age + “remaining” time of the pulsar of the system Correction factor : correction for pulsar beaming Number of sources : number of pulsars in inspiraling binaries in our Galaxy ( N tot ) Lifetime of a system Number of sources x correction factor R =

Statistical Method 1.Identify sub-populations of PSRs withpulse and orbital properties similar to each of the observed DNS 1.Identify sub-populations of PSRs with pulse and orbital properties similar to each of the observed DNS Model each sub-population in the Galaxy 2. Pulsar-survey simulation  consider selection effects of all pulsar surveys  consider selection effects of all pulsar surveys  generate ``observed’’ samples  generate ``observed’’ samples PSR-population models (luminosity & spatial distribution) + PSR-survey simulation N obs individual PSR: N tot number of detectable PSRs in a given PSR population

fill a model galaxy with N tot pulsars count the number of pulsars observed (N obs ) Earth Statistical Method 3. Derive rate estimate probability distribution P(R)

Statistical Analysis given total number of For a given total number of pulsars pulsars, N obs follows a Poisson distribution. best-fit We calculate the best-fit value of P(1; N tot ) value of as a function of N tot and the probability P(1; N tot ) We use Bayes ’ theorem to calculate P(N tot ) and finally P(R) P(N obs ) for PSR B

Properties of known coalescing DNS pulsars B º.23 B º.75 J º.9 Galactic Disk pulsars  c (Myr)  sd (Myr)  mrg (Myr) (yr -1 )  · Burgay et al. 2003

Results: P(R tot ) most probable rate R peak statistical confidence levels expected GW detection rates

Current Rate Predictions 3 NS-NS : a factor of 6-7 rate increase Initial LIGO Adv. LIGO per 1000 yr per yr ref model: peak % VK, Kim, Lorimer et al. 2004

Results: R peak vs model parameters

Global P(R gal ):  Global probability density function P global (R)  following Cordes & Chernoff (1997) intrinsic functions for L min and p P global (R) P(R; L min,p) f(L min ) g(p)

P global (R gal ) Galactic inspiral rate (Myr -1 ) Global P(R gal ) R peak ~ 15 Myr -1 following Cordes & Chernoff (1997) Update is needed ! in. LIGO: R peak ~ 6 per 1000 yr ad. LIGO: R peak ~ 35 per yr

NS-NS formation from Tauris & van den Heuvel (2003) Two NS are likely to be formed by SNe type Ib/c. Therefore, the SNe (Ib/c) rate can be considered as an upper limit to the NS-NS rate SN Ib/c = Myr -1 (Cappellaro et al. 1999) fraction However, the fraction of SN Ib/c actually involved in the formation of uncertain NS-NS systems is uncertain … From population synthesis: as low as ~1/100 It could be as low as ~1/100 but … Type Ib/c

Global P(R gal ) Galactic inspiral rate (Myr -1 ) SN Ib/c : Myr -1 (Cappellaro et al. 1999) 1/10 1/100 Ib/c SN rate uncertainty

Inspiral Rates for BH binaries  BH-NS binaries could in principle be detected as binary pulsars, BUT… the majority of NS in BH-NS are expected to be young short-lived hard-to-detect harder to detect than NS-NS by >~ ! So farrate predictions So far, inspiral rate predictions from population calculations only from population calculations with uncertainties of ~ 3 orders of mag We can use NS-NS empirical rates as constraints on population synthesis models

log ( events per yr ) PDF BH-BH BH-NS NS-NS Inspiral Rates from population models

merging Constraint from known merging NS-NS

PDF derived from observed sample of merging NS-NS log ( events per yr ) NS-NS empirical pop models log ( events per yr ) BH-BHBH-NS unconstrained constrained unconstrained

wide Constraint from known wide NS-NS

log ( events per yr ) unconstrained constrained BH-BHBH-NS log ( events per yr ) wide NS-NS empirical pop models PDF derived from observed sample of wide NS-NS preliminaryresults

merging NS-NS rate Both constraints together should give us much tighter constraints wide NS-NS rate

Current expectations for LIGO II (LIGO I) detection rates of inspiral events NS -NS BH -NS BH -BH D max (Mpc) (20) (40) (100) R det ,000 (1/yr) (5x ) (3x ) (4x ) from population synthesis from known merging NS-NS and Ib/c rates

Future work: Use as many empirical constraints as possible to constrain population synthesis predictions for BH binary event rates: merging NS-NS rates wide NS-NS rates eccentric NS-WD rates SN Ib/c rates binary properties ( separations, eccentricities,masses) Use the absence of known BH-PSR binaries to calculate an upper limit on the BH-NS rate: Use this upper limit as an additional constraint