An Explanation for the Slopes of Stellar Cusps in Galaxy Spheroids
  The stellar surface mass density profiles at the centers of typical ~L* and
lower-mass spheroids exhibit power law 'cusps' with $\Sigma \propto R^(-n)$,
where 0.5<n<1 for radii ~1-100 pc. Observations and theory support models in
which these cusps are formed by dissipative gas inflows and nuclear starbursts
in gas-rich mergers. At these comparatively large radii, stellar relaxation is
unlikely to account for or strongly modify the cuspy stellar profiles. We argue
that the power-law surface density profiles observed are a natural consequence
of the gravitational instabilities that dominate angular momentum transport in
the gravitational potential of a central massive black hole. The dominant mode
at these radii is an m=1 lopsided/eccentric disk instability, in which stars
torquing the gas can drive rapid inflow and accretion. Such a mode first
generically appears at large radii and propagates inwards by exciting
eccentricities at smaller and smaller radii, where M*(<R)<<M_BH. When the
stellar surface density profile is comparatively shallow with n<1/2, the modes
cannot efficiently propagate to R=0 and so gas piles up and star formation
steepens the profile. But if the profile is steeper than n=1, the inwards
propagation of eccentricity is strongly damped, suppressing inflow and bringing
n down again. Together these results produce an equilibrium slope of 1/2 < n <
1 in the potential of the central black hole. These physical arguments are
supported by nonlinear numerical simulations of gas inflow in galactic nuclei.
Together, these results naturally explain the observed stellar density profiles
of 'cusp' elliptical galaxies.
