Near-exponential surface densities as hydrostatic, nonequilibrium
  profiles in galaxy discs
  Apparent exponential surface density profiles are nearly universal in galaxy
discs across Hubble types, over a wide mass range, and a diversity of
gravitational potential forms. Several processes have been found to produce
exponential profiles, including the actions of bars and spirals, and clump
scattering, with star scattering a common theme in these. Based on reasonable
physical constraints, such as minimal entropy gradients, we propose steady
state distribution functions for disc stars, applicable over a range of
gravitational potentials. The resulting surface density profiles are generally
a power-law term times a Sersic-type exponential. Over a modest range of Sersic
index values, these profiles are often indistinguishable from Type I
exponentials, except at the innermost radii. However, in certain parameter
ranges these steady states can appear as broken, Type II or III profiles. The
corresponding velocity dispersion profiles are low order power-laws. A chemical
potential associated with scattering can help understand the effects of long
range scattering. The steady profiles are found to persist through constant
velocity expansions or contractions in evolving discs. The proposed
distributions and profiles are simple and solve the stellar hydrodynamic
equations. They may be especially relevant to thick discs, which have settled
to a steady form via scattering.
