Compact stars with ultrastrong magnetic fields in the approximation of exact spherical symmetry: Substantiation and application

A few systematizing remarks concerning a spherically symmetric approximation in the description of compact stars with gravitationally strong magnetic fields are given, including the problem of the definition of mass accounting for the electromagnetic mass contribution. The problem of effective magnetic charges associated with the approximation method is addressed. Two simple models of compact stars with ultrastrong magnetic fields of 1017-1018 Gs are studied in the limiting approximation of exact spherical symmetry, which is the limit of considered spherical approximations. Under this condition the characteristics of the magnetized MIT-bag strange quark star show scaling with the bag constant, which can be shown to be a result of a scaling symmetry of the equations of stellar structure. The model is compared with a neutron star model described by the UV14 + TNI equation of state. At the strongest fields, the masses of the modeled stars exceed values normally expected for compact stars and ascribed rather to black holes or models with exotic equations of state. Based on the considered neutron star example, it seems that too strong magnetic fields may render models of compact stars radially instable.