Massive Black Holes in Galactic Halos?

Abstract

We consider the idea that galaxy halos are composed of massive black holes, as a possible resolution of two problems: the composition of dark halos, and the heating of stellar disks. Scattering of disk stars by halo black holes with mass MH, velocity dispersion σH and number density nH causes the stellar velocity dispersion to increase with time t as σ≈(Dt)1/2 for t large, where D α nHM2H in Λ/σH, and in Λ is the Coulomb logarithm. This time-dependence is in good agreement with observations, as is the prediction for the axial ratios of the velocity ellipsoid σu: σv: σw. To account for the magnitude of the disk velocity dispersion in the solar neighbourhood, we require MH≈2 × 106M⊙. The stellar distribution function is predicted to be approximately isothermal at low epicyclic energies, in the Fokker-Planck regime in which the effect of the many distant, weak encounters dominates, but with a power-law tail at high energies produced by the relatively rare close encounters. This tail has the form N(E)αE−2, where E is the horizontal or vertical epicyclic energy, and N(E) is the number of stars per unit area of the disk, per unit E. The fraction of stars in this power-law tail depends only on the value of in Λ, and is about 1% for typical values. This provides a possible explanation for the high velocity A stars found in the solar neighbourhood. This disk heating mechanism can also account for the approximate constancy of the disk scaleheight with radius that is observed in other spiral galaxies, although this does not result as naturally as the other properties.