THERMAL STRUCTURE OF ACCRETING NEUTRON-STARS AND STRANGE STARS

Steady state models of accreting neutron stars and strange stars are presented, and their properties as a function of accretion rate are analyzed. The models have steady state envelopes, with stationary hydrogen burning taken into account, the helium shell flashes artificially suppressed, and the crust with a large number of secondary heat sources. The deep interiors are almost isothermal and are close to thermal equilibrium. A large number of models were calculated for many values of the accretion rates, with ordinary, pion-condensed, and strange cores, with and without secondary heat sources in the crust, and with the heavy element content of the accreting matter in the range 0.0002 < Z < 0.02. All models show a similar pattern of changes as the accretion rate is varied. For low accretion rates, Ṁ < Ṁ2, the hydrogen burning shell is unstable. For intermediate accretion rates, Ṁ2 < Ṁ < Ṁ3, the hydrogen burning shell is stable, but helium burning is not. The amount of mass between the two shell sources decreases with increasing accretion rate, and vanishes at Ṁ3. For high accretion rates, Ṁ3 < Ṁ, the two shell sources burn together and are unstable. We examine the dependence of the values of the critical accretion rates, Ṁ2 and Ṁ3, on several properties of the star: composition of the interior, equation of state, and chemical composition of the accreted matter. Typical values of the critical accretion rates for a standard neutron star vary from Ṁ2 ≈10-10.5 M⊙ yr-1 to 10-11.3 M⊙ yr-1, and from Ṁ3 ≈ 10-9.5 M⊙ yr-1 to 10-10.5 M⊙ yr-1, when the equation of state is varied and the chemical composition of the accreted matter changes by two orders of magnitude; for a strange star, or a neutron star with a pion condensed core, these values are Ṁ2 ≈ 10-10.3 M⊙ yr-1, and Ṁ3 ≈ 10-9.8 M⊙ yr-1, also with a range of variation due to chemical composition. These stars with exotic interiors have much cooler cores, because of the strongly enhanced neutrino emission. The complexity of the observed X-ray bursts and the complexity of theoretical shell flashes on accreting neutron stars will make it difficult to demonstrate or eliminate the possibility that some accreting neutron stars have pion-condensed or strange cores.