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Interest in the behavior of atmospheres around neutron stars has grown astronomically in the past few years. Some of this interest arrived in the wake of the explosion of Supernova 1987A and its elusive remnant; spawning renewed interest in a method to insure material ``fall-back'' onto the adolescent neutron star in an effort to transform it into a silent black hole. However, the bulk of the activity with atmospheres around neutron stars is concentrated in stellar models with neutron star, rather than white dwarf, cores; otherwise known as Thorne-Zytkow objects. First a mere seed in the imagination of theorists, Thorne-Zytkow objects have grown into an observational reality with an ever-increasing list of formation scenarios and observational prospects. Unfortunately, the analytic work of Chevalier on supernova fall-back implies that, except for a few cases, the stellar simulations of Thorne-Zytkow objects are missing an important aspect of physics: neutrinos. Neutrino cooling removes the pressure support of these atmospheres, allowing accretion beyond the canonical Eddington rate for these objects.
We present here the results of detailed hydrodynamical simulations in one and two dimensions with the additional physical effects of neutrinos, advanced equations of state, and relativity over a range of parameters for our atmosphere including entropy and chemical composition as well as a range in the neutron star size. In agreement with Chevalier, we find, under the current list of formation scenarios, that the creature envisioned by Thorne and Zytkow will not survive the enormous appetite of a neutron star. However, neutrino heating (a physical effect not considered in Chevalier's analysis) can play an important role in creating instabilities in some formation schemes, leading to an expulsion of matter rather than rapid accretion. By placing scrutiny upon the formation methods, we can determine the observational prospects for each.
