Condensation of slow $γ$-quanta in strong magnetic fields

Abstract

The implications of the root singularity of the vacuum polarization tensor near the first pair creation threshold on blackbody radiation are investigated for magnetic fields above the characteristic scale of quantum electrodynamics. We show that the vacuum birefringence in such a strong background leads to an anisotropic behavior of the Planck radiation law. The thermal spectrum is characterized by a resonance that competes with the Wien maximum, causing a crossover in the low $γ$-spectrum of the heat radiation. A light state resembling a many-body condensate with slow motion is linked to the high-temperature phase. This novel state of radiation may coexist with nuclear or quark matter in a neutron star's core, increasing its compactness and influencing its stability.

Figures (2)

• Figure 1: (a) Dispersion relations. The diagonal dotted line is linked to mode 3, whereas the solid curves belong to mode 2. The dashed curves follow from the first pair creation threshold $\omega=(\pmb{q}^2\cos^2(\theta)+4m^2)^{1/2}$. Curves sharing a color are linked to a common $\theta\in[0,\pi]$. (b) Dependence of the refraction indices $\mathpzc{n}_i(\omega,\theta)$ on $\omega$ for various angles $\theta$. (c) Behavior of the group velocity $\mathpzc{v}_{\pmb{q},i}(\omega,\theta)$ with $\omega$ for various angles $\theta$. The horizontal red dashed line shows the velocity needed to escape from a NS with $R_\star\approx 10\;\rm Km$, $M_\star\approx 1.4 M_{\odot}$. (d) Blackbody spectrum of the second (solid) and third (dashed) modes. Curves sharing a color are linked to a common temperature.
• Figure 2: (a) Temperature dependence of the ratio $\mathpzc{U}_2/\mathpzc{U}_3$ between the internal energy density due to the second and third propagating modes for various field strengths. The black dashed line gives for comparison a ratio of unity. The shaded sectors show where a condensate of photons either destabilizes a NS or leads to a violation of causality. (b) Asymmetry degree of heat radiation in a magnetized vacuum vs temperature for different $\mathfrak{b}$. (c) Condensate fraction of mode-2 photons occupying slow light states as a function of temperature for various fields. (d) Phase diagram for heat radiation. The dashed line describes the mean number of mode-3 photons.