Equilibrium states of magnetized toroid–central compact object systems

Equilibrium configurations of self‐gravitating magnetized toroid–central compact object systems have been constructed in the framework of the Newtonian gravity. We have succeeded in including not only poloidal but also toroidal magnetic fields under the ideal magnetohydrodynamic approximation. We find two new and interesting results about the critical equilibrium states of such systems beyond which no equilibrium states are allowed to exist. First, there appear critical distances from the central compact objects to the inner surfaces of the magnetized toroids. Furthermore, these critical distances are much larger than the distances of the innermost stable circular orbits. It implies that even if these systems would be treated in the framework of general relativity, there would appear cusp structures of the effective total potential of the gravitational and magnetic forces for strongly magnetized toroids which are different from the general relativistic cusp structures. Secondly, since the strength of the magnetic field for the critical equilibrium configurations is roughly 10 15  G if the mass of the central object is 1.4 M ⊙ and the maximum density of the toroid is 10 11  g cm −3 , the existence of equilibrium states of toroids around compact objects seems to set limit to the maximum value of the magnetic field of the system to be ∼10 15  G , i.e. no stronger magnetic fields can be realized for the systems consisting of magnetized toroids and central compact objects with the masses around the typical neutron star mass. The value of the maximum density of the toroid, 10 11  g cm −3 , is taken from the theoretical computational results of binary neutron star merging simulations in full general relativity.