The ~ 108−109 old neutron stars in the Galaxy may be undergoing low luminosity accretion from the interstellar medium (Ostriker et al. 1970; Shvartsman 1971). It was first recognized by Shvartsman (1971) that the accretion induced radiation from the stellar surface can heat the infalling material, which in turn inhibits further accretion. This preheating instability has been studied in detail in the high luminosity regime where equilibrium ionization and heating holds (e.g., Buff & McCray 1974; Ostriker et al. 1976; Cowie et al. 1978). In the low luminosity regime, however, dynamical timescales are typically much shorter than atomic timescales so the accretion flow dynamics is strongly coupled to non-equilibrium (NEQ) atomic processes (cf. Blaes et al. 1995).