Power-law Sersic profiles in hydrostatic stellar galaxy discs

Previously, we showed that surface density profiles of the form of a power-law times a Sersic function satisfy the hydrostatic Jeans equations, a variety of observational constraints, and the condition of a minimal radial entropy profile in two-dimensional galaxy discs with fixed power-law, halo potentials. It was assumed that such density profiles are generated by star scattering by clumps, waves, or other inhomogeneities. Here we generalize these models to self-gravitating discs. The cylindrically symmetric Poisson equation imposes strong constraints. Scattering processes favor smoothness, so the smoothest solutions, which minimize entropy gradients, are preferred. In the case of self-gravitating discs (e.g., inner discs), the gravity, surface density and radial velocity dispersion in these smoothest models are all of the form 1/r times an exponential. When vertical balance is included, the vertical velocity dispersion squared has the same form as the surface density, and the scale height is constant. In combined self-gravitating plus halo gravity cases, the radial dispersion has an additional power-law term. Nonetheless, the surface density profile has the same form at all radii, without breaks, satisfying the disc-halo conspiracy. The azimuthal velocity and velocity dispersions are smooth, though the former can have a distinct peak. In these models the vertical dispersion increases inwards, and scattering may mediate a transition to a secular bulge. If halo gravity dominates vertically in the outer disc, it flares. The models suggest a correlation between disc mass and radial scale length. The combination of smoothness, simplicity, ability to match generic observational features and physical constraints is unique to these models.