General relativistic calculations for white dwarfs

Abstract

The mass-radius relations for white dwarfs are investigated by solving the Newtonian aswell as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electrongas to be non-interacting. We find that the Newtonian limiting mass of 1.4562Mo is modifiedto 1.4166M⊙ in the general relativistic case for 42He (and 126 C) white dwarfs. Using the same generalrelativistic treatment, the critical mass for 5626Fe white dwarfs is obtained as 1.2230M⊙. In addition, departurefrom the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter's EoSalong with the TOV equation, yielding slightly lower values for the critical masses, namely 1.4081M⊙for 42He, 1.3916M⊙ for 126C and 1.1565M⊙ for 5626Fe white dwarfs. We also compare the critical densitiesfor gravitational instability with the neutronization threshold densities to find that 42He and 126 Cwhite dwarfs are stable against neutronization with the critical values of 1.4081M⊙ and 1.3916M⊙,respectively. However, the critical masses for 168 O, 2010Ne, 2412Mg, 2814Si, 3216S and 5626Fe white dwarfs arelower due to neutronization. Corresponding to their central densities for neutronization thresholds, weobtain their maximum stable masses due to neutronization by solving the TOV equation coupled withthe Salpeter EoS.