Relativistic Effects and Gamma-Ray Burst Polarization in Power-law Evolution

Despite decades of polarization observations and high significance of polarized γ -ray, X-ray, optical, and radio emissions in gamma-ray bursts (GRBs) accumulating in dozens of cases, people have yet to find a consistent scenario for understanding the globally observed timing properties of GRB polarization to date. Here, we report that the observed properties of GRB polarization exhibit a four-segment timing evolution at a cosmological distance: (i) an initial hump early on (within the first few seconds); (ii) a later-on power-law decay (from ∼10 1 to ∼10 4 s), which takes the form of π obs ∝ t −0.50 ± 0.02 ; (iii) afterward a late-time rebrightening hump (from ∼10 4 to ∼10 5 s); and (iv) finally a flattening power-law decay (from ∼10 5 to ∼10 7 s), with the form of π obs ∝ t −0.21 ± 0.08 . We show that these results can be explained by relativistic and geometric effects of a highly relativistic and magnetized jet generated by a central engine, and “magnetic patches” distributed as a globally random but locally coherent form. The long-term timing evolution of observed GRB polarization follows a scaling law π obs ∝ 1/ S obs , dominantly determined by how “magnetic patches” are randomly distributed in the observed emission region S obs on the jet plane of 1/Γ cone. It predicts the polarization hump and tail form in accordance with the luminosity jet-break phenomenon. Our analysis suggests that there is a single dominant mechanism (relativistic and geometric effects) that may account for the global observational properties of GRB polarization, and other emission mechanisms and effects may play a role in spatially local and temporally short effects on GRB polarization.