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A Recipe for Making Intermediate Mass Black Holes Doug Hamilton U. Maryland Review In collaboration with Cole Miller, Kayhan Gultekin, and Vanessa Lauberg Pathways to Intermediate Mass Black Holes Low Metallicity Normal Stars Colliding Stars Very Massive Stars Stellar Reviewmass BH BH mergers stellar mergers 100 Msun BH BH mergers 300 -1000 Msun BH Numerical Simulations 1. Start with an (X:10)Msun binary black hole 2. Wait until another 10Msun BH approaches 3. Resolve the encounter 4. Encounter Time > Merger Time? Yes No Merge Masses, Repeat History of 3 Body Encounters 100:10:10 Semimajor Axis Pericenter Distance History of 3 Body Encounters 1000:10:10 Semimajor Axis Pericenter Distance Semimajor Axis Distribution Just after the Last Encounter Eccentricity Distribution Just after the Last Encounter Eccentricity Distribution in the LISA Band Porb = 1000 s Gravitational Waves from IMBHs Lisa Sensitivity Curve Local Globular Virgo Cluster IMBH Mergers from Single-Binary Encounters In a cluster with vesc = 50km/s, 10Msun interlopers Number of Encounters Number of Ejections Merger Time 100+10 93 20 15Myr 1000+10 483 87 4.4Myr Binary Ejections: Probability of building up from 100 to 300: 16% Probability of building up from 50 to 300: 1% Process is very inefficient! Additional Effects that decrease efficiency ... Near Ejections that increase efficiency ... Mass Distribution of Black Holes Direct 2 -Body Capture (M > 500 Msun) Secular Effects in Triple Systems Halo Core Why Do Large Masses Exchange In? M3 M1 M2 1. Larger masses move more slowly & are more focused 2. Large mass M3 gives larger impulse to M2 Binary -Binary Interactions Any of the Mj can be tight binaries M3 M1 M2 A tight binary will often swap into a wide binary to form a hierarchal triple. Evolution of these triples by subsequent encounters is common and important! Secular Evolution of Triples Individual orbital energies are conserved. Angular momentum is exchanged. Oscillations in eccentricity and inclination. Timescale set by the tidal acceleration imposed by the distant object on the binary. Can be very rapid compared to encounter times. Kozai Resonance (Restricted Problem) Kozai (1962) considered a test particle in a binary influenced by a distant third companion. The test particle's pericenter and node librate with large correlated oscillations in eccentricity and inclination. The quantity Lz = sqrt(1-e^2)cos i is conserved. The Critical Inclination is 90o. Planetary Applications: Asteroids Oort Cloud comets Extrasolar Planets Distant Planetary Satellites What if the Moon had an i=90 Orbit? General Kozai Resonance Assume: No constraint on the masses, Hierarchal triple, Quadrupole order Then: Outer planet's eccentricity e2 is constant. Cyclic oscillations (often extreme) in e1 & i1 & i2. Critical Inclination 90o < i < 180o. Curiosity: start with counter-rotating coplanar orbits then outer orbit reverses and inner merges Kozai Critical Inclination Newtonian Gravity, m0=m1 The Loss Cone GR included Equal masses The Effect of Triples Much more rapid merger rates. Mergers without three-body recoil. Significantly fewer ejections. Bottom Line IMBH production efficiency greatly enhanced by triples. What do We Learn from a Detection of one or more IMBHs? If formed from collapse of a massive star: maximally spinning IMBH, J/M^2 ~ 0.7-0.8 If formed from merger of multiple black holes: low spin IMBH, J/M^2 ~ 0.1-0.3 Secular Exchange of Angular Momentum Outer eccentric orbit, Inner circular orbit Review Outer less eccentric Inner more eccentric Chandra ULX Sources M82