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Revised Inspiral Rates for Double Neutron Star Systems Chunglee Kim (Northwestern)

Revised Inspiral Rates for Double Neutron Star Systems Chunglee Kim (Northwestern). with Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester) 8 th Gravitational Wave Data Analysis Workshop Milwaukee, WI (Dec. 17, 2003).  PSR J0737-3039 (Burgay et al. 2003)

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Revised Inspiral Rates for Double Neutron Star Systems Chunglee Kim (Northwestern)

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  1. Revised Inspiral Rates for Double Neutron Star SystemsChunglee Kim (Northwestern) with Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester) 8th Gravitational Wave Data Analysis Workshop Milwaukee, WI (Dec. 17, 2003)

  2.  PSR J0737-3039 (Burgay et al. 2003) the 3rd coalescing DNS: strongly relativistic !! NEW Event rate estimation for inspiral search Galactic coalescence rate of DNSs 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. 2coalescing systems in the Galactic disk. (PSR B1913+16 and B1534+12)

  3. . Ps (ms) (ss-1) Porb (hr) e Mtot ( ) Ps M  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) Galactic disk pulsars Properties of pulsars in DNSs J0737-3039 22.70 2.4x10 -18 2.4 0.087 2.6 (1.24)

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

  5. Number of sources R = x correction factor Lifetime of a system • Correction factor : beaming correction for pulsars • Lifetime of a system = current age + merging time • of a pulsar of a system Coalescence rate R(Narayan et al.; Phinney 1991) • 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?

  6. luminosity & spatial distribution functions • spin & orbital periods from each observed PSR binary Earth populate a model galaxy with NtotPSRs (same Ps& Porb) count the number of pulsars observed (Nobs) Method - Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 ) 1. Model pulsar sub-populations 2. Simulate pulsar-survey selection effects Nobsfollows the Poisson distribution, P(Nobs; <Nobs>)

  7. Bayes’ theorem P(R) P(<Nobs>) For an each observed system i, Pi(R) = Ci2R exp(-CiR) where Ci = combine all P(R)’s calculate P(Rtot) <Nobs> τlife Ntot fb i 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) P(1; <Nobs>) Method (cont.) -Statistical Analysis 3. Calculate a probability density function of coalescence rate R

  8. most probable rate Rpeak statistical confidence levels detection rates for GW detectors  Double neutron star (DNS) systems 3coalescing systems in the Galactic disk (PSRB1913+16, B1534+12, and J0737-3039) ground based fgw~10-1000 Hz P(Rtot)

  9. Results (Kalogera, Kim, Lorimer et al. 2003, ApJL submitted)

  10. +477 +80 -144 -23 +0.2 0.075 +1073 180 27 405 -0.06 -325 Coalescence rate R Rpeak (revised)(Myr-1) Rpeak (previous) (Myr-1) (Ref.) Detection rate Rdet (ini. LIGO) (yr-1) Rdet (adv. LIGO) (yr-1) (Ref.) Detection rate = R x number of galaxies within Vmax where Vmax= maximum detection volume of LIGO (DNS inspiral) Results Detection rates of DNS inspirals for LIGO

  11. The most probable inspiral detection rates for LIGO Rdet(ini. LIGO) = 1 event per 5 – 250 yrs (all models) Rdet (adv. LIGO) = 20 – 1000 events per yr (all models) Rpeak (revised) ~ 6-7 Rpeak (previous)  The Galactic coalescence of DNSs is more frequent than previously thought! ~1 event per 1.5 yr (95% CL, most optimistic) Summary ~ 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 !

  12. 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) (talk by Richard O’Shaughnessy) 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

  13. +477 +32 -144 -16 180 27 Rpeak (revised) The Galactic coalescence of DNSs is more frequent than previously thought! ~ 6-7 Rpeak (previous) (Ref.) (all models) Rpeak = 10 – 500 per Myr Summary  Galactic coalescence rate of DNSs Rpeak (revised)(Myr-1) Rpeak (previous) (Myr-1)

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

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