Mass–radius relationship of strongly magnetized deformed white dwarfs

The masses and radii of strongly magnetized anisotropic deformed white dwarf stars are investigated using the stellar structure equations in the parameterized $\gamma$-metric formalism. The Equation of State (EoS) of a completely degenerate relativistic electron gas in strong quantizing density-dependent magnetic field is developed. The fluid and field pressure anisotropy among the parallel and perpendicular components to the magnetic field is taken into consideration. This anisotropy in the EoS causes axisymmetric deformation of the star. We found stable solutions of deformed super-Chandrasekhar ultramassive white dwarfs. At a fixed central electron number density, the mass first increases from the traditional Chandrasekhar limit with increase of central magnetic field strength, reaches a maximum and then decreases with further increase of central magnetic field. For lower central magnetic field strengths, both the pressure anisotropy and the resulting deformation are very less, and hence the mass increases. In the higher central magnetic field regime, the magnetic field pressure anisotropy becomes significantly strong. This leads to greater deformation from spherical symmetry and hence reduces the stellar mass. We also see that the maximum mass and its corresponding equatorial radius both decrease as central magnetic field strength increases. We also notice that the maximum mass occurs at higher central density as the magnetic field increases. These phenomena also occur because of the deviation from spherical symmetry due to higher pressure anisotropy. High magnetic field increases stellar compactness.