Quark stars in strong magnetic fields

Within the confined isospin- and density-dependent mass model, we study the properties of strange quark matter (SQM) and quark stars (QSs) in strong magnetic fields. The equation of state of SQM under a constant magnetic field is obtained self-consistently and the pressure perpendicular to the magnetic field is shown to be larger than that parallel to the magnetic field, implying that the properties of magnetized QSs generally depend on both the strength and the orientation of the magnetic fields distributed inside the stars. Using a density-dependent magnetic field profile which is introduced to mimic the magnetic field strength distribution in a star, we study the properties of static spherical QSs by assuming two extreme cases for the magnetic field orientation in the stars, i.e., the radial orientation in which the local magnetic fields are along the radial direction, and the transverse orientation in which the local magnetic fields are randomly oriented but perpendicular to the radial direction. Our results indicate that including the magnetic fields with radial (transverse) orientation can significantly decrease (increase) the maximum mass of QSs, demonstrating the importance of the magnetic field orientation inside the magnetized compact stars.

Figure 1

Energy per baryon and the corresponding longitudinal and transverse pressures as functions of the baryon density for SQM in constant magnetic fields with strengthes of $B=1\times 10^{18}\mathrm{G}$, $2\times 10^{18}\mathrm{G}$, and $3\times 10^{18}\mathrm{G}$ within the CIDDM model with DI-85 ($z=1.8$).

Figure 2

Transverse and longitudinal pressures together with the pressure splitting factor ${\delta }_p$ as functions of the magnetic field strength $B$ for SQM at baryon number densities of $n_B=3n_0$, $5n_0$, and $7n_0$ within the CIDDM model with DI-85 ($z=1.8$). The corresponding pressures at $B=0$ ($P_0$) are also included for comparison.

Figure 3

Baryon density dependence of the magnetic field strength $B$ and the longitudinal and transverse pressures, as well as the pressure splitting factor ${\delta }_p$ for SQM in QSs using the slow B-profile (solid lines) and fast $B$-profile (dashed lines) within the CIDDM model with DI-85 ($z=1.8$). $B_0=4\times 10^{18}\mathrm{G}$ (left panels) and $1\times 10^{19}\mathrm{G}$ (right panels) are considered.

Figure 4

Maximum mass of static QSs using the transverse and radial orientations of the magnetic fields as a function of $B_0$ with the fast $B$-profile (a) and the slow $B$-profile (b) within the CIDDM model with DI-85($z=1.8$). The shaded band represents the pulsar mass of $2.01\pm 0.04M_{\odot }$ from PSR $\mathrm{J}0348+0432$ [62].