Magnetized color superconducting quark matter under compact star conditions: Phase structure within the ${\mathrm{SU}(2)}_{\mathrm{f}}$ NJL model

The properties of magnetized color superconducting cold dense quark matter under compact star conditions are investigated using an $SU(2{)}_f$ Nambu Jona-Lasinio (NJL)-type model in which the divergences are treated using a magnetic field independent regularization scheme in order to avoid unphysical oscillations. We study the phase diagram for several model parametrizations. The features of each phase are analyzed through the behavior of the chiral and superconducting condensates together with the different particle densities for increasing chemical potential or magnetic field. While confirming previous results derived for the zero magnetic field or isospin symmetric matter case, we show how the phases are modified in the presence of $\beta$-equilibrium as well as color and electric charge neutrality conditions.

Figure 1

$M$, $\mathrm{\Delta }$, ${\mu }_8$ and ${\mu }_e$ vs $\mu$ for $H/G=0.75$ and $\tilde{e}B=0.07{\mathrm{GeV}}^2$, Set 1. Black dotted vertical lines separate $B\text{−}D\text{−}A$ phases while the red ones separate $2SC\text{−}g2SC$ phases.

Figure 2

$M$, $\mathrm{\Delta }$, ${\mu }_8$ and ${\mu }_e$ vs $\mu$ for the two values of $H/G$ considered and three representative values of $\tilde{e}B$, Set 1.

Figure 3

Quarks and leptons densities vs $\mu$ for the two values of $H/G$ considered and three representative values of $\tilde{e}B$, Set 1. The labels in the intermediate left panel indicate the different phases described in Fig. 1.

Figure 4

Phase diagrams for the two values of $H/G$ considered, for both Set 1 (left panels) and Set 2 (right panels). Full lines correspond to first order transitions and dotted lines to second order transitions. Black lines represent phase transitions. VA-dH transitions for unit charged species are colored as: blue for $ub$ quarks, violet for electrons and green for muons. Red lines indicate $g2SC-2SC$ transitions. Note that the sets are plotted in different intervals of the $\mu$ axis, even though the scale is the same.

Figure 5

$M$, $\mathrm{\Delta }$, ${\mu }_8$ and ${\mu }_e$ vs $\tilde{e}B$ for the two values of $H/G$ considered and three representative values of $\mu$, Set 1.

Figure 6

Quarks and leptons densities vs $\tilde{e}B$ for the two values of $H/G$ considered and three representative values of $\mu$ differents for each value of $H/G$, Set 1.

Figure 7

Phase diagram of $\mu$ vs $H/G$ for $\tilde{e}B=0$, Set 1. Full black lines correspond to first order transitions and dotted lines to second order transitions.