Relativistic Thomas-Fermi equation of state for magnetized white dwarfs

The relativistic Feynman-Metropolis-Teller treatment of compressed atoms is extended to treat magnetized matter. Each atomic configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy which varies insignificantly with the magnetic field. In the relativistic treatment, the limiting configuration is reached when the Wigner-Seitz cell radius equals the radius of the nucleus with a maximum value of the electron Fermi energy which cannot be attained in the presence of magnetic field due to the effect of Landau quantization of electrons within the Wigner-Seitz cell. This treatment is implemented to develop the equation of state for magnetized white dwarf stars in the presence of Coulomb screening. The mass-radius relations for magnetized white dwarfs are obtained by solving the general relativistic hydrostatic equilibrium equations using Schwarzschild metric description suitable for nonrotating and slowly rotating stars. The explicit effects of the magnetic energy density and pressure contributed by a density-dependent magnetic field are included to find the stable configurations of magnetized super-Chandrasekhar white dwarfs.

Figure 1

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $1.53\times {10}^7\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^4\mathrm{He}$.

Figure 2

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $4.96\times {10}^8\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^4\mathrm{He}$.

Figure 3

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $1.53\times {10}^7\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{12}\mathrm{C}$.

Figure 4

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $4.96\times {10}^8\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{12}\mathrm{C}$.

Figure 5

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $1.53\times {10}^7\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{16}\mathrm{O}$.

Figure 6

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $4.96\times {10}^8\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{16}\mathrm{O}$.

Figure 7

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $1.53\times {10}^7\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{56}\mathrm{Fe}$.

Figure 8

Plots for $n_e(x)/n_0$ as functions of dimensionless radial coordinate $x$ at density $4.96\times {10}^8\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{56}\mathrm{Fe}$.

Figure 9

Plots for ${\nu }_{\max }$ as functions of dimensionless radial coordinate $x$ at density $1.53\times {10}^7\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{56}\mathrm{Fe}$.

Figure 10

Plots for ${\nu }_{\max }$ as functions of dimensionless radial coordinate $x$ at density $4.96\times {10}^8\mathrm{gm}{\mathrm{cm}}^{-3}$ for ${}^{56}\mathrm{Fe}$.

Figure 11

Plots for maximum (critical) masses of magnetized white dwarfs as a function of central magnetic field.

Figure 12

Plots for radii of maximum (critical) masses of magnetized white dwarfs as a function of central magnetic field.