Dynamics of Nuclear Star Clusters

David Merritt* “Central Massive Objects” ESO Garching, 22-25 June 2010

*with: Fabio Antonini Pat Cote Roberto Capuzzo-Dolcetta Alessandra Mastrobuono Battisti Slawomir Piatek Eugene Vasiliev ....

Image: NASA/JPL-Caltech/S. Stolovy (Spitzer Science Center /Caltech)

Thursday, July 1, 2010 I. Formation via cluster infall

II. Evolution over relaxation time scales

III. Triaxiality and its consequences

Thursday, July 1, 2010 I. Formation

Black Holes Nuclear Star Clusters

Rees 1988 Milosavljevic 2008

Thursday, July 1, 2010 Why Migration of Star Clusters?

1. Infall time scales for globular clusters are roughly correct

2. While they often contain young stars, the dominant populations of NSCs are old

4 6 3. Migration of 10 -10 M⊙ objects to the center is common to both gas- and stellar-dynamical models

4. A massive “seed” is probably required for gas infall scenarios to work

5. Stars are easier than gas 4

Thursday, July 1, 2010 Miocchi & Capuzzo- Dolcetta (2009)

Also:

Fellhauer & Kroupa (2002)

Bekki et al. (2004)

Thursday, July 1, 2010 Sequential Mergers of Clusters

Energy conservation implies

Ef = Ei + Eorb + Ecl where

Ei,f = initial, ﬁnal energy of nucleus E = cluster internal energy = Gm2/2r cl − E = cluster orbital energy = αGmM /2R , α 1 orb − i i ≈ Then

Mj+1 =(j + 1)M1 (M1 = m)

jEj+1 =(j + α)Ej + jE1

2 1 1 1 (j + 1) Rj−+1 = j(j + α)Rj− + R1−

Thursday, July 1, 2010 Sequential Mergers of Clusters

α =0.8 Radius-mass relation

α =1.2

Thursday, July 1, 2010 M = 10 m 1 GC

M = m 1 GC

Predicted relation

Piatek et al. (unpublished)

Thursday, July 1, 2010 Now Add a Supermassive Black Hole...

Complete disruption occurs when M 1/3 r • R ≈ M GC GC i.e. 1/6 1/3 r M − MGC − RGC • 2 7 6 rinﬂ ≈ 10 M 10 M 3pc ⊙ ⊙

∴ The smallest NSCs should have sizes ~ a few x rinfl in galaxies with SMBHs

6 E. g. M● = 10 M⊙, rmin ~ 3 pc ? 7 M● = 10 M⊙, rmin ~ 10 pc ✓

Thursday, July 1, 2010 Cluster:

6 MGC = 4x10 M⊙ (untruncated) 6 = 1.1x10 M⊙ (truncated) σ(0) = 35 km s-1

Galaxy:

ρ(1 pc) = -3 400 Msun pc ρ ~ r -0.5

A. Battisti et al.

Thursday, July 1, 2010 Cluster:

6 MGC = 4x10 M⊙ (untruncated) 6 = 1.1x10 M⊙ (truncated) σ(0) = 35 km s-1

Galaxy:

ρ(1 pc) = -3 400 Msun pc ρ ~ r -0.5

A. Battisti et al.

Thursday, July 1, 2010 Surface Density Profiles First Infallt Second Infallt Third Infallt

Galaxy :lnΣ =lnΣ b(R/r )1/n +1 e − e 1 2 2 − Cluster : Σ = Σ0 1+R /r0 Battisti et al. (2010) 11

Thursday, July 1, 2010 Mass-Radius Relation

R ∝ M

BH influence radius Initial cluster radius Battisti et al. (2010)

Thursday, July 1, 2010 First Infallt

Battisti et al. (2010) 13

Thursday, July 1, 2010 Second Infallt

Battisti et al. (2010) 14

Thursday, July 1, 2010 Third Infallt

Battisti et al. (2010) 15

Thursday, July 1, 2010 Growth Timescales - dE Galaxies

Lotz et al. (2001): Examined globular cluster systems in 51 Virgo, Fornax dE galaxies.

Summed radial distributions Observed/predicted NSC magnitudes16

Thursday, July 1, 2010 Growth Timescales - gE Galaxies

Assume that the mass density of the galaxy follows

γ ρ(r)=ρa(r/ra)−

The time for a GC at initial radius r0 to spiral in to the center is (6 γ)/2 C(γ) r3 ρ 1/2 r − ∆t = a a 0 ln Λ MGC G ra 3 1 1/2 (6 γ)/2 10 ra MGC − ρa r0 − 9 10 yr 5 3 ≈ × 1kpc 10 M 1M pc− ra ⊙ ⊙ The time for GCs initially within Re to spiral to the center is

1.8 1 R M − ∆t 3 1011yr e GC 1/2 ≈ × 1kpc 105M ⊙ 17

Thursday, July 1, 2010 Cote et al. (2007)

Thursday, July 1, 2010 II. Relaxation

Half-mass relaxation times*

• galaxy

✡ NSC

*assuming no SMBHs

Thursday, July 1, 2010 Net effect of two-body relaxation depends on whether the galaxy is “hotter” or “colder” than the NSC.

If the galaxy is hotter, it transfers heat to the NSC on a timescale:

ρ 1/2 V 1/2 τ nuc nuc (t t )1/2 heat ≈ ρ V nuc gal gal gal 1/2 (tnuctgal)

roughly the geometric mean of the galaxy and NSC relaxation times.

Dokuchaev & Ozernoi (1985) Kandrup (1990) Quinlan (1996)

Thursday, July 1, 2010 This heat transfer will reverse core collapse if

1 1 τ τ ξ− t 10 ξ− 300 heat cc ≡ nuc i.e.

M ξ 1 2 r 5 nuc 104 − nuc M 100 r gal gal

More generally, one finds a critical size:

M r B nuc = A nuc M r gal gal above which a NSC expands rather than contracts; A and B depend (weakly) on the galaxy density profile

Thursday, July 1, 2010 Core Collapse vs. Core Expansion

Merritt (2009)

Thursday, July 1, 2010 Evidence of NSC Evaporation?

expand M r B } nuc = A nuc Mgal rgal gal /r nuc r O tevol ⪆ 10 Gyr collapse ● tevol ⪅10 Gyr

Merritt (2009)

Thursday, July 1, 2010 Adding a Black Hole

A large BH reverses the temperature gradient, slowing M /Mgal =0.03 • the transfer of heat from galaxy to NSC

4 A small BH inhibits core M /Mgal = 10− • collapse, causing the NSC to expand more quickly

Merritt (2009)

Thursday, July 1, 2010 van den Bergh (1986):

Nucleation fraction vs. galaxy magnitude

Perhaps NSCs in fainter spheroids were destroyed by heating from the galaxy.

MB = -16 -14 -12 -10 25

Thursday, July 1, 2010 III. Triaxiality Poon & Merritt (2001)

(g-i) pyramids (a) chaotic Orbits in Triaxial BH Nuclei (b-c) tubes

Thursday, July 1, 2010 Self-Consistent Triaxial NSCs

γ =1,T=0.75 γ =2,T=0.75 γ ρ r− ∝ a2 b2 T − ≡ a2 c2 − F = orbital fraction

Pyramid Tube

Chaotic Poon & Merritt (2004)

Thursday, July 1, 2010 Pyramid Orbits

• ~ Keplerian ellipses • Librate about short axis • Integrable (regular)* • e ⇒ 1 at the corners! 1 e2 −

*for rGR r rinﬂ

Merritt & Vasiliev (2010)

Thursday, July 1, 2010 Pyramid Orbits

The time for pyramid orbits to “drain” T, yr 10 10 2-body relaxation is: Tdrain –2 9 =10 2/3 10 8 T M Scalar RR –3 • =10 tpyr 3 10 yr 2 6 ≈ × 10− 10 M 108 ⊙ Relativistic precession –3 7 =10 where T is the dimensionless 10 precession –2 =10 coefficient of triaxiality. 6 10 Vector RR Newtonian precession 105 rbh

104 Dynamical time The BH feeding rate can be much r, pc 103 greater than that due to two-body 10–3 10–2 10–1 1 10 relaxation. Merritt & Vasiliev (2010)

Thursday, July 1, 2010 Summary

• Accretion of globular clusters appears to be a viable model for NSC formation, at least in bulge-dominated systems

• Disappearance of NSCs in spheroids with MB > -16 may be due to relaxation effects (heating from the galaxy)

• Stellar tidal disruption rates might be very high in triaxial NSCs (if SMBHs are present)

Thursday, July 1, 2010