Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization

We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i. e. , in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al. , Phys. Lett. B 750, 45 (2015), we consider the fluid to have a nonzero magnetization. First, we assume a constant magnetic susceptibility ₌ and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i. e. , with ₌>0), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i. e. , with ₌<0), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time with a power law ^-a, two distinct solutions can be found depending on the values of a and ₌. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the nonvanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. It is only for magnetic fields about an order of magnitude larger than expected for heavy-ion collisions that the system is substantially reheated and the lifetime of the quark phase might be extended.