Exponential galaxy discs as the quasi-stationary distribution in a Markov chain model simulating stellar scattering

Previous models have shown that stochastic scattering of stars in a two-dimensional galaxy disc can generate a time-independent surface density distribution that is an exponential divided by radius when a constant inward scattering bias is present. Here we show, using a Markov chain model, that similar profiles result from an outward scattering bias, although the disc surface density decreases slowly with time because of a net stellar outflow. The trend towards a near-exponential surface profile is robust, as it exists even if the scattering intensity has moderate radial and time dependences, subject to some limitations on the scattering rates discussed in the text. The exponential scale length of the pseudo-equilibrium disc depends on the scattering bias, the scattering length, and the size of the disc where scattering is important.