Inhomogeneous Nuclear Matter of Neutron Stars with Strong Magnetic Field

The central density of neutron star is considered as high as 5-10 times the normal nuclear density. However, we have only limited information on the property of matter at high density. Particularly the equation of state (EOS) is the most important quantity which determines the upper limit of mass of neutron stars.

There are several phase transitions of cold nuclear/quark matter relevant to neutron stars. Some of them are of the first order, where mixed phase should appear. The EOS of the mixed phase in general is obtained by solving the Gibbs conditions. The mechanical balance of the surface tension and the Coulomb interaction between two phases should be taken account. As a result, a series of regular geometrical structures called "pasta" emerge to minimize the sum of the surface and the Coulomb energies. The resulting EOS of the mixed phase is found to be between the Maxwell construction and a bulk Gibbs calculation without the surface and the Coulomb energies.

On the other hand, some neutron stars have very strong magnetic field. But the effects of magnetic field have not been discussed enough. We investigate the response of inhomogeneous structure against the strong magnetic field such as the change of energy, pressure, chemical ingredient, and density distributions.