Radial oscillation of compact stars in the presence of magnetic field

Compact stars are classified into three categories: neutron stars (NSs), quark stars (QSs) and hybrid stars (HSs). Stars having only hadronic matter are NSs, QSs having only quark matter up to u, d and s quarks and stars having quark core surrounded by a mixed matter (hadronic matter and quark matter) followed by hadronic matter are HSs. The mixed matter is well distributed to both hadron and quark matters. A huge magnetic field is predicted in the core of the neutron star and is observed in the surface of the neutron star. We study the effect of such huge magnetic field in the matter inside the compact objects basically the equation of state (EOS) of the matters. Since matter inside the star are very dense both hadronic and quark matter, we consider relativistic mean field theory in the hadronic matter and simple MIT bag model in the quark matter in the presence of strong magnetic field. We calculate the phase transition between hadronic and quark phases, maximum mass and eigenfrequencies of radial pulsation of NS, HS and QS in the presence of such a huge magnetic field. The mixed phase is constructed by using Glendenning conjecture in between hadron and quark phases. We find in the presence of magnetic field, the EOS in both matter becomes soft. As a result, the maximum mass is reduced and the period of oscillation is changed significantly and there is a sudden dip in the period of oscillations in the HS, which signifies the transition from one to another matter.