Gamma-ray burst polarization reduction induced by the Lorentz invariance violation

TL;DR

This paper investigates how Lorentz invariance violation (LIV) affects gamma-ray burst polarization, showing that LIV-induced polarization rotation causes oscillations in polarization degree, which can be constrained by observations across different energies and redshifts.

Contribution

It provides a detailed calculation of polarization evolution due to LIV, revealing oscillatory behavior and conditions under which polarization is preserved, aiding in constraining LIV effects.

Findings

Polarization degree oscillates with a quasi-period of about π.

More than 60% of initial polarization can be preserved at specific rotation angles.

Higher energy, softer spectra, and higher redshift GRBs improve LIV constraints.

Abstract

It has been observed that photons in the prompt emission of some gamma-ray bursts (GRBs) are highly polarized. The high polarization is used by some authors to give a strict constraint on the Lorentz invariance violation (LIV). If the Lorentz invariance is broken, the polarization vector of a photon may rotate during its propagation. The rotation angle of polarization vector depends on both the photon energy and the distance of source. It is believed that if high polarization is observed, then the relative rotation angle (denoted by $\alpha$) of polarization vector of the highest energy photon with respect to that of the lowest energy photon should be no more than $\pi/2$. Otherwise, the net polarization will be severely suppressed, thus couldn't be as high as what was actually observed. In this paper, we will give a detailed calculation on the evolution of GRB polarization arising from LIV effect duration the propagation. It is shown that the polarization degree rapidly decrease as $\alpha$ increases, and reaches a local minimum at $\alpha\approx \pi$, then increases until $\alpha\approx 3\pi/2$, after that decreases again until $\alpha \approx 2\pi$, etc. The polarization degree as a function of $\alpha$ oscillates with a quasi-period $T\approx \pi$, while the oscillating amplitude gradually decreases to zero. Moreover, we find that a considerable amount (more than $60\%$ of the initial polarization) of polarization degree can be conserved when $\alpha\approx \pi/2$. The polarization observation in a higher and wider energy band, a softer photon spectrum, and a higher redshift GRB is favorable in order to tightly constrain LIV effect.