Binary population synthesis implications for gravitational wave sources

1. Tomasz Bulik CAMK Binary population synthesis implications for gravitational wave sources with Dorota Gondek-Rosińska Krzyś Belczyński Bronek Rudak

2. Questions • What are the expected rates? • How uncertain the rates are? • What are the properties of the sources? • Are the methods credible?

3. Binary compact objects Only few coalescing NSNS known: • Hulse-Taylor PSR1913+16, t=300 Myrs • B1534+12, t=2700 Myrs • B2127+11C, t=220 Myrs • Binary Pulsar J0737 – 3039, t=80 Myrs BHNS? BHBH?

4. Rate estimate Method I: observations • Use real data • Selection effects • Very low or even zero statistics • Large uncertainty

5. RATES – METHOD 1 Find the galactic density of coalescing sources from the model Obtain galactic merger rate Extrapolate from the Galaxy further out: Scale by: mass density? galaxy density? blue luminosity? Supernovae rate density? The result is dominated by a single object: J0737-3039!! Kalogera etal 2004

6. Rate estimate Method II: binary population synthesis • Binary evolution • Formation of NS i BH binaries • Dependence on the parametrization • Unknowns in the stellar evolution

7. Population synthesis -single stars • Numerical models • Helium stars • Evolutionary times • Radii • Internal structure: mass and radius of the core • Convection • Winds • NS i BH formation, supernovae

8. Binary evolution • Mass transfers • Rejuvenation • Supernovae and orbits • Masses of BH i NS • Orbit changes - circularization • Parameter study: many models

9. Simulations Initial masses Mass ratios Orbits A chosen parameter set Typically we evolve binaries

10. An example of a binary leading to formation of a coalescing binary BH-BH:

11. Parameter study • Initial conditions: m, q, a ,e • Mass transfers: mass loss, ang momentum loss and mass transfer • Compact object masses • Supernovae explosions: kick velocities • Metallicity, winds • Standard model

12. Evolutionary times Short lived NSNS are not observable as pulsars

13. Chirp mass distribution

14. Detection Inspiral phase: Amplitude and frequency depend on chirp mass: Signal to noise: Sampling volume:

15. From simulations to rates • Requirements: • model of the detector, signal to noise, sampling volume • normalisation

16. Simulation to rates: normalisation • Galactic supernova rate, Galactic blue luminosity + blue luminosity density in the local Universe: • Coalescence rate ~ blue luminosity • Star formation rate history + initial mass function + evolutionary times: • Calculate the coalescence rate as a function of z

17. Assumptions: Star formation rate: What was it at large z? Does it correspond to the local SFRa few Gyrs ago? Cosmological model (0.3, 0.7) and H=65 km/s/Mpc

18. Initial mass function Needed to convert from SFR mass to number of stars formed We do not simulate all the stars only a small fraction that may produce compact object binaries

19. Results is observed

20. Uncertainty in rate • Star formation history • IMF – shape and range • Stellar evolution model • Non-stationary noise A factor of 10 Together a factor of at least 30 A factor of 10

21. RATES – METHOD 1 Find the galactic density of coalescing sources from the model Obtain galactic merger rate Extrapolate from the Galaxy further out: Scale by: mass density? galaxy density? blue luminosity? Supernovae rate density? The result is dominated by a single object: J0737-3039!! Kalogera etal 2004

22. METHOD 1+2 • Population synthesis predicts ratios • What types of objects were used for Method 1? Long lived NSNS binaries • Observed NSNS population dominated by the short lived objects • Observed objects dominated by BHBH

24. Number of “observed” binaries ________________________________ = 200 (from 10 to 1000) Number of “observed” long lived NSNS • BHBH – have higher chirp mass • BHBH have longer coalescing times

25. This brings the expected VIRGO rate to 1-60 per year!

26. Such an estimate leans on a single object..... PSR J0737-3039 Seeing this : Imagine

27. THIS !

28. Expected object types • NSNS • BHNS • BHBH Population of observed objects in the mass vs mass ratio space

29. BHBH binaries

30. NSNS binaries

31. BHNS binaries

32. SHOULD YOU BELIEVE IN ANY OF THIS?

33. Observed masses of pulsars

34. The initial-final mass relation depends on the estimate of the mass of the core, and on numerical simulations of supernovae explosions. Some uncertainty may cancel out if one considers mass ratios not masses themselves

35. The intrinsic mass ratio distribution: burst star formation, all stars contained in a box. T> 100 Myrs

36. Simulated radio pulsars: Observability proportional to lifetime. Constant SFR. Assume that one sees objects in a volume limited sample, eg. Galaxy. Sample is dominated by long lived objects. Typical mass ratio shifted upwards.

37. Gravitational waves: Constant SFR. A flux limited sample. Low mass ratio objects have larger chirp masses. Long libed pulsars are a small fraction of all systems

38. Summary • Uncertainty of rates is huge • First object: BHBH with similar masses • NSNS binaries –less than 5-10% • Important to consider no equal mass neutron star binaries.

39. What next? • Binaries in globular clusters, different formation channels, three body interactions • Population 3 binaries • ?

40. Resonant detectors Requirements: mass, ccooling, specified frequency bands, strongly directional AURIGA, EXPLORER, NAUTILUS

41. First detection attempts J. Weber – the 1960-ies

42. Sensitivity Narrow bands corresponding to resonant frequencies of the bar

43. Interferometers Michelsona-Morley design Noise: seismic, therma, quantum (shot)

44. Czułość LIGO

45. Gravitational wave sources Requirements: mass asymmetry, size Frequencies: 10 to 1000Hz

46. Gravitational waves Predicted by the General Relativity Theory Binary pulsars: Indirect observations of gravitational waves Weak field approximation PSR 1913+16

47. Present and future detectors Resonant: bars and spheres Typical frequencies: around 1kHz, but in a narrow band Interferometric: LIGO, VIRGO, TAMA300, GEO600 Typical frequencies: 50 – 5000 Hz – wide bands LISA 0.001 – 0.1 Hz

49. Astronomical objects • Pulsars • Supernovae • Binary coalescences

50. Interferometers