Oscillations and convective motion in stars with URCA shells

It is shown that in presence of URCA shell pulsational energy losses due to neutrino emission and nonequilibrium beta heating are much less than energy losses by excitation of shortwavelength acoustic waves. Convective motion in presence of URCA shell is considered, and equations generalizing the mean free path model of convection are derived. 2 Introduction It was suggested in [15] that in the convective region cooling of matter may be enhanced in presence URCA shells appearing when matter contains an isotope with a threshold Fermi energy for an electron capture, coresponding to a density less then the central one. Presence of such isotope leads to existence of a jump in the composition at a density, corresponding to a threshold energy. During convective motion the matter in eddies around this density crosses periodically the boundary. That implies continious beta capture and beta decay in the matter of these eddies. Because of heating of a degenerate matter due to nonequilibrium beta processes [4], with account of convective URCA shell different conclusions had been done with respect to stabilizing or destabilizing the carbon burning in the convective degenerate core [6, 8, 16, 7, 13, 11, 12, 2, 14, 17]. Here we calculate damping of stellar oscillations in presence of URCA shell (see [1]), analyze physical processes in the convective URCA shells and formulate approximate quantitative approach to the solution of this problem. 3 Linear oscillations of a slab with a phase transition Consider the plane-parallel layer in the constant gravitational field with an acceleration g, with a phase transition at the pressure P∗, and polytropic equation of state P = Kρ γ , withK = K1 at P < P∗ and K = K2 at P > P∗, K1 > K2. In static equilibrium P = gM ( 1− m M )