Constraints on Alternatives to Supermassive Black Holes
Constraints on Alternatives to Supermassive Black Holes
Constraints on Alternatives to Supermassive Black Holes
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<str<strong>on</strong>g>C<strong>on</strong>straints</str<strong>on</strong>g> <strong>on</strong> <strong>Alternatives</strong> <strong>to</strong><strong>Supermassive</strong> <strong>Black</strong> <strong>Holes</strong>Cole MillerUniversity of Maryland
Outline• Current observati<strong>on</strong>s.• Alternative #1: stellar clustersC<strong>on</strong>servative assumpti<strong>on</strong>s.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
Assumpti<strong>on</strong>s: Stellar Clusters• Want <strong>to</strong> be c<strong>on</strong>servative: make cluster lastas l<strong>on</strong>g as possible! (Maoz 1998)Point masses; minimizeinteracti<strong>on</strong>s. Identical masses; nomass segregati<strong>on</strong>. No bulk moti<strong>on</strong>(decreases time). Not centrallyc<strong>on</strong>centrated.
Relaxati<strong>on</strong> Time• Total mass M=10 8 M 8M sunin radius R,composed of mass m objects.• Relaxati<strong>on</strong> time ist rlx~10 9 yr M 81/2(M sun/m)(R/1 pc) 3/2
Evaporati<strong>on</strong>• Ultrac<strong>on</strong>servative c<strong>on</strong>straint: 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 <strong>to</strong> infinite central density in ~16t rlx• 20x shorter than evaporati<strong>on</strong>.• Normally, binary-single interacti<strong>on</strong>s willheat the cluster and stall collapse.• Are there limits <strong>to</strong> this heating?
Three-body heating
The Insufficiency of Binaries• Only hard binaries can heat.• Basic idea: if velocity dispersi<strong>on</strong> is highenough, binaries merge via gravitati<strong>on</strong>alradiati<strong>on</strong> before they can scatter.• N<strong>on</strong> point mass objects would collide.• Less massive binaries merge faster.…and now the details!
Gravitati<strong>on</strong>al Radiati<strong>on</strong>• Velocity dispersi<strong>on</strong> v, hard/soft boundary isat semimajor axis a~2Gm/v 2 .• For a given a, merger time is l<strong>on</strong>gest 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)
C<strong>on</strong>diti<strong>on</strong> for Heating• T merge>T 3-bodthen requiresm>20M sun(v/1000 km/s) 5/2 M 8.• Therefore, larger masses needed <strong>to</strong> avoidcore collapse.• But this reduces relaxati<strong>on</strong> time,accelerating evaporati<strong>on</strong>.
Minimum mass for binary heating
Exotic Stars and Dark Matter• Suppose mass c<strong>on</strong>sists of elementaryparticles or is an exotic star.• Relaxati<strong>on</strong> time is large or irrelevant.• What other c<strong>on</strong>straints enter?
Accelerated Stellar Dynamics• If dark matter pervades regi<strong>on</strong>, normaldynamical processes and mass segregati<strong>on</strong>are accelerated.• Stars undergo core collapse, merge in centeranyway!• What if dark mass is c<strong>on</strong>centrated in center?
Stellar-Mass <strong>Black</strong> <strong>Holes</strong>• Suppose stellar-mass BH exist as normal.• If dark mass is very c<strong>on</strong>centrated (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 c<strong>on</strong>sumesentire object quickly.• If n<strong>on</strong>-interacting dark matter, BH stillc<strong>on</strong>sumes if it moves around.
C<strong>on</strong>clusi<strong>on</strong>s• Milky Way, NGC 4258, M31 all presentextremely str<strong>on</strong>g cases for SMBH.• To rule out stellar clusters, core collapsetime is usually relevant.• Existence of stellar-mass black holesimplies SMBH in many cases.