The photon time delay in magnetized vacuum magnetosphere

TL;DR

This paper investigates how strong magnetic fields in neutron star magnetospheres affect photon propagation, revealing that higher-energy photons experience longer delays, contrary to traditional expectations, due to radiative corrections in a magnetized vacuum.

Contribution

It provides an analytic solution for photon dispersion in magnetized vacuum considering radiative corrections, highlighting the impact of magnetic field strength on photon time delays.

Findings

Higher magnetic fields lower photon phase velocity.

Photon time delay increases with photon energy in magnetized vacuum.

Deviation from light-cone dispersion becomes significant at strong magnetic fields.

Abstract

We study the transverse propagation of photons in a magnetized vacuum considering radiative corrections in the one-loop approximation. The dispersion equation is modified due to the magnetized photon self-energy in the transparency region ($0<\omega<2m_e$). The aim of our study is to explore propagation of photons in a neutron star magnetosphere (described by magnetized vacuum). The solution of the dispersion equation is obtained in terms of analytic functions. The larger the magnetic field, the lower the phase velocity and the more the dispersion curve deviates from the light-cone. For fixed values of the frequency, we study the dependence of photon time delay with the magnetic field strength, as well as with distance. For the latter, we adopt a magnetic dipole configuration and obtain that -- contrary to the expectation, according to the traditional time delay of photons in the interstellar medium -- photons of higher energy experience a longer time delay. A discussion of potential causes of this behaviour is presented.