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)

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

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

GW astronomy NS-NS ground-based (f gw ~a few x Hz) NS-WD space-based f gw ~ mHz NS-BH

Our work (Kim et al. 2003; Kalogera et al. 2004; Kim et al. 2004) 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) 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.

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

Method Two key ingredients to model: (1)PSR population (2)PSR survey selection effects

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

Basic strategy Consider one system at a time (e.g., J ) P(N obs ) PSR population models (luminosity & spatial distribution) + PSR survey simulation obtain N obs (given N pop ) apply Bayes’ theorem Input parameters & results are relevant to PSR J

PSR population model a PSR population can be defined Spatial distribution R=(x 2 +y 2 ) 1/2 Luminosity distribution PSR i (R,Z,L) i fix P s, pulse width, & P orb f(R,z)  exp R o : radial scale length, z o : vertical height |Z| ZoZoZoZo R2R2R2R2 2R o 2 -- Spatial distribution (Narayan 1991) Reference model: R o =4.0 kpc, z o =1.5 kpc

PSR population model Radio PSR luminosity distribution (Cordes and Chernoff 1997) power-law: L min : cut-off luminosity (L min < L) Reference model: L min =0.3 mJy kpc 2, p=2.0 log L log N ? L min slope: p  (L; L min, p) determines a fraction of faint PSRs in a given population

Orbital motion effects are taken into account PSR B credit: M. Kramer Survey Selection effects

N obs follows the Poisson distribution, P(N obs ; ) Earth PSR survey simulation - SEARCH Calculate N obs,i varying N pop, i Same P s & P b, but diff. radio flux densities S = L/d 2 L d

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

For an each observed system i, P i (R) = C i 2 R exp(-C i R) where C i =  life N pop f b i f b : beaming correction factor  Combine individual P(R)’s and calculate P(R tot )  Individual P(R) P(R tot )

NS-NS binaries Livingston Observatory Hanford Observatory Merging binaries in Galactic disk: PSRs B , B , and J

Galactic NS-NS merger rate (Myr -1 ) P(R gal ) Detection rate for the initial LIGO (yr -1 ) Probability density function of R gal N J0737 ~ 1600 (most abundant) Lifetime ~ 185 Myr (shortest) N J1534 ~ 400 N J1913 ~ 600 Reference model Detection rate for the initial LIGO (yr -1 )

 P(R gal ) in a linear scale (reference model) Detection rate for the initial LIGO (yr -1 ) Galactic NS-NS merger rate (Myr -1 ) R peak R peak ( ) R peak ( ) ~ 6-7 Increase rate factor

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

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

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

Global P(R gal ): Result Probability Density Galactic NS-NS merger rate (Myr -1 )

from Tauris & van den Heuvel (2003) SN rate constraints 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 = 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… Type Ib/c

Global P(R gal ) and SN rate constraints Probability Density Galactic NS-NS merger rate (Myr -1 ) SN U5 SN L5 SN Ib/c = Myr -1 (Cappellaro, Evans, & Turatto 1999) SN L5 = SN (lower)x0.05 = 30 Myr -1 SN U5 = SN (upper)x0.05 = 80 Myr -1 Suppose, ~5% of Ib/c SNe are involved in the NS-NS formation. The empirical SNe rate

Global P(R gal ) and SN rate constraints Probability Density Galactic NS-NS merger rate (Myr -1 ) SN L5 : Conservative upper limit of R NS-NS SN U5

Implications of new discoveries (1)PSR J (Faulkner et al. 2005) (2)PSR J (Lorimer et al. 2006)

Implications of J  J : 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 J  Contribution of J to the Galactic DNS merger rate. No significant change in the total rate. R peak (3 PSRs + J1756) R peak (3 PSRs) ~ 1.04 J ~ another example of 1913-like population

Implications of J  J : a young pulsar in a relativistic binary in the Galactic disk (Lorimer et al. 2006) PSR name P s (ms) P b (hr) e  life (Gyr) B B J A J J Characteristic age ~ 112 kyr ! Death time ~ 82 Myr (< t mrg ) ~lifetime J

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

NS-WD binaries (1)Merging binaries: PSRs J , J , and J (2) Eccentric binaries: PSRs J and B

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 f gw < 3 mHz Calculate the contribution from NS-WD binaries to the GW background for LISA. In-spiraling NS-WD binaries emit gravitational waves in a frequency range f gw ~ 0.01 – 100 mHz Consider 3 merging systems (PSR J , J , and J )

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

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

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

Compare theoretical & empirical estimates Empirical estimates -Kalogera, CK, Ihm, Belczynski 2005 (error CL) “Lower Limits” - Kalogera, CK, Ihm, Belczynski 2005 (StarTrack) Nelemans, Portegies Zwart, & Yungelson 2001 (upper limit) Tauris & Sennels 2001 Brown et al Portegies Zwart & Yungelson Davies, Ritter, King 2003 REF : 4 Myr -1 Theoretical estimates No beaming correction J and B

~h 2 d M chirp f h: GW amplitude f: GW frequency = 2/P orb d: distance to the source 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 V det )  M BH binaries (BH-BH, BH-NS) are even stronger GW sources than NS binaries. However, they have not been observed, yet. NS-BH binaries

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

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

NS-NS binaries  NS-NS binaries Empirical rate constraints Galactic merger rate (Myr -1 ) log (Probability Density) StarTrack results wide NS-NS merging NS-NS Only a few % of models satisfy both constraints simultaneously Merging B , B , J Wide (  mrg > Hubble time ) J , J , J Consistent with empirical rates

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

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

NS-BH binaries: discussions  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 death-time (Myr) spin-down age (Gyr) observable lifetime ~ 10% of MSP lifetime

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