ON THE STRUCTURE AND SECULAR STABILITY OF PLANE-PARALLEL STELLAR OBJECTS

The structure of self-gravitating, plane-parallel, vertically stratifi ed stellar objects, with the energy generation and opacity given by th e power laws epsilon = epsilon0rhoT(eta), kappa = kappa0rho(alpha)T(-b eta), is studied. It is shown that the condition for secular stability in such objects is 5 + alpha + beta - eta > 0, whereas for spherical stars the corresponding condition is eta + beta - 3 - 3alpha > 0. Exac t solutions (in closed form) are presented both for fully radiative mo dels and for models with a convective central region. Approximate anal ytic solutions are given for models with a convective central region a nd radiative outer layers. Numerical models are readily calculated.