Anomalous spontaneous induction of magnetic and electric fields in dense quark matter

TL;DR

The paper studies dense quark matter in the DCDW/MDCDW phases to understand whether inhomogeneous chiral condensates can sustain magnetization and induce electromagnetic fields. A generalized Ginzburg-Landau framework reveals that the Lowest Landau Level generates a density-dependent permanent magnetization $M_0$ that survives as $B\to 0$, while the axial anomaly enables a magnetoelectric coupling that produces a spontaneous induced magnetic field up to ~$10^{16}$ G and a much weaker collinear electric field. The results show that the MDCDW phase can remove the Landau-Peierls instability and provides a microscopic mechanism for strong interior magnetic fields in magnetars, with potential enhancement if coexisting with color superconductivity. These findings have significant implications for the electrodynamic phenomenology and magnetic evolution of compact stars.

Abstract

In this paper, we will demonstrate that a dense quark-matter system in the dual chiral density wave (DCDW) phase behaves as a ferromagnet in the sense that its magnetic-field dependent magnetization remains different from zero even at $B\rightarrow 0$. The corresponding permanent magnetization is a function of the baryonic chemical potential $μ$, decreasing up to zero as $μ$ increases in the range of intermediate densities ($312$ MeV $\leqslant μ\leqslant 342$ MeV) and then increasing from zero in the higher density interval $490$ MeV$\leqslant μ\leqslant 550$ MeV. We will show that this system's ability to generate permanent magnetization, together with the existence of the axial anomaly, open up the possibility of spontaneously generating a magnetic field coupled to a collinear electric field. The generated magnetic field can reach values up to $10^{16}$ G, depending on $μ$, and the electric field will be 3 orders smaller. The fact that the DCDW phase is able to induce a magnetic field can be seen as its spontaneous tendency to remove the so called Landau-Peierls instability that is present in this single-modulated phase in the absence of a magnetic field. The spontaneous induction of a strong magnetic field at intermediate to high densities can be of interest for the astrophysics of compact stellar objects exhibiting strong magnetic fields as magnetars.

Figures (6)

• Figure 1: (Color online) Minimum solutions at $T=0$ of the condensate amplitude $m$ and modulation $b$ as function of chemical potential, at $B=0$ in (a) and at $B=1.5 \times10^{18}$ G in (b).
• Figure 2: (Color online) Minimum solutions at $T=0$ of the condensate amplitude $m$ and modulation $b$ as function of the magnetic field , at $\mu=312$ MeV in (a) and at $\mu=530$ MeV in (b).
• Figure 3: The permanent magnetization, $M_{ 0} (B=0)$, as a function of the chemical potential $\mu$ is given in panel (a), and $M_0(B)$ at $B=1.5 \times10^{18}$ G in (b). Both graphs are obtained from the GL expansion (\ref{['omega']}) at $N=10$ and with condensate parameters $m$ and $b$ found from the minimum equations (\ref{['min-m']}) and (\ref{['min-b']}) respectively.
• Figure 4: (Color online) Magnetization $M(B)$ as a function of magnetic field at $\mu=312$ MeV in (a) and at $\mu=530$ MeV in (b). In each graph we plotted $M_0$ and $M_0+M_1 B$ versus $B$.
• Figure 5: Contributions of $M_1B$ in (a) and $M_2 B^3$ in (b) versus magnetic field for $\mu=312$ MeV