24 Apr 2003Astrogravs '031 Astrophysics of Captures Steinn Sigurdsson Dept Astro & Astrop, & CGWP Penn State

24 Apr 2003Astrogravs '032 M BH >> m * Consider supermassive black holes in centres of galaxies. M BH ~ 10 6 M sun 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 ~ M sun ) can coalesce with central SMBH through emission of gravitational radiation –The gravitational radiation is detectable by LISA

24 Apr 2003Astrogravs '033 Centres of galaxies Central density cusp inside r h = GM BH /v 2 –   r -3/2-p p(r) –  [-1,1], average  ~ 10 6 M sun pc -3 –Relaxation time scale t r  r p –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

24 Apr 2003Astrogravs '034 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? WD; NS; 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?

24 Apr 2003Astrogravs '035 Capture Dynamical time scales in cusp ~ 10 4 years Stars initially on orbits that avoid SMBH Main sequence stars are depleted inside some r coll << r h - MS scattering becomes ineffective t r increases at r coll - compact remnants can scatter off each other (or hydrodynamical collisions) Gravitational potential is not smooth, there is diffusion and scattering in angular momentum

24 Apr 2003Astrogravs '036 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?

24 Apr 2003Astrogravs '037 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

24 Apr 2003Astrogravs '038 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 r h population through relaxation, dynamical processes or from star formation followed by stellar evolution may sustain a high coalescence rate in principle

24 Apr 2003Astrogravs '039 Orbits Far inside r h orbits are approximately Keplerian. Capture orbits are initially high eccentricity – e ~ Some fraction of orbits scatter down through event horizon after capture, and therefore do not lead to significant emission of gravitational radiation

24 Apr 2003Astrogravs '0310 Loss-cone growth When star coalesces with SMBH, the black hole grows, and r S 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

24 Apr 2003Astrogravs '0311 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 ≤ 10 6 M sun, in the range of masses of interest to LISA

24 Apr 2003Astrogravs '0312 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 r h increases the population available for capture Gravitational radiation capture less effective for high energy orbits. Up-scattering may reduce relevance for LISA signals.

24 Apr 2003Astrogravs '0313 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?

24 Apr 2003Astrogravs '0314 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

24 Apr 2003Astrogravs '0315 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?

24 Apr 2003Astrogravs '0316 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?

24 Apr 2003Astrogravs '0317 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.