Anisotropy in the equation of state of strongly magnetized quark matter within the Nambu–Jona-Lasinio model

In this article, we calculate the magnetization and other thermodynamical quantities for strongly magnetized quark matter within the Nambu–Jona-Lasinio model at zero temperature. We assume two scenarios: chemically equilibrated charge neutral matter present in the interiors of compact stars and zero-strangeness isospin-symmetric matter created in nuclear experiments. We show that the magnetization oscillates with density but in a much more smooth form than what was previously shown in the literature. As a consequence, we do not see the unphysical behavior in the pressure in the direction perpendicular to the magnetic field that was previously found. Finally, we also analyze the effects of a vector interaction on our results.

Figure 1

Number density of each quark flavor for zero-strangeness isospin-symmetric matter. The different curves show density-independent magnetic field strengths of ${10}^{17}$ and ${10}^{18}$ G. All curves overlap.

Figure 2

Same as Fig. 1 but for charge neutral $\beta$-equilibrated neutron-star matter with electrons (the muons do not appear), also showing a realistic stellar chemical-potential-dependent magnetic field from Ref. [55].

Figure 3

Magnetization for zero-strangeness isospin-symmetric matter. The different curves show density-independent magnetic field strengths of ${10}^{17}$ and ${10}^{18}$ G.

Figure 4

Same as Fig. 3 but for charge neutral $\beta$-equilibrated neutron-star matter with electrons, also showing a realistic stellar chemical potential-dependent magnetic field from Ref. [55].

Figure 5

Parallel and perpendicular pressures for zero-strangeness isospin-symmetric matter. The different curves show density-independent magnetic field strengths of ${10}^{17}$ and ${10}^{18}$ G. All curves overlap.

Figure 6

Same as Fig. 5 but for charge neutral $\beta$-equilibrated neutron-star matter with electrons, also showing a realistic stellar chemical potential-dependent magnetic field from Ref. [55]. All curves overlap.

Figure 7

Parallel (solid lines) and perpendicular (dotted lines) pressures for charge neutral $\beta$-equilibrated neutron-star matter with electrons as a function of magnetic field strength. The different curves show the pressures at different baryon number densities.

Figure 8

Same as Fig. 2 but including a vector interaction.

Figure 9

Same as Fig. 4 but including a vector interaction.

Figure 10

Same as Fig. 6 but including a vector interaction.