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The stellar surface mass density profiles at the centres of typical  ∼ L  *   and lower mass spheroids exhibit power‐law ‘cusps’ with  Σ∝ R  −η  , where  0.5 ≲η≲ 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 disc 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  * (&lt;  R ) ≪ M  BH  . When the stellar surface density profile is comparatively shallow with  η &lt; 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  η= 1 , the inward propagation of eccentricity is strongly damped, suppressing inflow and bringing η down again. Together these results produce an equilibrium slope of  1/2 ≲η≲ 1  in the potential of the central black hole. These physical arguments are supported by non‐linear numerical simulations of gas inflow in galactic nuclei. Together, these results naturally explain the observed stellar density profiles of ‘cusp’ elliptical galaxies.

An explanation for the slopes of stellar cusps in galaxy spheroids