8th Gravitational Wave Data Analysis Workshop Revised Inspiral Rates for Double Neutron Star Systems Chunglee Kim (Northwestern) Advanced School and Conference on Sources of Gravitational Waves, ICTP, Trieste, Italy (Sep. 15-26, 2003) with Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester) 8th Gravitational Wave Data Analysis Workshop Milwaukee, WI (Dec. 17, 2003)

Why are they interesting?  Coalescing Double Neutron Star (DNS) systems are strong candidates of GW detectors.  Before 2003 5 systems are known in our Galaxy. 2 coalescing systems in the Galactic disk. (PSR B1913+16 and B1534+12) Event rate estimation for inspiral search Galactic coalescence rate of DNSs Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)  PSR J0737-3039 (Burgay et al. 2003) the 3rd coalescing DNS: strongly relativistic !! NEW

Properties of pulsars in DNSs Ps (ms) (ss-1) Porb (hr) e Mtot ( ) Ps .  M Galactic disk pulsars B1913+16 59.03 8.6x10-18 7.8 0.61 2.8 (1.39) B1534+12 37.90 2.4x10 -18 10.0 0.27 2.7 (1.35) J0737-3039 22.70 2.4x10 -18 2.4 0.087 2.6 (1.24) Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)

Properties of pulsars in DNSs (cont.) c (Myr) sd (Myr) mrg (Myr) (yr-1) ·  Galactic disk pulsars B1913+16 110 65 300 4º.23 B1534+12 250 190 2700 1º.75 Lifetime=185 Myr J0737-3039 160 100 85 16º.9 Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003) ~4 times larger than B1913+16

Coalescence rate R (Narayan et al.; Phinney 1991) Lifetime of a system Number of sources x correction factor R = Correction factor : beaming correction for pulsars Lifetime of a system = current age + merging time of a pulsar of a system Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003) Number of sources : number of pulsars in coalescing binaries in the galaxy Q: How many pulsars “similar” to the Hulse-Taylor pulsar exist in our galaxy?

Method - Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 ) 1. Model pulsar sub-populations 2. Simulate pulsar-survey selection effects luminosity & spatial distribution functions spin & orbital periods from each observed PSR binary populate a model galaxy with Ntot PSRs (same Ps & Porb) count the number of pulsars observed (Nobs) Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003) Earth Nobs follows the Poisson distribution, P(Nobs; <Nobs>)

Method (cont.) - Statistical Analysis 3. Calculate a probability density function of coalescence rate R We consider each observed pulsar separately. Calculate the likelihood of observing just one example of each observed pulsar, P(1; <Nobs>) (e.g. Hulse-Taylor pulsar) Bayes’ theorem P(<Nobs>) P(R) P(1; <Nobs>) For an each observed system i, Pi(R) = Ci2R exp(-CiR) where Ci = calculate P(Rtot) <Nobs> τlife Ntot fb i combine all P(R)’s Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)

most probable rate Rpeak P(Rtot) statistical confidence levels detection rates for GW detectors  Double neutron star (DNS) systems 3 coalescing systems in the Galactic disk (PSR B1913+16, B1534+12, and J0737-3039) ground based fgw~10-1000 Hz Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)

Results (Kalogera, Kim, Lorimer et al. 2003, ApJL submitted) Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)

Results  Detection rates of DNS inspirals for LIGO Detection rate = R x number of galaxies within Vmax where Vmax= maximum detection volume of LIGO (DNS inspiral) 180 +477 -144 27 +80 -23 (Ref.) Rpeak (revised) (Myr-1) Rpeak (previous) (Myr-1) Coalescence rate R Rdet (ini. LIGO) (yr-1) Rdet (adv. LIGO) (yr-1) 0.075 +0.2 -0.06 405 +1073 -325 (Ref.) Detection rate Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)

Summary  The Galactic coalescence of DNSs is more frequent than previously thought! Rpeak (revised) Rpeak (previous) ~ 6-7 Rdet (adv. LIGO) = 20 – 1000 events per yr (all models) Rdet (ini. LIGO) = 1 event per 5 – 250 yrs (all models)  The most probable inspiral detection rates for LIGO ~1 event per 1.5 yr (95% CL, most optimistic) Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003) ~ 4000 events per yr (95% CL, most optimistic) Inspiral detection rates as high as 1 per 1.5 yr (at 95% C.L.) are possible for initial LIGO !

Future work  Apply the method to other classes of pulsar binaries (e.g. NS-NS in globular clusters)  Give statistical constraints on binary evolution theory (talk by Richard O’Shaughnessy) determine a favored parameter space based on the rate calculation can be used for the calculation of coalescence rates of BH binaries (e.g.NS-BH) Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)

Summary  Galactic coalescence rate of DNSs (Ref.) 180 27 Rpeak (revised) (Myr-1) Rpeak (previous) (Myr-1) (Ref.) 180 +477 -144 27 +32 -16 (all models) Rpeak = 10 – 500 per Myr Rpeak (revised) Rpeak (previous) ~ 6-7 The Galactic coalescence of DNSs is more frequent than previously thought! Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003)

the merger rate with parameters of PSR population models Results: correlation between Rpeak and model parameters  Luminosity distribution power-law: f(L)  L-p, Lmin < L (Lmin: cut-off luminosity) Correlations between the merger rate with parameters of PSR population models Conference at ICTP, Trieste, Italy (Sep. 15-26, 2003) give constraint to modeling of a PSR population