Radial modes of slowly rotating compact stars in the presence of magnetic field

Abstract

Compact stars are composed of very high-density hadron matter. When the matter is above nuclear matter density, then there is a chance of different phases of matter such as hadron matter to quark matter. There is a possible phase which, having the quark core surrounded by a mixed phase followed by hadronic matter, may be considered as a hybrid phase inside the stars called hybrid star (HS). The star which consists of only u, d and s quarks is called quark star (QS) and the star which has only hadronic matter is called neutron star (NS). For the equation of state (EOS) of hadronic matter, we have considered the Relativistic Mean Field (RMF) theory and we incorporated the effect of strong magnetic fields. For the EOS of the quark phase we use the simple MIT bag model. We have assumed Gaussian parametrization to make the density dependent for both bag pressure in quark matter and magnetic field. We have constructed the intermediate mixed phase by using the Glendenning conjecture. Eigenfrequencies of radial pulsations of slowly rotating magnetized compact stars (NS, QS, HS) are calculated in a general relativistic formalism given by Chandrasekhar and Friedman. We have studied the effect of central density on the square of the frequencies of the compact stars in the presence of zero and strong magnetic field.