Forming Intermediate-Mass Black Holes in Dense Clusters Through Collisional Run-away

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1 Forming Intermediate-Mass Black Holes in Dense Clusters Through Collisional Run-away Marc Freitag ARI, Heidelberg Collaboration with Atakan Gürkan & Frederic Rasio (NU) SFB 439: Galaxies in young universe A5: Formation and growth of black holes in galactic nuclei

2 Routes to form (I)MBHs Cluster of MS stars with IMF Core collapse through mass segregation Is there "not too hard" binaries? no Collapse stalls T cc > 3 Myrs? no Collapse reversed until......stellar remnants collapse Binaries form (3 body interac.) Efficient ejection? Role of remnant MF? Massive stars evolve before core collapse Strong mass loss (if metallicity high enough) Dense cluster of compact stars σ v c? no Gas lost from cluster?? no (very unlikely) no Stellar formation? no Massive gas cloud + stars? Disruptive collisions σ v GM R 500 km s 1? VMS grows into a SMS? What limits its mass? VMS turn into an IMBH? Role of metallicity? no Sticking collisions Run away formation of VMS M 100 M no no Remnants evaporate Cluster with very long evol. time Remnants merge by GW emission Role of GW recoil? IMBH has formed! Growth to MBH? Delivery to galactic centre?

3 Run-away collisions to form (I)MBHs? (Rasio, Freitag & Gürkan, 2003; Gürkan, F & R, 2004; Freitag, G & R, in prep.) How it should work 1 If collisions (mergers) faster than stell. evol.: Run-away formation of a very massive star (VMS, M > 100 M ). Mass-segr. T coll! 2 If low metallicity, VMS leaves an IMBH as remnant. It worked... in previous numerical simulations Quinlan & Shapiro 90: Fokker-Planck models of proto-galactic nuclei. But: unphysical IMF (single-mass) & treatment of collisions Portegies Zwart & McMillan 02; Portegies Zwart et al. 04: N-body models of populous young clusters. Binaries may foster collisions. But can it really work in proto-galactic nuclei, with σ v few 100 km s 1? Binaries play little role. Single single collisions occur as ρ c. Mergers (δm > 0) vs. disruptive collisions (δm < 0)??

4 Monte Carlo stellar dynamics code (Joshi et al. 2000, ApJ 540, 969; 2001 ApJ 550, 691) (Freitag & Benz 2001, A&A 375, 711; 2002, A&A 395, 345) Goal: simulate cluster over yrs Chosen method: Hénon s MC scheme Direct N-body: T CPU N 2 3 MC code: T CPU N ln(n) Strengths and limitations from 3 assumptions: Spherical sym. Dyn. equilibrium Diffusive relaxation Cluster = set of spherical shells Shell = symmetrised contribution of 1 many with same properties Time step: fraction of T relax (R) and/or T coll (R) Avoids explicit orbital integration Allows rich physics: Cluster (+central BH) self-gravity; V anisotropy; Any M spectrum 2-body relaxation; Stellar collisions (from SPH); Stellar evolution Tidal disruptions; Horizon-crossings; GW-captures ( loss-cone )

5 Phase I: Mass-segregation induced core collapse PC_1522

6 Mass-segregation induced core collapse Following the central densities and velocity dispersions evolution with gaseous model (15 mass components)... The velocity dispersion of the most massive stars do not increase until very late collapse.

7 How fast can core-collapse be? Plummer models with various mass functions.

8 How fast can core-collapse be? King models with various concentrations. With a broad mass spectrum, T cc T rc (0)!

9 How fast need core-collapse be? Goal: bring massive stars to the centre before they evolve off the MS.

10 Phase II: Let the massive stars collide! Collision probability between neighboring particles: P (12) coll = nv rel S (12) coll δt with S(12) coll = πb 2 max = π(r 1 + R 2 ) 2»1 + V (12) = p 2G(M 1 + M 2 )/(R 1 + R 2 ) Monte Carlo sampling of collision initial conditions: particles properties V rel, M 1, M 2 impact parameter according to dp db b b max V (12) /V rel 2 Any prescription can be used for the outcome of collisions = BEWARE: Interpolation between the results of SPH simulations by Delaunay triangulation in 4D (M 1, M 2, V rel, b) space (Longing for fitting formulae... ) Extrapolation for M > 75 M. interpolation artifacts!

11 Collisions in the MC runs: Collisional rejuvenation Stellar evolution of collisional products: unsolved problem We assume: Stars contract back to thermal equilibrium instantaneously They always have MS structure with univocal M R relation Minimal rejuvanation during collisions: the He cores merge together, the H envelopes combine to form new envelope, only H is lost during collisions. Effective age set by mass of core He: M He c (t) = Mc He TMS t t MS

12 Missing the run-away phase... Note the second collapse, caused by stellar BHs. Their density reaches pc 3 at the end!

13 Run-away formation of a very massive star PC_1579, PC_1613

14 Run-away formation of a very massive star Merging tree for the formation of a 5000 M star. Most mass comes from stars of 100 M PC_1579

15 The fast core-collapse domain Condition for Run-away collisions: T cc < 3 Myr T rc < 20 Myr

16 Open questions... Stellar dynamics Role of binaries Loss-cone effects for collision with the VMS What is the minimum number of stars in the core for the run-away to work? Hydrodynamics Collisions featuring VMS (is there a transparency problem?) Stellar evolution Role of pre-ms phase Stability and evolution of VMS subject to constant accretion of other stars End product of VMS evolution: an IMBH?