We present a new analytical solution to the steady-state distribution of stars close to a central supermassive black hole of mass M • in the center of a galaxy. Assuming a continuous mass function of the form dN / dm ∝ m γ , stars with a specific orbital energy x = GM •/r − v 2/2 are scattered primarily by stars of mass m d(x) ∝ x −5/(4γ+10) that dominate the scattering of both lighter and heavier species at that energy. Stars of mass m d(x) are exponentially rare at energies lower than x, and follow a density profile n ( x ′ ) ∝ x ′ 3 / 2 at energies x ′ > x . Our solution predicts a negligible flow of stars through energy space for all mass species, similarly to the conclusions of Bahcall & Wolf, but in contrast to the assumptions of Alexander & Hopman. This is the first analytic solution that smoothly transitions between regimes where different stellar masses dominate the scattering.
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The authors would like to thank Nicholas Stone for useful discussions and suggestions. This research was partially supported by an ISF grant. I.L. acknowledges support from the Adams Fellowship.
© 2022. The Author(s). Published by the American Astronomical Society.