Astrophysics of Captures

1. Astrophysics of Captures Steinn Sigurdsson Dept Astro & Astrop, & CGWP Penn State Astrogravs '03

2. MBH >> m* • Consider supermassive black holes in centres of galaxies. MBH ~ 106 Msun • Surrounded by a dense cluster of stars • Some of those stars will fall into the black hole. Main sequence stars are tidally disrupted • White dwarfs, neutron stars and low mass black holes (m ~ 10-100 Msun ) can coalesce with central SMBH through emission of gravitational radiation • The gravitational radiation is detectable by LISA Astrogravs '03

3. Centres of galaxies • Central density cusp inside rh = GMBH/v2 •   r-3/2-p p(r) •  [-1,1], average  ~ 106 Msun pc-3 • Relaxation time scale tr  rp • Outer cusp generally unrelaxed, at current epoch, for SMBH of interest. Inner cusp may be relaxed. May have been relaxed initially even if not relaxed now! • Cusp need not be spherical or axisymmetric • Velocity distribution generally anisotropic Astrogravs '03

4. Stellar populations • Initially there are main sequence stars. • Is nuclear IMF normal or top heavy • Was initial IMF (pop III?) top heavy • Was SMBH in place as massive object or did it form from a slow growing seed with low initial mass? • 0.1-0.3 WD; 10-3 NS; 10-4 LMBH • What are WD and LMBH mass functions? • Do NS all leave cusp because of kicks? • Do they matter even if some remain to merge? • Do significant fraction of low mass black holes formed leave because of natal kicks? Astrogravs '03

5. Capture • Dynamical time scales in cusp ~ 104 years • Stars initially on orbits that avoid SMBH • Main sequence stars are depleted inside some rcoll << rh - MS scattering becomes ineffective • tr increases at rcoll - compact remnants can scatter off each other (or hydrodynamical collisions) • Gravitational potential is not smooth, there is diffusion and scattering in angular momentum Astrogravs '03

6. Gravitational radiation • Some stars plunge directly into event horizon • Close peribothron passage leads to gravitational radiation losses, if large enough, star committs to coalescence before it can be scattered to higher J • This is the loss-cone. It is initially empty. • Loss cone can be filled in a variety of ways • Question is how rapidly, with what, and from where? Astrogravs '03

7. Diffusion and scattering • “Brownian” diffusion moves stars into the edge of the loss cone • Large angle star-star scattering injects stars into the middle of the loss-cone • These processes provide the base rate for LISA events, modulo uncertainties in BH and stellar mass function and stellar velocity anisotropy in the cusp Astrogravs '03

8. Enhanced scattering • Other processes may enhance this rate • If the rate is too high, the SMBH grows and leaves the LISA band - capture may continue at astrophysically interesting rates, but not of LISA interest • Compact remnants that are captured from inner cusp deplete the population available for capture, and deplete the population available for scattering • Compact remnants brought in from outside rh population through relaxation, dynamical processes or from star formation followed by stellar evolution may sustain a high coalescence rate in principle Astrogravs '03

9. Orbits • Far inside rh orbits are approximately Keplerian. • Capture orbits are initially high eccentricity • e ~ 0.99-0.9999999 • Some fraction of orbits scatter down through event horizon after capture, and therefore do not lead to significant emission of gravitational radiation Astrogravs '03

10. Loss-cone growth • When star coalesces with SMBH, the black hole grows, and rS increases • So loss-cone grows • For large m/M - ie low mass SMBH, or if the captured object is relatively massive, the growth is runaway - sudden increase in loss-cone leads to increased growth of SMBH • May be important for early stages of SMBH growth Astrogravs '03

11. BH wandering • Infinite mass SMBH is fixed to r=0 • Stellar mass BH moves with stars • Somewhere in between SMBH wandering transits: • from regime where SMBH carries inner cusp with it to where the SMBH wanders out of the loss-cone. Provides rapid refilling of loss cone. • Transition mass is ≤ 106 Msun, in the range of masses of interest to LISA Astrogravs '03

12. Non-axisymmetry • Non-axisymmetry: triaxiality or time dependent structure in potential rotates the loss-cone. Significant fractional filling of loss-cone on dynamical time scales. Occurs post galaxy merger, or due to persistent triaxial cusp configuration • Stars are brought in from outside rh increases the population available for capture • Gravitational radiation capture less effective for high energy orbits. Up-scattering may reduce relevance for LISA signals. Astrogravs '03

13. Star formation • Is the compact remnant population replenished? In particular, are LMBHs replenished after they segregate to centre and coalesce? • Evidence for high mass star formation near centre of Milky Way • Do these stars form black holes? • Key issue: what is cut-off mass for BH formation at different metallicities, hence given IMF what is the fraction of stars which evolve to LMBH? • If high Z and therefore fallback LMBH, is there a kick? Astrogravs '03

14. Pop III or Pop I • Low Z gas may form massive stars and many high mass LMBH == IMBH. • IMBH-SMBH mergers may be important LISA sources. • Nuclear gas at low z is high Z • Evidence that high Z high mass stars don’t form LMBH due to high mass loss • Any LMBH formation channel at high Z may be important in replenishing population • Or maybe some mergers may bring in low Z gas Astrogravs '03

15. Astrophysics of detection • Detection from high z probes Pop III population and era of SMBH formation • Local rate tells us about late nuclear star formation and possibly galactic structure • Integrated rate tells us about SMBH distribution and evolution, especially the low mass end of the SMBH population • May see sign of post SMBH-SMBH mergers in a subset of coalescence events - spin signature? Astrogravs '03

16. Issues needing to be clarified • Black Hole mass function, quantitative mass cut-off for LMBH formation • What fraction of LMBH receives natal kicks significant compared to cusp velocity dispersion? • Does velocity anisotropy or triaxiality exist in real systems at levels that matter for LISA rates and will the predicted signal be affected • Does the LMBH population replenish at late times in galactic nuclei at interestingly large levels • Is Z too large for LMBH formation? • Are there channels for nuclear LMBH formation in spite of high mean metallicity? Astrogravs '03

17. Conclusion • Coalescence of captured compact stars is an important LISA source • May probe high z and high Z stellar population and SMBH formation • Local sources are good astrophysical probes • Excellent fundamental physics probes. Astrogravs '03