Magnetic field effect on neutral color superconductivity as a mechanism to boost the inner magnetic field of magnetars

Abstract

In this paper, we review the impact of a strong magnetic field on the neutral two-flavor color superconducting (2SC) phase of dense quark matter. Using a Nambu-Jona-Lasinio (NJL) model approach in the mean-field approximation, we first solve the gap equations for the diquark condensate $Δ$ and the electric chemical potential $μ_e$ under a uniform external magnetic field, and discuss the coupled evolution of the chiral and diquark order parameters. We then evaluate the field-dependent Meissner masses of the rotationally charged gluons for a wide range of densities and moderate diquark coupling strengths. Combining the "zero-mode problem" mechanism with the neutrality condition, we show that the gluon masses become tachyonic even at moderate magnetic-field values, signaling a chromomagnetic instability in density regions where the system was stable at zero field. This instability can be resolved through the restructuring of the ground state with the formation of a gluon vortex condensate. A remarkable consequence of the vortex configuration is the paramagnetic amplification of the in-medium magnetic field: seed fields of the order of $10^{15}$ G can be enhanced by up to two orders of magnitude, reaching $\sim 10^{17}$ G, precisely the range predicted for magnetar cores. We compare this microscopic mechanism with the conventional dynamo explanation and discuss how it offers a plausible explanation for the extremely high magnetic fields expected to be realized in magnetar interiors.