Anisotropic pressure in strange quark matter under the presence of a strong magnetic field

Thermodynamic properties of strange quark matter in strong magnetic fields $H$ up to ${10}^{20}$ G are considered within the MIT bag model at zero temperature implying the constraints of total baryon number conservation, charge neutrality and chemical equilibrium. The pressure anisotropy, exhibiting in the difference between the pressures along and perpendicular to the field direction, becomes essential at $H>H_{th}$, with the estimate ${10}^{17}<H_{th}\lesssim {10}^{18}$ G. The longitudinal pressure vanishes in the critical field $H_c$, which can be somewhat less or larger than ${10}^{18}$ G, depending on the total baryon number density and bag pressure. As a result, the longitudinal instability occurs in strange quark matter, which precludes: (1) a significant drop in the content of $s$ quarks, which, otherwise, could happen at $H\sim {10}^{20}$ G; (2) the appearance of positrons in weak processes in a narrow interval near $H\sim 2\cdot {10}^{19}$ G (replacing electrons). The occurrence of the longitudinal instability leaves the possibility only for electrons to reach a fully polarized state, while for all quark flavors the polarization remains mild even for the fields near $H_c$. The anisotropic equation of state is determined under the conditions relevant to the interiors of magnetars.