Revised Inspiral Inspiral Rates for Double Rates for Double Revised Neutron Star Systems Neutron Star Systems Chunglee Kim (Northwestern) Kim (Northwestern) Chunglee with with Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester) Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester) 8 th Gravitational Wave Data Analysis Workshop Milwaukee, WI (Dec. 17, 2003)
Why are they interesting? Why are they interesting? • Coalescing Double Neutron Star (DNS) systems are • Coalescing Double Neutron Star (DNS) systems are strong candidates of GW detectors. strong candidates of GW detectors. Galactic coalescence Event rate estimation Galactic coalescence Event rate estimation rate of DNSs DNSs for inspiral inspiral search search rate of for • Before 2003 • Before 2003 5 systems are known in our Galaxy. 5 systems are known in our Galaxy. 2 coalescing systems in the Galactic disk. 2 coalescing systems in the Galactic disk. PSR B1913+16 and B1534+12 ) ( PSR B1913+16 and B1534+12 ) ( • PSR J0737-3039 (Burgay et al. 2003) • NEW NEW the 3rd coalescing DNS: strongly relativistic !!
Properties of pulsars in DNSs DNSs Properties of pulsars in . P s (ms) (ss -1 ) P orb (hr) e M tot ( ) M P s • 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)
Properties of pulsars in DNSs DNSs (cont.) (cont.) Properties of pulsars in · τ c (Myr) τ sd (Myr) τ mrg (Myr) ω (yr -1 ) Galactic disk pulsars B1913+16 110 65 300 4º.23 B1534+12 250 190 2700 1º.75 J0737-3039 160 100 85 16º.9 ~4 times larger than Lifetime=185 Myr B1913+16
R (Narayan et al.; Phinney 1991) Coalescence rate R Coalescence rate Number of sources Number of sources R = R = x correction factor x correction factor Lifetime of a system Lifetime of a system � Correction factor : beaming correction for pulsars Correction factor : beaming correction for pulsars � � Lifetime of a system = current age + merging time Lifetime of a system = current age + merging time � of a pulsar of a system of a system of a pulsar � Number of sources : number of pulsars in coalescing Number of sources : number of pulsars in coalescing � binaries in the galaxy binaries in the galaxy Q: How many pulsars “similar” to the Hulse-Taylor pulsar exist in our galaxy?
Method - - Modeling & Simulation Method Modeling & Simulation (Kim et al. 2003, ApJ , 584, 985 ) 1. Model pulsar sub- -populations populations 1. Model pulsar sub � luminosity & spatial distribution functions luminosity & spatial distribution functions � � spin & orbital periods from each observed PSR binary spin & orbital periods from each observed PSR binary � 2. Simulate pulsar- -survey selection effects survey selection effects 2. Simulate pulsar populate a model count the number of galaxy with N tot PSRs pulsars observed (N obs ) (same P s & P orb ) Earth Earth N obs follows the Poisson distribution, P(N obs ; <N obs >)
Method (cont.) - - Statistical Analysis 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; <N obs >) (e.g. Hulse-Taylor pulsar) Bayes’ theorem P(R) P(1; <N N obs >) P(1; < obs >) P(<N N obs >) P(< obs >) For an each observed system i For an each observed system i , , combine combine P i (R) = C C i R exp(- -C C i R) ) P i (R) = 2 R exp( i R i2 P(R R tot ) calculate P( tot ) calculate all P(R) P(R)’ ’s s all <N N obs > τ < obs > τ life life where C C i where = i = N tot f b N tot f i i b
most probable rate R R peak most probable rate peak P(R tot ) P(R tot ) statistical confidence levels statistical confidence levels detection rates for GW detectors detection rates for GW detectors • Double neutron star (DNS) systems • Double neutron star (DNS) systems ground based f gw ~10-1000 Hz 3 coalescing s 3 coalescing sy ystems in the Galactic disk stems in the Galactic disk PSR B1913+16 B1913+16 , B1534+12 , and J0737- -3039 3039 ) ( PSR , B1534+12 , and J0737 ) (
Results (Kalogera, Kim, Lorimer et al. 2003, ApJL submitted) Results
Results Results • Detection rates of DNS • Detection rates of DNS inspirals inspirals for LIGO for LIGO Detection rate = R x number of galaxies within V max where V max = maximum detection volume of LIGO (DNS inspiral) Coalescence Coalescence R peak (revised) (Myr (Myr - ) R R peak (previous) (Myr - ) R R peak (revised) 1 ) peak (previous) (Myr 1 ) rate R -1 -1 rate (Ref.) (Ref.) +477 +477 +80 +80 180 27 180 27 -144 - 144 -23 - 23 Detection Detection R det (ini ini. LIGO) (yr . LIGO) (yr - ) R R det (adv. LIGO) (yr - ) R det ( 1 ) det (adv. LIGO) (yr 1 ) -1 -1 rate rate (Ref.) +0.2 +0.2 (Ref.) 0.075 +1073 +1073 0.075 405 405 - -0.06 0.06 -325 - 325
Summary Summary • The Galactic coalescence of The Galactic coalescence of DNSs DNSs is more frequent is more frequent • than previously thought! than previously thought! R peak R peak (revised) (revised) ~ 6 6- -7 7 ~ R peak R (previous) peak (previous) • The most probable The most probable inspiral inspiral detection rates for LIGO detection rates for LIGO • R det = 1 event per 5 – – 250 yrs (all models) 250 yrs (all models) R . LIGO) = 1 event per 5 ~1 event per 1.5 yr (95% CL, most optimistic) ~1 event per 1.5 yr (ini ini. LIGO) (95% CL, most optimistic) det ( R det = 20 – – 1000 events per yr (all models) 1000 events per yr (all models) R (adv. LIGO) = 20 ~ 4000 events per yr (95% CL, most optimistic) ~ 4000 events per yr (95% CL, most optimistic) det (adv. LIGO) Inspiral detection rates as high as 1 per 1.5 yr (at 95% C.L.) are possible for initial LIGO !
Future work Future work • Apply the method to other classes of pulsar binaries • Apply the method to other classes of pulsar binaries (e.g. NS NS- -NS in globular clusters NS in globular clusters) ) (e.g. • Give statistical constraints on binary evolution theory • 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)
Summary Summary • Galactic coalescence rate of • Galactic coalescence rate of DNSs DNSs R peak (revised) (Myr (Myr - ) R R peak (previous) (Myr - ) R peak (revised) 1 ) peak (previous) (Myr 1 ) -1 -1 (Ref.) (Ref.) +477 +477 +32 +32 180 27 180 27 - -144 144 -16 - 16 (all models) R (all models) R peak = 10 – – 500 per 500 per Myr Myr peak = 10 The Galactic coalescence of The Galactic coalescence of R peak R peak (revised) (revised) DNSs is more frequent than is more frequent than ~ 6 6- -7 7 DNSs ~ previously thought! R peak previously thought! R (previous) peak (previous)
Results: correlation between Results: correlation between R R peak and model parameters peak and model parameters • Luminosity distribution • Luminosity distribution ∝ L f(L) ∝ L - -p p , , L L min < L ( law: f(L) min < L power- -law: (L L min : cut- -off luminosity) off luminosity) power min : cut Correlations between Correlations between the merger rate with the merger rate with parameters of PSR parameters of PSR population models population models give constraint give constraint to modeling of a to modeling of a PSR population PSR population
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