An Examination of Distinct Spheroidal Deformations of Highly Magnetized Neutron Stars

Traditional models of non-rotating neutron stars in the framework of general relativity assume perfect spherical symmetry. However, for classes of neutron stars where high magnetic fields are present, these objects can exhibit anistropies and break from spherical symmetry deforming them into oblate or prolate spheroids. Recent work on the global stellar structure of these deformed compact objects show that stellar properties such as mass, radii, and gravitational redshift can be significantly different from spherical models due to the deformation. Additionally, the mass distribution of these oblate and prolate objects is inhomogeneous and thus they are expected to have a non-zero gravitational quadrupole moment. In this work, we calculate the gravitational quadrupole moment of these objects for varying degrees of deformation. The inhomogeneous distribution of mass is also investigated via statistical methods and visualizations which suggest a distinction between the two spheroid types.