Speed of Sound for Hadronic and Quark Phases in a Magentic Field

It is well known that for a fermion system with an isotropic equation of state (EOS), the stiffness of the EOS and the square of the speed of sound (SOS²) are equivalent. However, in the presence of a magnetic field the EOS becomes anisotropic with two different pressures arising, one directed parallel to the field direction and one perpendicular to it, which in principle may generate an anisotropy in the SOS. We determine the sense in which the stiffness of the parallel and perpendicular EOS may be interpreted as SOS and investigate the degree to which the magnetic field induced anisotropy affects the SOS of hadrons and quarks respectively. We find that for the systems considered, the affects of the magnetic field on the SOS anisotropy are mild up to 10¹⁸G. Links to neutron star physics are discussed throughout.