Stability of strange dwarfs. I. Static criterion for stability. Statement of the problem

This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M _0core /M _⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons, and radius of strange dwarfs are uniquely determined by the central energy density ρ _c and the energy density ρ _tr of the crust at the surface of the quark core. Thus, the entire range of variation of ρ _c and ρ _tr must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations with a fixed rest mass M ₀ (total baryon number) of the quark core and different masses of the crust. In each series, ρ _tr ranges from the value for white dwarfs to ρ _drip = 4.3∙10¹¹ g/cm³, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an individual series when the mass of the strange dwarf reaches a maximum as a function of ρ _tr .