Exponential Disks from Stellar Scattering: III. Stochastic Models
  Stellar scattering off irregularities in a galaxy disk has been shown to make
an exponential radial profile, but no fundamental reason for this has been
suggested. Here we show that exponentials are mathematically expected from
random scattering in a disk when there is a slight inward bias in the
scattering probability. Such a bias was present in our previous scattering
experiments that formed exponential profiles. Double exponentials can arise
when the bias varies with radius. This is a fundamental property of scattering
and may explain why piece-wise exponential profiles are ubiquitous in galaxies,
even after minor mergers and other disruptive events.
