# Presentation: 042309

## Astrophysics of Captures

- Steinn Sigurdsson
- Dept Astro & Astrop, & CGWP
- Penn State

- Astrogravs '03

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003

## 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

- 24 Apr 2003