We present a new analytical solution to the steady-state distribution of
stars close to a central supermassive black hole of mass ${M}_{\bullet}$ in the
center of a galaxy. Assuming a continuous mass function of the form $dN/dm\propto {m}^{\gamma}$ , stars with a specific orbital energy $x=G{M}_{\bullet}/r-{v}^{2}/2$ are scattered primarily by stars of mass ${m}_{\mathrm{d}}(x)\propto {x}^{-5/(4\gamma +10)}$ that dominate the scattering of both lighter and heavier
species at that energy. Stars of mass ${m}_{\mathrm{d}}(x)$ are exponentially rare at
energies lower than $x$ , and follow a density profile $n({x}^{\prime})\propto {x}^{\prime 3/2}$
at energies ${x}^{\prime}\gg x$ . Our solution predicts a negligible flow of stars
through energy space for all mass species, similarly to the conclusions of
Bahcall & Wolf (1977), but in contrast to the assumptions of Alexander & Hopman
(2009). This is the first analytic solution which smoothly transitions between
regimes where different stellar masses dominate the scattering.