Constraints on the central density and chemical composition of the white dwarf RX J0648.0-4418 with a record period of rotation in a model with the equation of state of an ideal degenerate electron gas

Abstract

A system of equations and inequalities that allows one to determine the constraints on central density ρc and the chemical composition, which is governed by parameter μe, of the white dwarf RX J0648.0- 4418 with a record short period of rotation T = 13.18s and mass m = (1.28 ± 0.05)m⊙, has been derived. The analysis of numerical solutions of this system reveal a complex dependence of μe on ρc. The intervals of variation of μe and ρc are as follows: 1.09 ≤ μe ≤ 1.21 and 9.04 ≤ μe/ρ0 ≤ 103 (ρ0 = 0.98 × 106 g/cm3). This range of μe values suggests that the white dwarf RX J0648.0-4418 is not made of pure hydrogen and should contain 9–21% of heavy elements. Calculations have been performed with the equation of state of an ideal degenerate electron gas. Approximate analytic expressions (with an accuracy of 10-3) for the minimum period Tmin and mass m of the white dwarf are obtained. It is demonstrated that the white-dwarf mass is almost doubled (compared to the case of no rotation at a fixed central density) as period T approaches Tmin.