2. Binary Compact Object Inspiral: Rate Expectations Vicky Kalogera with Chunglee Kim Richard O’Shaughnessy Tassos Fragkos Physics & Astronomy Dept

3. In this talk : In this talk : Gravitational Waves and Double Neutron Stars Gravitational Waves and Double Neutron Stars PSR J0737-3039 the most relativistic binary pulsar: PSR J0737-3039 the most relativistic binary pulsar: NS-NS Inspiral Rates BH-NS, BH-BH Inspirals: BH-NS, BH-BH Inspirals: How PSRs can help in predictions … What to expect in the near future What to expect in the near future

4. Double Neutron Star Inspiral Do they exist ? YES! First known NS -NS: radio pulsar PSR B1913+16 What kind of signal ? inspiral chirp GW emission causes orbital shrinkage leading to higher GW frequency and amplitude orbital decay PSR B1913+16 Weisberg & Taylor 04

5. Sensitivity to coalescing binaries What is the expected detection rate out to D max ? Scaling up from the Galactic rate Inspiral Event Rates

6. Inspiral Rates for the Milky Way Theoretical Estimates Based on models of binary evolution until binary compact objects form. for NS -NS, BH -NS, and BH -BH Empirical Estimates Based on radio pulsar properties and survey selection effects. for NS -NS only

7. Properties of known coalescing DNS pulsars B1913+16 59.03 8.6x10 -18 B1534+12 37.90 2.5x10 -18 J0737-3039 22.70 2.4x10 -18 Galactic Disk pulsars P s (ms) (ss -1 ) PsPs. Burgay et al. 2003

8. Properties of known coalescing DNS pulsars Galactic Disk pulsars B1913+16 59.03 8.6x10 -18 7.8 B1534+12 37.90 2.4x10 -18 10.0 J0737-3039 22.70 2.4x10 -18 2.4 P s (ms) (ss -1 ) P orb (hr) PsPs. Burgay et al. 2003

9. Properties of known merging NS-NS pulsars Galactic Disk pulsars B1913+16 59.03 8.6x10 -18 7.8 0.61 B1534+12 37.90 2.4x10 -18 10.0 0.27 J0737-3039 22.70 2.4x10 -18 2.4 0.09 P s (ms) (ss -1 ) P orb (hr) e PsPs. Burgay et al. 2003

10. Properties of known coalescing DNS pulsars 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 0.09 2.6 (1.24) P s (ms) (ss -1 ) P orb (hr) e M tot ( ) PsPs. MoMo Burgay et al. 2003

11. Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates (Phinney ‘91; Narayan et al. ‘91; Lorimer & vdHeuvel ‘97; Arzoumanian et al. ‘99) Bayesian analysis developed to derive the probability density of NS-NS inspiral rate Small number bias and selection effects for faint pulsars are implicitly included in our method. It is possible to assign statistical significance to NS-NS rate estimates with Monte Carlo simulations Kim, VK, Lorimer 2002

12. Inspiral rate R Lifetime of a system = current age + “remaining” time of the pulsar of the system Correction factor : correction for pulsar beaming Number of sources : number of pulsars in inspiraling binaries in our Galaxy ( N tot ) Lifetime of a system Number of sources x correction factor R =

13. Statistical Method 1.Identify sub-populations of PSRs withpulse and orbital properties similar to each of the observed DNS 1.Identify sub-populations of PSRs with pulse and orbital properties similar to each of the observed DNS Model each sub-population in the Galaxy 2. Pulsar-survey simulation  consider selection effects of all pulsar surveys  consider selection effects of all pulsar surveys  generate ``observed’’ samples  generate ``observed’’ samples PSR-population models (luminosity & spatial distribution) + PSR-survey simulation N obs individual PSR: N tot number of detectable PSRs in a given PSR population

14. fill a model galaxy with N tot pulsars count the number of pulsars observed (N obs ) Earth Statistical Method 3. Derive rate estimate probability distribution P(R)

15. Statistical Analysis given total number of For a given total number of pulsars pulsars, N obs follows a Poisson distribution. best-fit We calculate the best-fit value of P(1; N tot ) value of as a function of N tot and the probability P(1; N tot ) We use Bayes ’ theorem to calculate P(N tot ) and finally P(R) P(N obs ) for PSR B1913+16

16. Properties of known coalescing DNS pulsars B1913+16 110 65 300 4º.23 B1534+12 250 190 2700 1º.75 J0737-3039 160 100 85 16º.9 Galactic Disk pulsars  c (Myr)  sd (Myr)  mrg (Myr) (yr -1 )  · Burgay et al. 2003

17. Results: P(R tot ) most probable rate R peak statistical confidence levels expected GW detection rates

18. Current Rate Predictions 3 NS-NS : a factor of 6-7 rate increase Initial LIGO Adv. LIGO per 1000 yr per yr ref model: peak 35 175 95% 10 - 120 35 - 630 VK, Kim, Lorimer et al. 2004

19. Results: R peak vs model parameters

20. Global P(R gal ):  Global probability density function P global (R)  following Cordes & Chernoff (1997) intrinsic functions for L min and p P global (R) P(R; L min,p) f(L min ) g(p)

21. P global (R gal ) Galactic inspiral rate (Myr -1 ) Global P(R gal ) R peak ~ 15 Myr -1 following Cordes & Chernoff (1997) Update is needed ! in. LIGO: R peak ~ 6 per 1000 yr ad. LIGO: R peak ~ 35 per yr

22. NS-NS formation from Tauris & van den Heuvel (2003) Two NS are likely to be formed by SNe type Ib/c. Therefore, the SNe (Ib/c) rate can be considered as an upper limit to the NS-NS rate SN Ib/c =600-1700 Myr -1 (Cappellaro et al. 1999) fraction However, the fraction of SN Ib/c actually involved in the formation of uncertain NS-NS systems is uncertain … From population synthesis: as low as ~1/100 It could be as low as ~1/100 but … Type Ib/c

23. Global P(R gal ) Galactic inspiral rate (Myr -1 ) SN Ib/c : 600-1700 Myr -1 (Cappellaro et al. 1999) 1/10 1/100 Ib/c SN rate uncertainty

24. Inspiral Rates for BH binaries  BH-NS binaries could in principle be detected as binary pulsars, BUT… the majority of NS in BH-NS are expected to be young short-lived hard-to-detect harder to detect than NS-NS by >~10-100 ! So farrate predictions So far, inspiral rate predictions from population calculations only from population calculations with uncertainties of ~ 3 orders of mag We can use NS-NS empirical rates as constraints on population synthesis models

25. log ( events per yr ) PDF BH-BH BH-NS NS-NS Inspiral Rates from population models

26. merging Constraint from known merging NS-NS

27. PDF derived from observed sample of merging NS-NS log ( events per yr ) NS-NS empirical pop models log ( events per yr ) BH-BHBH-NS unconstrained constrained unconstrained

28. wide Constraint from known wide NS-NS

29. log ( events per yr ) unconstrained constrained BH-BHBH-NS log ( events per yr ) wide NS-NS empirical pop models PDF derived from observed sample of wide NS-NS preliminaryresults

30. merging NS-NS rate Both constraints together should give us much tighter constraints wide NS-NS rate

31. Current expectations for LIGO II (LIGO I) detection rates of inspiral events NS -NS BH -NS BH -BH D max 350 700 1500 (Mpc) (20) (40) (100) R det 2 - 400 1.5 -1500 15 -10,000 (1/yr) (5x10 -4 - 0.1) (3x10 -4 -0.3) (4x10 -3 -3) from population synthesis from known merging NS-NS and Ib/c rates

32. Future work: Use as many empirical constraints as possible to constrain population synthesis predictions for BH binary event rates: merging NS-NS rates wide NS-NS rates eccentric NS-WD rates SN Ib/c rates binary properties ( separations, eccentricities,masses) Use the absence of known BH-PSR binaries to calculate an upper limit on the BH-NS rate: Use this upper limit as an additional constraint