The quark matter symmetry free energy and the thermodynamical properties of strange quark matter (SQM) in strong magnetic fields and non-zero temperature cases are discussed in this work within Nambu–Jona-Lasinio (NJL) model by considering two kinds of vector interactions. The properties of the proto-quark stars (PQSs) are also studied by introducing a density-dependent magnetic field strength distribution and assuming two ‘extreme’ magnetic orientation cases inside the quark stars (QSs). The results indicate that the strength and orientation distribution of the magnetic fields in the QSs and the heating/cooling process during the star evolution may both influence the star mass of QSs within SU(3) NJL model.

中文翻译：

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Nambu–Jona-Lasinio模型中强磁场下有限温度下的夸克物质

在Nambu–Jona-Lasinio（NJL）模型中，通过考虑两种矢量相互作用，讨论了夸克物质对称自由能和奇夸克物质（SQM）在强磁场和非零温度情况下的热力学性质。还通过引入密度相关的磁场强度分布并假设夸克星（QSs）内部有两个“极端”磁取向情况，研究了夸克星（PQSs）的特性。结果表明，在SU（3）NJL模型中，QSs中的磁场强度和取向分布以及恒星演化过程中的加热/冷却过程都可能影响QSs的恒星质量。