Compact Binaries as Gravitational-Wave Sources

Transcription

1 Compact Binaries as Gravitational-Wave Sources Chunglee Kim Lund Observatory Extreme Astrophysics for All 10 February, 2009

2 Outline Introduction Double-neutron-star systems = NS-NS binaries Neutron star white dwarf binaries = NS-WD binaries Black hole binaries (e.g. NS-BH, BH-BH binaries) this work is to be done in Lund with Melvyn Davies Collaborators: Vicky Kalogera!Northwestern", Richard O Shaughnessy!PSU", Dunc Lorimer!WVU", Chris Belczynski!NMU"

3 Compact binaries as GW sources Gravitational-wave detectors based on laser interferometry: ground-based (LIGO,GEO,VIRGO,TAMA), and space-borne (LISA) 4 km Detection freq ~ Hz NS-NS, NS-BH binaries Detection freq ~ Hz NS-WD binaries

4 Pulsar binaries and the detection of gravitational waves Consider merging binaries (! mrg < Hubble time) Source merger rate R GW detection rate for LIGO PSR B Weisberg & Taylor (2003)

5 Pulsar binaries and the detection of gravitational waves Consider merging binaries (! mrg < Hubble time) Source merger rate R GW detection rate for LIGO

6 Merger Rate R R = Population size (N pop ) Lifetime of a system (! life ) x PSR beaming correction factor (f b )! N pop : number of pulsars in merging binaries in disk!! life = current age + merging time of a pulsar of a system Merging binaries: merging timescale < age of the Universe (e.g., PSR J ; merging timescale = 85 Myr)! life and f b can be estimated from observations. We calculate N pop using a Monte-Carlo method.

7 Detected or Not? Fix spin period, pulse width, and orbital period of model binaries in order to mimic one of the known system (e.g. J A) Calculate S PSR = L / d 2 (flux density) a model pulsar! for a pulsar i (x,y,z,l) i log N slope: p!"#"$% & '( & ') & * +,&" L min log L Calculate a survey sensitivity using a radiometer equation S min : Minimum detectable flux of a survey Compare S PSR and S min A model pulsar is considered to be detected, if S PSR > S min

8 Detected or Not?

9 Probability density function of R

10 Galactic merger rate of NS-NS binaries CK (2006) Ph.D Thesis As of 2009 February, there are 5 merging NS-NS binaries known in the Galactic disk. PSRs B , B , J , and J (PSR J is ignored in this work) Pi(R)=Ci 2 R exp(-cir) and i=1,2,3,4 P(R tot ) dr 1 dr 2 dr 3 dr 4!(R tot R 1 R 2 R 3 R 4 )! P 1 (R 1 ) P 2 (R 2 )P 3 (R 3 )P 4 (R 4 )

11 P(R) = PSR1913+PSR1534+PSR0737+PSR1906 Reference model N J1534 ~ 400 N J1913 ~ 600 Lifetime ~ 82 Myr N J1906 ~ 300 P(R) N J0737 ~ 1800 Lifetime ~ 230 Myr Galactic NS-NS merger rate (Myr -1 )

12 P(R) in a linear scale (reference model) R peak = 120 per 68% 95% 99% Galactic NS-NS merger rate (Myr -1 )

13 Detection rate of NS-NS inspirals for LIGO R det ~ R NS-NS x detection volume Max. detection distance (ini. LIGO) = 20 Mpc (adv. LIGO) = 350 Mpc (Finn 2001) Reference peak: R det (ini. LIGO) ~ 1 event per century R det (adv. LIGO) ~ 270 events per yr (~20 events per month) Reference 95% upper limit R det (ini. LIGO) ~ 1 event per 10 yr R det (adv. LIGO) ~ 660 events per yr (~ 2 events per day)

14 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 GW frequencies below 3 mhz GW amplitude chirpmass GW freq. source number density observation time We calculate N o relevant to NS-WD binaries (up to z = 5) considering, PSRs J , J , and J

15 GW signals from NS-WD binaries confusion noise level due to WD-WD binaries CK et al. (2004) ApJ 616, 1109 GW amplitude (h rms ) J0751+J1757+J1141 f max, yr obs J1757+J1141 f max,1757 f max,1141 The contribution from NS-WD binaries to the J1141 GW background would be negligible

16 NS-BH binaries h ~ M chirp f d 2 h: GW amplitude f: GW frequency = 2/P orb d: distance to the source M chirp : chirp mass Detection distance for advanced LIGO: NS-NS (1.4 M sun ) ~ up to 350 Mpc NS-BH (10 M sun ) ~ up to 740 Mpc (almost an order of magnitude increase in V det )

17 NS-BH binaries h ~ M chirp f d 2 h: GW amplitude f: GW frequency = 2/P orb d: distance to the source M chirp : chirp mass BH Detection binaries distance (BH-BH, for BH-NS) advanced are LIGO: even NS-NS stronger (1.4 MGW sun ) ~ sources up to 350 than Mpc NS binaries. However, NS-BH (10 they M sun have ) ~ up not to yet 740 been Mpc observed. (almost an order of magnitude increase in V det )

18 Constraining theoretical models (to be done with M Davies) O Shaughnessy, CK et al. 2008, ApJ, 672, 479 Applying empirical rate estimates (NS-NS, NS-WD) More than 92% models are ruled out by Galactic NS-NS merger rate Theoretical models should be consistent with observations. Detection rates for BH-NS binaries: (e.g., ~ 1 event orbital per period decade to eccentricity 1000 years (initial relation LIGO) of pulsar binaries) ~ 100 event per year (Advanced LIGO/Virgo) parameter space used in theoretical models for a binary evolution accepted range of parameters Use only these models to explore BH binaries

19 Summary Compact binaries are strong sources of gravitational waves. Pulsar binaries provide indirect evidence of GWs. NS-NS binaries are prime targets for the GW detectors. The Galactic merger rate of NS-NS binaries is most likely to be ~120 per Myr. The next generation of GW detectors will be able to detect GW signals from NS- NS inspirals in next decade! NS-WD binaries emit GW in low frequencies (~mhz) that is within a LISA frequency band. The GW background formed by cosmic NS-WD binaries are negligible comparing with that of WD-WD binaries in our Galaxy.

20 Future Work in Lund Developing a realistic Galactic pulsar model & pulsar survey model make pulsars search pulsars Obtaining the best empirical rate estimates for known pulsar populations in our Galaxy (e.g. globular cluster pulsars vs disk pulsars) Constraining theoretical models by applying empirical merger rates as well as known properties of pulsar binaries. This work will be useful to calculate GW detection rates relevant to BH binaries.