X-ray polarimetric features of Gamma-ray Bursts across varied redshifts and hints for Axion-Like-Particles

Polarimetric features during the prompt phase of Gamma-ray Bursts (GRBs) have been essential for elucidating the debated emission mechanisms and gaining insight into the inner structure of GRBs. However, the potential impact of photon-Axion-Like-Particle (ALP) mixing in extragalactic magnetic fields, leading to significant modifications to the initial polarization state, has been overlooked in discussions concerning prompt phase constraints. In this work, we first examine the statistical characteristics of linear polarization degree (Π_L) in GRBs, by utilizing data from polarimetric missions focusing on sub-MeV emissions. Our analysis, conducted with a restricted sample of GRBs spanning various redshifts, reveals a diverse distribution of Π_L, which currently shows no correlation with the GRBs' spectral parameters or properties of candidate host galaxies. We then explore alternations to the initial Π_L due to photon-ALP mixing within a domain-like structure of the intergalactic magnetic field (B_ IGM). With the existence of ALPs with m_a≲10^-14eV and g_aγ≃0.5×10^-11, the mixing leads to a decrease in the polarization degree of initially fully linearly polarized photons, while it induces a certain degree of polarization to initially unpolarized photons. To ensure that the effect of mixing is small enough to be negligible, the mixing term Δ_aγ≡ 1/2 g_aγ B_ IGM should be less than 1.5× 10^-4 Mpc^-1. Currently, the number of GRBs with both sub-MeV polarization measurement and redshift confirmation remains very limited. Certification of redshift for GRBs with low Π_L would further constrain the parameter space of ALPs or provide an independent means to determine the upper limit on B_ IGM.