General Relativistic Calculations for White Dwarf Stars

Arun Mathew; Malay K. Nandy

doi:10.1088/1674-4527/17/6/61

paper

General Relativistic Calculations for White Dwarf Stars

arXiv:1401.0819 · doi:10.1088/1674-4527/17/6/61

Abstract

The mass-radius relations for white dwarf stars are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of $1.4562 M_{⊙}$ is modified to $1.4166 M_{⊙}$ in the general relativistic case for $_{2}^{4}$ He (and $_{6}^{12}$ C) white dwarf stars. Using the same general relativistic treatment, the critical mass for $_{26}^{56}$ Fe white dwarf is obtained as $1.2230 M_{⊙}$ . In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter's EoS along with the TOV equations yielding slightly lower values for the critical masses, namely $1.4081 M_{⊙}$ for $_{2}^{4}$ He, $1.3916 M_{⊙}$ for $_{6}^{12}$ C and $1.1565 M_{⊙}$ for $_{26}^{56}$ Fe white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that $_{2}^{4}$ He and $_{6}^{12}$ C white dwarf stars are stable against neutronization with the critical values of $1.4081 M_{⊙}$ and $1.3916 M_{⊙}$ , respectively. However the critical masses for $_{8}^{16}$ O, $_{10}^{20}$ Ne, $_{12}^{24}$ Mg, $_{14}^{28}$ Si, $_{16}^{32}$ S and $_{26}^{56}$ Fe white dwarf stars are lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.

General Relativistic Calculations for White Dwarf Stars

Abstract

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