Constraints on Alternatives to Supermassive Black Holes

<strong>Constraints</strong> on Alternatives toSupermassive Black HolesCole MillerUniversity of Maryland

Outline• Current observations.• Alternative #1: stellar clustersConservative assumptions.The insufficiency of binary heating.• Alternative #2: exotic stars or dark matter.The role of stellar-mass black holes.See M. C. Miller, astro-ph/0512194

SourceMilky WayNGC 4258M31M87NGC 3115I1459NGC 4649NGC 4374NGC 4261Cyg Alog 10M (M sun)6.67.68.09.69.09.49.39.28.79.4v res(km/s)12000290020801430940910740650400310

Assumptions: Stellar Clusters• Want to be conservative: make cluster lastas long as possible! (Maoz 1998)Point masses; minimizeinteractions. Identical masses; nomass segregation. No bulk motion(decreases time). Not centrallyconcentrated.

Relaxation Time• Total mass M=10 8 M 8M sunin radius R,composed of mass m objects.• Relaxation time ist rlx~10 9 yr M 81/2(M sun/m)(R/1 pc) 3/2

Evaporation• Ultraconservative constraint: after ~300t rlx,cluster will evaporate.• Shorter than Hubble time for Milky Way,NGC 4258, but nothing else.• Argument by Maoz (1998).

Core Collapse• A Plummer sphere without binaries willcollapse to infinite central density in ~16t rlx• 20x shorter than evaporation.• Normally, binary-single interactions willheat the cluster and stall collapse.• Are there limits to this heating?

Three-body heating

The Insufficiency of Binaries• Only hard binaries can heat.• Basic idea: if velocity dispersion is highenough, binaries merge via gravitationalradiation before they can scatter.• Non point mass objects would collide.• Less massive binaries merge faster.…and now the details!

Gravitational Radiation• Velocity dispersion v, hard/soft boundary isat semimajor axis a~2Gm/v 2 .• For a given a, merger time is longest forcircular orbit.For e=0.7, 10 times shorter.• T merge~(5/8)(c/v) 5 (Gm/v 3 )~6x10 6 yr (1000 km s -1 /v) 8 (m/M sun)

Condition for Heating• T merge>T 3-bodthen requiresm>20M sun(v/1000 km/s) 5/2 M 8.• Therefore, larger masses needed to avoidcore collapse.• But this reduces relaxation time,accelerating evaporation.

Minimum mass for binary heating

Exotic Stars and Dark Matter• Suppose mass consists of elementaryparticles or is an exotic star.• Relaxation time is large or irrelevant.• What other constraints enter?

Accelerated Stellar Dynamics• If dark matter pervades region, normaldynamical processes and mass segregationare accelerated.• Stars undergo core collapse, merge in centeranyway!• What if dark mass is concentrated in center?

Stellar-Mass Black Holes• Suppose stellar-mass BH exist as normal.• If dark mass is very concentrated (e.g.,exotic star), BH still merge with it at no lessthan 10 -8 /yr (e.g., Pau, Marc, EMRI calcs).• If pressure-supported star, BH consumesentire object quickly.• If non-interacting dark matter, BH stillconsumes if it moves around.

Conclusions• Milky Way, NGC 4258, M31 all presentextremely strong cases for SMBH.• To rule out stellar clusters, core collapsetime is usually relevant.• Existence of stellar-mass black holesimplies SMBH in many cases.