Speed of sound for hadronic and quark phases in a magnetic field

Abstract

In this paper we calculate the speed of sound for three phases that may exist inside a magnetized hybrid neutron star at different density regions: A hadronic phase at low densities, quark-matter in the magnetic dual chiral density wave (MDCDW) phase at intermediate densities and a free-quark phase modeled by the MIT bag model at higher densities. It is found that the speed of sound exhibits a non-monotonic behavior, that goes from values smaller than the conformal limit (cs2<1/3) in the hadronic phase, to peak (cs2>1/3) in the MDCDW phase, to finally reach the conformal limit (cs2∼1/3) at higher densities for quarks in the MIT bag model. Also, the anisotropic speed of sound in the presence of a magnetic field is derived from first principles. This is a consequence of the anisotropy in the system's pressures produced by the breaking of the rotational symmetry in the presence of a magnetic field. The role played by the lowest Landau level contribution in affecting the speed of sound in the magnetized phases is discussed.