Deformation of quark stars under strong internal magnetic fields

The pulsar detector has observed the existence of a strong magnetic field on compact stars. So much we can learn from this observation, one of them is the deformation of a compact star under strong magnetic fields. In this note, we study the deformation of quark stars due to a magnetic field. Note that quark stars and neutron stars have a fundamental difference in their equation of states such as the composition and crusts. Here, we used two equation of states of quark matter, i.e., CIDDM model with the scalar and with vector Coulomb terms included [1]. In both equation of states, we vary the magnetic field value in the center of the star to see how the internal magnetic field affects the shape of the quark star.