1. Dynamics of Galactic Nuclei MODEST 6 Evanston, 2005

2. Sersic n > 4 Σ ~ R -Γ Γ < 0.5 Σ R M B < -20

3. Sersic n > 4 Σ ~ R -Γ Γ < 0.5 Σ R M B < -20

4. Sersic n > 4 Sersic n ≈ 4 Σ ~ R -Γ Γ < 0.5 Σ ~ R -Γ 0.5 < Γ < 1.2 Σ R R M B < -20-18 < M B < -20

5. Sersic n > 4 Sersic n ≈ 4 Σ ~ R -Γ Γ < 0.5 Σ ~ R -Γ 0.5 < Γ < 1.2 Σ R R M B < -20-18 < M B < -20

6. Sersic n > 4 Sersic n ≈ 4 Sersic n < 4 Σ ~ R -Γ Γ < 0.5 Σ ~ R -Γ 0.5 < Γ < 1.2 ? PSF Σ R R R M B < -20-18 < M B < -20M B < -18

7. Sersic n > 4 Sersic n ≈ 4 Sersic n < 4 Σ ~ R -Γ Γ < 0.5 Σ ~ R -Γ 0.5 < Γ < 1.2 ? PSF Σ R R R M B < -20-18 < M B < -20M B < -18

8. Local-Group-Galaxy Density Profiles Genzel et al. 2003Lauer et al. 1998 rhrh

9. Nuclear Relaxation Times ● BH mass from M-sigma relation ○ BH mass from M-L relation * “Core” galaxies Luminosity profile data: Coté et al. ACS Virgo Survey

10. Nuclear Relaxation Times Relaxation times begin to drop below 10 10 yr for M B > -19 M32

11. Preto, Merritt & Spurzem 2004 “Collisional” Cusp In ~ one relaxation time T r, a power-law cusp of slope ρ ~ r -7/4 grows around a black hole, within a distance ~r h : r h ≡ GM bh /σ 2 (Bahcall & Wolf 1976).

12. “Collisional” Cusp In ~ one relaxation time T r, a power-law cusp of slope ρ ~ r -7/4 grows around a black hole, within a distance ~r h : r h ≡ GM bh /σ 2 (Bahcall & Wolf 1976). At the Galactic center, r h ≈ 2 pc, T r (r h ) ≈ 3 Gyr. Preto, Merritt & Spurzem 2004 Baumgardt et al. 2004 rhrh

13. Milky Way Density Profile Schödel et al. (in prep.) r h ≈ 50" Σ ~ R -3/4

14. Black Hole Feeding Rates Based on: “Nuker” luminosity profiles Cohn-Kulsrud loss- cone boundary conditions (Not quite self-consistent.) Wang & Merritt 2004 MW

15. Nuclear Expansion Loss of stars via tidal disruption represents a heat source for the nucleus, causing it to expand. The expansion time scale is ~T r. (Shapiro 1977) This expansion may be described by the self-similar, post-collapse solutions of Henon, Heggie and others. → Dense nuclei were once denser. Baumgardt et al. 2005

16. Low-Density Nuclei Bright galaxies have (non-isothermal) “cores” This is plausibly due to mergers, and the “scouring” effects of binary SMBHs. NGC 3348 A. Graham 2004

17. Binary Black Holes Galaxies merge Binary forms Binary decays, via: -- ejection of stars -- interaction with gas

18. Binary Evolution in Power-Law Nucleus a Szell, Merritt & Mikkola 2005

19. Binary Evolution in Power-Law Nucleus Szell, Merritt & Mikkola 2005 Also: Makino & Funato 2004 Berczik, Merritt & Spurzem 2005 a

20. What Values of N are Required? N fixes the ratio of relaxation time to crossing time: N T relax /T cross 10 2 2.2 10 3 14.5 10 4 109 10 5 870 10 6 7250 10 11 3.9x10 8 Any process that depends on the separation of the two time scales, requires a large N.

21. In loss-cone problems, this requirement is more severe. Stars are scattered by other stars into the loss cone, where they can interact with the central object(s). Scattering time is ~θ 2 T relax <<T relax and separation of the two time scales requires T relax >>θ -2 T cross single or binary black hole θ star

22. Minimum Number of Stars Required to “Resolve” Central Object Minimum N required to “resolve” central object. r t = size of central object r h = influence radius of black hole(s) Binary BH

23. Binary Evolution in Power-Law Nucleus a Full loss cone Empty loss cone Szell, Merritt & Mikkola 2005

24. Binary Evolution in Plummer – Law Galaxy Berczik, Merritt & Spurzem 2005

25. Eccentricity Evolution N = 8K 16K 32K 65K 131K 262K Szell, Merritt & Mikkola 2005 eccentricity time

26. Eccentricity Evolution N = 8K 16K 32K 65K 131K 262K Szell, Merritt & Mikkola 2005 eccentricity time

27. “Mass Deficits” N = 8K 16K 32K 65K 131K 262K Szell, Merritt & Mikkola 2005 “Mass deficit” produced by equal-mass binary.

28. Cusp Regeneration After being destroyed by a binary SBH, a power-law cusp can regenerate itself. Condition: relaxation time after cusp destruction must be < 10 10 yr. Initial binary: m 2 /m 1 = 0.1 T r (r h ) = 340 Merritt & Szell 2005

29. For the Future… Algorithms/hardware for N >>10 6, direct-integration algorithms. Further development of chain-regularization algorithms for BH(s) Evolution of binary SBHs, starting from realistic initial conditions “Mass deficits” produced by multiple mergers Better understanding of SBH-driven nuclear expansion Interplay of dark and luminous matter Effects of mass spectra Feeding rates in non-relaxed nuclei -- ….. !

30. Title