Massive Hybrid Quark Stars with Strong Magnetic Field

We estimate the critical magnetic field strength at which the lowest or second Landau levels play an important role in the quark phase inside the hybrid stars, and show that the magnetic field should be in the order of $10^{19}$ Gauss at the nuclear density $\sim0.16$ fm$^{-3}$. We also find that the pressure of quark matter settling only in the lowest Landau level can be expressed as a function of the energy density independently of the magnetic field strength, which corresponds to the causality limit of a stiff equation of state. Adiabatic index of quark matter well exceeds 4/3 in the core, and we find a possibility to construct massive hybrid star models occupied in large part by quark matter, whose maximum mass becomes larger than two solar mass.