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Galactic Merger Rates of Pulsar Binaries

Galactic Merger Rates of Pulsar Binaries. Chunglee Kim Thesis advisor: Dr. Vicky Kalogera Thesis Defense April 26, 2006. Outline.  Introduction  Method  Results (NS-NS, NS-WD, NS-BH binaries). ~20 ms - 200 ms. We consider NS-NS, NS-WD, NS-BH . Pulsars in these systems are

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Galactic Merger Rates of Pulsar Binaries

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  1. Galactic Merger Rates of Pulsar Binaries Chunglee Kim Thesis advisor: Dr. Vicky Kalogera • Thesis Defense • April 26, 2006

  2. Outline  Introduction  Method  Results (NS-NS, NS-WD, NS-BH binaries)

  3. ~20 ms - 200 ms We consider NS-NS, NS-WD, NS-BH. Pulsars in these systems are - rare (~8 + 30 in the Galactic disk) - typically old, mildly recycled - strong sources of GW ~1500 known PSRs (Credit: M. Kramer) Pulsar binaries

  4. We are interested in ‘inspiral’ signals consider merging binaries (mrg < Hubble time) GW signals from pulsar binaries Credit: K. Thorne

  5. NS-WD space-based fgw~0.01-100 mHz NS-NS ground-based (fgw~a few x10-103 Hz) NS-BH GW astronomy

  6. We introduce an analysis method to give a statistical significance of the rate estimates. Small number bias and selection effects for faint pulsars are implicitly included in our analysis. Problems in pulsar binary event rates until recently: - rate predictions highly uncertain (by more than two orders of magnitude) - lack of quantitative understanding of uncertainties (statistical & systematic) Our work(Kim et al. 2003; Kalogera et al. 2004; Kim et al. 2004)

  7. Implications for GW detection Goal : Calculate P(R) based on the observation

  8. Method Two key ingredients to model: • PSR population • PSR survey selection effects

  9. beaming Number of sources x correction factor R = Lifetime of a system adapted from PSR & binary properties We calculate the number of sources (Npop) using SEARCH Lifetime = current age + remaining time (PSR) (GW emission) Beaming correction factor = 1/ PSR beaming fraction Merger rate R

  10. Consider one system at a time (e.g., J0737-3039) PSR population models (luminosity & spatial distribution) + PSR survey simulation obtain Nobs (given Npop) P(Nobs) apply Bayes’ theorem Basic strategy Input parameters & results are relevant to PSR J0737-3039

  11. Spatial distribution (Narayan 1991) f(R,z)  exp Spatial distribution R=(x2+y2)1/2 Luminosity distribution |Z| R2 - - Ro: radial scale length, zo: vertical height 2Ro2 Zo Reference model: Ro=4.0 kpc, zo=1.5 kpc fix Ps, pulse width, & Porb (R,Z,L)i PSR i a PSR population can be defined PSR population model

  12. Radio PSR luminosity distribution(Cordes and Chernoff 1997) power-law: Lmin: cut-off luminosity (Lmin < L) Reference model: Lmin=0.3 mJy kpc2, p=2.0 ? log N slope: p Lmin log L (L; Lmin, p) determines a fraction of faint PSRs in a given population PSR population model

  13. Survey Selection effects Orbital motion effects are taken into account PSR B1913+16 credit: M. Kramer

  14. Earth Calculate Nobs,i varying Npop, i Same Ps & Pb, but diff. radio flux densities S = L/d2 L d PSR survey simulation - SEARCH Nobs follows the Poisson distribution, P(Nobs; <Nobs>)

  15. Nobs = 1 ; assume P(Nobs)=const. P(1; <Nobs>) chain rule Pi(<Nobs>) Pi(R) <Nobs>  Npop; and R Npop  For an each observed system i, lifetime  Apply Bayes’ theorem to calculate P(<Nobs>) posteria PDF  data likelihood x prior PDF P(<Nobs>)  P(Nobs; <Nobs>) x P(Nobs) where P(Nobs; <Nobs>) is obtained from SEARCH. P(1; <Nobs>) Statistical Analysis

  16. i For an each observed system i, Pi(R) = Ci2R exp(-CiR) where Ci = <Nobs>life fb: beaming correction factor Npop fb  Individual P(R)  Combine individual P(R)’s and calculate P(Rtot) P(Rtot)

  17. NS-NS binaries Merging binaries in Galactic disk: PSRs B1913+16, B1534+12, and J0737-3039 Hanford Observatory Livingston Observatory

  18. NJ1534 ~ 400 NJ1913 ~ 600 NJ0737 ~ 1600 (most abundant) Lifetime ~ 185 Myr (shortest) Detection rate for the initial LIGO (yr-1) Reference model Detection rate for the initial LIGO (yr-1) P(Rgal ) Probability density function of Rgal Galactic NS-NS merger rate (Myr-1)

  19. Increase rate factor Rpeak Detection rate for the initial LIGO (yr-1) Rpeak (1913+1534+0737) ~ 6-7 Rpeak (1913+1534) Galactic NS-NS merger rate (Myr-1) P(Rgal) in a linear scale (reference model)

  20. Rdet(ini. LIGO) ~ 1 event per 30 yr Rdet (adv. LIGO) ~ 200 events per yr due to the discovery of PSR J0737-3039 The most probable DNS inspiral detection rates for LIGO Reference model: Detection rate of DNS inspirals for LIGO All models: Rdet(ini. LIGO) ~ 1 event per 10 – 400 yr Rdet (adv. LIGO) ~ 10 – 500 events per yr

  21. Global P(R) and supernovae constraints for NS-NS binaries

  22. following Cordes & Chernoff (1997) – Based on 22 PSRs with spin period < 20 ms intrinsic functions for Lmin and p P(R; Lmin,p) f(Lmin) g(p) Pglobal(R) = dp dLmin p Lmin Rpeak is strongly dependent on the PSR luminosity func. Global probability density function Pglobal(R) Global P(Rgal): calculation f(R,z) is relatively poorly constrained, but the rate estimates are NOT sensitive to the assumed distribution function.

  23. Probability Density Galactic NS-NS merger rate (Myr-1) Global P(Rgal): Result

  24. SN rate constraints Type Ib/c Type Ib/c from Tauris & van den Heuvel (2003) Two NS are likely to be formed by SNe type Ib/c. Therefore, SNe (Ib/c) rate can be considered as an upper limit to the NS-NS rate. SN Ib/c=600-1600 Myr-1 (Cappellaro et al. 1999) However, the fraction of SN Ib/c actually involved in the formation of NS-NS systems is uncertain. Based on population syntheses, the fraction could be ~ 5% or less…

  25. The empirical SNe rate SN Ib/c = 600-1600 Myr-1 (Cappellaro, Evans, & Turatto 1999) Suppose, ~5% of Ib/c SNe are involved in the NS-NS formation. SNL5= SN (lower)x0.05 = 30 Myr-1 SNU5= SN (upper)x0.05 = 80 Myr -1 Probability Density SNU5 SNL5 Galactic NS-NS merger rate (Myr-1) Global P(Rgal) and SN rate constraints

  26. Probability Density SNL5 SNU5 Galactic NS-NS merger rate (Myr-1) : Conservative upper limit of RNS-NS Global P(Rgal) and SN rate constraints

  27. Implications of new discoveries • PSR J1756-2251 (Faulkner et al. 2005) • PSR J1906+0746 (Lorimer et al. 2006)

  28.  Contribution of J1756-2251 to the Galactic DNS merger rate. Rpeak (3 PSRs + J1756) ~ 1.04 No significant change in the total rate. Rpeak (3 PSRs) J1756-2251 ~ another example of 1913-like population J1756-2251: The 4-th merging NS-NS known in the Galactic disk (Faulkner et al. 2005)  discovered by the Parkes Multibeam Pulsar Survey with the acceleration search technique. Detailed simulations for acceleration searches are needed to calculate P(R) including J1756-2251. Implications of J1756-2251

  29. PSR name Ps (ms) Pb (hr) e life (Gyr) B1913+16 59.03 7.752 0.617 0.365 B1534+12 37.90 10.098 0.274 2.7 J0737-3039A 22.70 2.45 0.088 0.185 J1756-2251 28.46 7.67 0.181 2.0 J1906+0746 144.07 3.98 0.0853 0.82 Characteristic age ~ 112 kyr ! Death time ~ 82 Myr (< tmrg) ~lifetime J1906+0746: a young pulsar in a relativistic binary in the Galactic disk (Lorimer et al. 2006) Implications of J1906+0746 J1141-6545 393.90 4.744 0.172 0.105

  30.  Assume J1906+0746 is a NS-NS binary:  total mass ~ 2.61 ± 0.02 M   companion is an NS or WD N1906 ~ 300 t1906 ~ 82 Myr N0737 ~1600 t0737 ~ 185Myr ~ 0.5 x Rpeak (3 PSRs + J1906) ~ 2 Rpeak (3 PSRs)  Follow-up (optical/timing) observations are crucial Implications of J1906+0746

  31. NS-WD binaries • Merging binaries: PSRs J0751+1807, J1757-5322, and J1141-6545 (2) Eccentric binaries: PSRs J1141-6545 and B2303+46

  32. In-spiraling NS-WD binaries emit gravitational waves in a frequency range fgw ~ 0.01 – 100 mHz NS-WD binaries as GW sources for LISA The GW background due to the large number of sources limits the detectability of weak sources in fgw < 3 mHz Calculate the contribution from NS-WD binaries to the GW background for LISA. Consider 3 merging systems (PSR J0751+1807, J1757-5322, and J1141-6545)

  33. GW signals from NS-WD binaries source number density chirpmass GW freq. confusion noise level due to WD-WD binaries integration time 1 yr obs GW amplitude (hrms) fmax,0751 J0751+J1757+J1141 fmax,1757 J1757+J1141 fmax,1141 The contribution from NS-WD binaries to the GW background would be negligible J1141

  34. Galactic birthrate of eccentric NS-WD binaries standard binary scenario predicts - circular orbit - NS formation first - recycled PSR J1141-6545 : e=0.172 (Kaspi et al. 2000, Bailes et al. 2003) B2303+46 : e=0.658 (Stokes et al. 1985, van Kerkwijk & Kulkarni 1999) “non-zeroeccentricity” implies - WD formed first - non-recycled PSR

  35. Theoretical predictions on birthrates Empirical estimates • Kalogera, CK, Ihm, Belczynski 2005 (StarTrack) Nelemans, Portegies Zwart, & Yungelson 2001 (upper limit) Tauris & Sennels 2001 Brown et al. 2002 Portegies Zwart & Yungelson 1999 • Davies, Ritter, King 2003 Theoretical estimates

  36. No beaming correction Empirical estimates • Kalogera, CK, Ihm, Belczynski 2005 (error bar @95% CL) “Lower Limits” • Kalogera, CK, Ihm, Belczynski 2005 (StarTrack) Nelemans, Portegies Zwart, & Yungelson 2001 (upper limit) Tauris & Sennels 2001 Brown et al. 2002 Portegies Zwart & Yungelson 1999 • Davies, Ritter, King 2003 J1141-6545 and B2303+46 Theoretical estimates REF : 4 Myr-1 Compare theoretical & empirical estimates

  37. M  h: GW amplitude f: GW frequency = 2/Porb d: distance to the source 2 Mchirp f h ~ d Detection distance for advanced LIGO: NS-NS ~ up to 350 Mpc NS-BH (10 ) ~ up to 740 Mpc (almost an order of magnitude increase in Vdet) NS-BH binaries BH binaries (BH-BH, BH-NS) are even stronger GW sources than NS binaries. However, they have not been observed, yet.

  38. Empirical estimates using SEARCH Probability density 0 200 600 1000 Galactic merger rate (Myr-1)  Fix Ps = 50ms,  pulse width = 0.15  Adapt flux degradation factors from known NS-NS binaries Calculate P(R) given Nobs=0 RNS-BH < 1000 Myr-1 (upper limit @ 95% prob.) with beaming correction

  39. Establish a set of models (or parameters), which are consistent with the estimated RNS-NS based on our empirical method Calculate Rgal of BH binaries using only those models. parameter space used in theoretical model (StarTrack) accepted range of parameters Give strong constraints on Rdet of BH binaries and population synthesis models O’shaughnessy, CK, et al.2005, ApJ,633, 1076  Theoretical predictions on RNS-BH ~ 10-8 – 10-5 yr -1 Constrain theoretical models

  40. Empirical rate constraints StarTrack results merging NS-NS Consistent with empirical rates log (Probability Density) Merging B1913+16, B1534+12, J0737-3039 10-2 0.1 1 10 102 103 wide NS-NS log (Probability Density) Only a few % of models satisfy both constraints simultaneously Wide (mrg > Hubble time) J1181-1736, J1518+4904, J1829+2456 10-2 0.1 1 10 102 103 Galactic merger rate (Myr-1) NS-NS binaries

  41. Constrained predictions w/ StarTrack log (Probability Density) 10-2 0.1 1 10 102 Galactic merger rate in (Myr-1) Dashed lines: unconstrained Solid lines: constrained (NS-NS) BH-BH more than 95% of models are ruled out; Still, wide range of parameters are possible. NS-BH no recycled PSR-BH NS-NS

  42. Recycled PSR-BH StarTrack results: << 10-4 and R NS-NS < 10-4 yr-1 NS-NS Pfahl et al. (2005) suggested that the Galactic birthrate of recycled PSR-BH binaries ~ less than 10-7 yr-1 consistent with our work (RMSP-BH < 10-8 yr-1) NS-BH binaries: discussions If any, presumably, slow/normal PSR-BH binaries dominate the NS-BH population

  43. observable lifetime ~ 10% of MSP lifetime death-time (Myr) spin-down age (Gyr)  Observational challenges pulsars in NS-BH binaries are expected to have relatively short observable lifetimes, large accelerations in orbital motions than those of NS-NS binaries.  Large-scale interferometers Square Kilometer Array (SKA) … radio (EM) GEO/LIGO/TAMA/VIRGO … GW NS-BH binaries: discussions

  44. Pulsar binaries are one of the most promising targets for GW detectors, and they are likely to provide some of the first GW detections. We study  empirical Rgal of pulsar binaries (NS-NS & NS-WD)  detectability of such systems for GW detectors constraints on theoretical models and BH rate estimates Summary

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