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Apparent exponential surface density profiles are nearly universal in galaxydiscs across Hubble types, over a wide mass range, and a diversity ofgravitational potential forms. Several processes have been found to produceexponential profiles, including the actions of bars and spirals, and clumpscattering, with star scattering a common theme in these. Based on reasonablephysical constraints, such as minimal entropy gradients, we propose steadystate distribution functions for disc stars, applicable over a range ofgravitational potentials. The resulting surface density profiles are generallya power-law term times a Sersic-type exponential. Over a modest range of Sersicindex values, these profiles are often indistinguishable from Type Iexponentials, except at the innermost radii. However, in certain parameterranges these steady states can appear as broken, Type II or III profiles. Thecorresponding velocity dispersion profiles are low order power-laws. A chemicalpotential associated with scattering can help understand the effects of longrange scattering. The steady profiles are found to persist through constantvelocity expansions or contractions in evolving discs. The proposeddistributions and profiles are simple and solve the stellar hydrodynamicequations. They may be especially relevant to thick discs, which have settledto a steady form via scattering.

Near-exponential surface densities as hydrostatic, nonequilibrium profiles in galaxy discs