Dynamics of Galactic Nuclei

MODEST 6

Evanston, 2005

Sersic n > 4

Σ ~ R-Γ

Γ < 0.5Σ

R

MB < -20

Sersic n > 4

Σ ~ R-Γ

Γ < 0.5Σ

R

MB < -20

Sersic n > 4

Sersic n ≈ 4

Σ ~ R-Γ

Γ < 0.5

Σ ~ R-Γ

0.5 < Γ < 1.2

Σ

R R

MB < -20 -18 < MB < -20

Sersic n > 4

Sersic n ≈ 4

Σ ~ R-Γ

Γ < 0.5

Σ ~ R-Γ

0.5 < Γ < 1.2

Σ

R R

MB < -20 -18 < MB < -20

Sersic n > 4

Sersic n ≈ 4

Sersic n < 4

Σ ~ R-Γ

Γ < 0.5

Σ ~ R-Γ

0.5 < Γ < 1.2?

PSFΣ

R RR

MB < -20 -18 < MB < -20 MB < -18

Sersic n > 4

Sersic n ≈ 4

Sersic n < 4

Σ ~ R-Γ

Γ < 0.5

Σ ~ R-Γ

0.5 < Γ < 1.2?

PSFΣ

R RR

MB < -20 -18 < MB < -20 MB < -18

Local-Group-Galaxy Density Profiles

Genzel et al. 2003 Lauer et al. 1998

rh

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

Nuclear Relaxation Times

Relaxation times begin to drop below 1010 yr for MB > -19

M32

Preto, Merritt & Spurzem 2004

“Collisional” Cusp

In ~ one relaxation time Tr , a power-law cusp of slope

ρ ~ r -7/4

grows around a black hole, within a distance ~rh:

rh ≡ GMbh/σ2

(Bahcall & Wolf 1976).

“Collisional” Cusp

In ~ one relaxation time Tr , a power-law cusp of slope

ρ ~ r -7/4

grows around a black hole, within a distance ~rh:

rh ≡ GMbh/σ2

(Bahcall & Wolf 1976).

At the Galactic center,

rh ≈ 2 pc, Tr (rh) ≈ 3 Gyr.

Preto, Merritt & Spurzem 2004

Baumgardt et al. 2004

rh

Milky Way Density Profile

Schödel et al. (in prep.)

rh ≈ 50"

Σ ~ R-3/4

Black Hole Feeding Rates

Based on:

• “Nuker” luminosity profiles

• Cohn-Kulsrud loss- cone boundary conditions

(Not quite self-consistent.)

Wang & Merritt 2004

MW

Nuclear Expansion

Loss of stars via tidal disruption represents a heat source for the nucleus, causing it to expand.

The expansion time scale is ~Tr .

(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

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

Binary Black Holes

Galaxies merge

Binary forms

Binary decays, via:-- ejection of stars-- interaction with gas

Binary Evolution in Power-Law Nucleus

a

a

1

Szell, Merritt & Mikkola 2005

Binary Evolution in Power-Law Nucleus

adt

d 1

a

1

Szell, Merritt & Mikkola 2005Also:Makino & Funato 2004Berczik, Merritt & Spurzem 2005

a

What Values of N are Required?

N fixes the ratio of relaxation time to crossing time:

crossrelax TN

NT

ln

1.0

N Trelax/Tcross

102 2.2

103 14.5

104 109

105 870

106 7250

1011 3.9x108

Any process that depends on the separation of the two time scales, requires a large N.

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

~θ2Trelax<<Trelax

and separation of the two time scales requires

Trelax>>θ-2Tcross

single or binary black hole

θ

star

Minimum Number of Stars Required to “Resolve” Central Object

Minimum N required to “resolve” central object.

rt = size of central objectrh = influence radius of black hole(s)

Binary BH

Binary Evolution in Power-Law Nucleus

aFull loss cone

Empty loss coneSzell, Merritt & Mikkola 2005

Binary Evolution in Plummer – Law Galaxy

Berczik, Merritt & Spurzem 2005

Eccentricity Evolution

N = 8K 16K 32K 65K 131K 262K

Szell, Merritt & Mikkola 2005

ecce

ntric

ity

time

Eccentricity Evolution

N = 8K 16K 32K 65K 131K 262K

Szell, Merritt & Mikkola 2005

ecce

ntric

ity

time

“Mass Deficits”

N = 8K 16K 32K 65K 131K 262K

Szell, Merritt & Mikkola 2005

“Mass deficit” produced by equal-mass binary.

Cusp Regeneration

After being destroyed by a binary SBH, a power-law cusp can regenerate itself.

Condition: relaxation time after cusp destruction must be < 1010 yr. • Initial binary:

m2/m1 = 0.1

• Tr(rh) = 340

Merritt & Szell 2005

For the Future…

• Algorithms/hardware for N >>106, 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

• -- ….. !

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