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

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 α) of polarization vector of the highest energy photon with respect to that of the lowest energy photon should be no more than π/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 α increases, and reaches a local minimum at α ≈ π, then increases until α ≈ 3π/2, after that decreases again until α ≈ 2π, etc. The polarization degree as a function of α oscillates with a quasi-period T ≈ π, 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 α ≈ π/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.

New constraints on Lorentz invariance violation with polarized gamma-ray bursts

“…Following the process of calculating the polarization evolution in Lin et al (2016), we assume that there is a beam of non-coherent light emitted from a source, in which the propagation direction is selected as the z-axis and the polarization direction is in the xy-plane. The intensity of photons with electric vector in the infinitesimal azimuth angle interval dθ and with energy in the infinitesimal interval dk is given by…”

“…As most GRBs have a relatively large level of polarization (McConnell 2017), we consider that the photon beam is initially completely polarized, e.g., along the x-axis. To ensure f (θ) is periodic, i.e., f (θ + π) = f (θ), the sum of δ-functions is adopted (Lin et al 2016):…”

“…Owing to the high energy polarimetry of prompt emission and their large cosmological distances, gamma-ray bursts (GRBs) have been viewed as promising sources for searching for LIV-induced vacuum birefringence (Mitrofanov 2003;Jacobson et al 2004;Kostelecký & Mewes 2006, 2007Fan et al 2007;Laurent et al 2011;Stecker 2011;Toma et al 2012;Götz et al 2013Götz et al , 2014Lin et al 2016). If Lorentz invariance is broken then group velocities of photons with right-and left-handed circular polarizations should differ slightly, leading to a phase rotation of linear polarization.…”

“…All these limits were based on the assumption that the differential rotation angle ∆Θ is smaller than π/2. However, Lin et al (2016) calculated the evolution of GRB polarization arising from the LIV effect, and found that more than 60% of the initial polarization (depending both on the photon spectrum and the photon energy range) can still be conserved at ∆Θ ≤ π/2. It is interesting to constrain the LIV effect under the framework of calculating GRB polarization evolution.…”

Limits on quantum gravity effects from Swift short gamma-ray bursts

“…Figure 1 portrays the limits currently derived with GRBs and other extragalactic sources. Measures of GRB polarisation have been used to constrain the vacuum birefringence effect (Fan et al 2007;Laurent et al 2011;Toma et al 2012;Götz et al 2013Götz et al , 2014Lin et al 2016). Bolmont et al (2008) and Ellis et al (2008) performed a statistical study on samples of long GRBs (L-GRBs) with redshift detected by several instruments (HETE-2, BATSE and Swift), deriving that the energy scale E QG > 2 × 10 15 GeV and E QG > 9 × 10 15 GeV, respectively (see Fig.…”