Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
Shi Pu🇩🇪 · Victor Roy🇩🇪 · Luciano Rezzolla🇩🇪 · Dirk H. Rischke🇩🇪
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 non-zero magnetization. First, we assume a constant magnetic susceptibility and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with ), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with ), 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 , two distinct solutions can be found depending on the values of 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 non-vanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. Only for magnetic fields which are about an order of magnitude larger than expected for heavy-ion collisions, the system is substantially reheated and the lifetime of the quark phase might be extended.