The inverse problem of the theory of degenerate dwarfs

Abstract

Based on the radii and masses of degenerate dwarfs derived from HIPPARCOS and other observations, we estimate the microscopic parameters of a Chandrasekhar model (the relativistic parameter at the stellar center x ₀, and the chemical-composition parameter µ _e = A/Z, where A is the mass number and Z is the nuclear charge). We have obtained analytical expressions for the macroscopic characteristics (mass, radius, energy) as functions of x ₀ and µ _e . From the calculated dependence of the energy on these parameters, we have found constraints on the range of variability of x ₀, which are in good agreement with the observed radius distribution of dwarfs. The critical value of x ₀ at which stability breaks down due to general-relativisitc effects is found more accurately than previously. We propose a generalized model with an inhomogeneous (coordinate-dependent) chemical composition, with µ _e = µ _e ( r).