Investigating field burial by magnetically confined accretion mounds on Neutron Stars

We explore the problem of magnetic confinement of accreted matter forming an accretion mound near the magnetic poles of a neutron star. We calculate the magnetic field geometry of the accreted mound by solving the magnetostatic Grad Shafranov (GS) equation in radially stretched spherical coordinates with high resolution and an extended domain. In this work, we propose a new physically motivated multipolar current free boundary condition at the outer radial boundary. We have evaluated a large suite of GS solutions for different neutron star magnetic fields and mound configurations. We find that with sufficient resolution, the ring-shaped mound profiles spread latitudinally on the neutron star surface, towards the equator, with a potential decline in dipole moment at outer radii, demonstrating the onset of field burial. A higher latitudinal spread towards the equator leads to more effective magnetic field burial. Along with the ring-shaped mound profile on a hard crust majorly used in this work, we also model mounds formed on a pre-existing ocean, which is more physically motivated. Additionally, we explore different GS solutions for a quadru-dipolar surface magnetic field. We find that such configurations lead to asymmetric polar mounds. We discuss the validity of such solutions for different relative strengths of the quadrupole and dipolar components.