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Cusp Formation in Galactic Nuclei . Brian Murphy ( Butler University ) Kim Phifer, Brian Geiss, and Michael McFall. A Bit of History. Peebles (1972) : Suggests possible observable light cusp near black hole suggest a non thermal power-law cusp r -9/4 Bachall & Ostriker (1975)
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Cusp Formation in Galactic Nuclei Brian Murphy (Butler University) Kim Phifer, Brian Geiss, and Michael McFall
A Bit of History • Peebles (1972) : • Suggests possible observable light cusp near black hole • suggest a non thermal power-law cusp r-9/4 • Bachall & Ostriker (1975) • Propose MBHs as source of X-rays in globular star clusters • Bachall & Wolf (1976,1977) • Using a rudimentary 1D Fokker-Planck treatment show that the cusp should have the form r-7/4. • Young (1978) • Observes light cusp in M87 • Grindlay et al. (1984) • Radial offsets of X-ray sources in globular clusters argues against MBHs • Djorgovski & King (1984) • Observe stellar cusp in a number of globular star clusters.
Clusters With No Central Black Hole Star-Star scatterings lead to diffusion in orbital energy leading to an expanding halo and contracting core. After roughly 15 half-mass relaxation times the core collapses. In the idealized identical star case the resulting cusp slope ρ ~ r-2.2 .
Core Collapsed Globular Cluster M15 But the surface brightness profile is more like Σ ~ r-0.7 Indicating that ρ~ r-1.7 Why? Unlike the idealized case, stars are not of equal masses.
Mass Segregation Equipartition drives mass segregation ½ m1v12 = ½ m2v22 The most massive stars fall inward accelerating core collapse by nearly a factor of 5 for a typical mass function. The result is that luminous but less massive giants stars to have a flatter profile that the more massive remnants: ρ1 ~ r –β Where β= 1.9m1/m2+0.35 .
Clusters with Central Black Holes A Keplerian potential is introduce and tidal disruption of stars become a factor. These conditions lead to (Bachall & Wolf 1976). In the multimass scenario the most dominant group will have a -7/4 slope with the lower mass groups nearing a cusp slope of -3/2 (Bachall and Wolf 1977).
Stellar Collisions The rate of collisions given by Collisions will be most frequent in the high density high velocity region of the nucleus. Thus collisions tend to deplete stellar orbits bound to the MBH. Therefore the collisionally dominated regions will be populated by stars on unbound orbits. This results in
Evolving Model of the Galactic Center • Assume Kroupa (2001) mass function • Use stellar evolution prescription of Hurley et al. (2000) • Initial mass of the nucleus set at 6.4×107 Msun • Initial half-mass radius of 6 pc. • Initial seed black hole of 10-5 Mnucleus • Growth of MBH fueled by cluster mass loss
Galactic Center Total Stars
Mall Loss Mechanisms Total Stellar Evolution Tidal Disruptions Stellar Collisions
Summary • Stellar mass black holes and other remnants dominate the inner 0.5 parsec. • In the Galactic Center tidal disruptions are the primary destruction mechanism. • In higher density nuclei stellar collisions dominate • Tidal disruptions can flatten the cusp for bright giant stars but only for r < 0.1 parsec.
