Steeper stellar cusps in galactic centers from binary disruption
  The relaxed distribution of stars around a massive black hole is known to
follow a cusp profile $\rho(r)\propto r^{-\alpha}$ with characteristic slope
$\alpha=7/4$. This follows from energy conservation and a scattering rate as
given by two body encounters. However, we show that injection of stars close to
the black hole, i.e. a source term in the standard cusp picture, modifies this
profile. In the steady-state configuration, the cusp develops a central region
with typical slope $\alpha=9/4$ in which stars diffuse outward. Binary
disruption by the intense tidal field of the massive black hole is among the
phenomena that take place in the Galactic Center. In such disruption, one of
the binary members remains bound to the black hole, thus providing a source
term of stars close to the black hole. Assuming a binary fraction of $0.1$ and
an orbital circularization efficiency of $0.35$, we show that this source is
strong enough to modify the cusp profile within $\approx 0.07$ pc in the
Galactic Center. If the binary fraction at the influence radius is of order
unity and the orbits of all the captured stars are efficiently circularized,
the steeper cusp extends almost as far as the radius of influence of the black
hole.
