Linear polarization in gamma-ray burst prompt emission

Despite being hard to measure, GRB prompt γ-ray emission polarization is a valuable probe of the dominant emission mechanism and the GRB outflow’s composition and angular structure. During the prompt emission the GRB outflow is ultra-relativistic with Lorentz factors Γ ≫ 1. We describe in detail the linear polarization properties of various emission mechanisms: synchrotron radiation from different magnetic field structures (ordered: toroidal Btor or radial B∥, and random: normal to the radial direction B⊥), Compton drag, and photospheric emission. We calculate the polarization for different GRB jet angular structures (e.g. top-hat, Gaussian, power-law) and viewing angles θobs. Synchrotron with B⊥ can produce large polarizations, up to 25% Π 45%, for a top-hat jet but only for lines of sight just outside (θobs − θj ∼ 1/Γ) the jet’s sharp edge at θ = θj. The same also holds for Compton drag, albeit with a slightly higher overall Π. Moreover, we demonstrate how Γ-variations during the GRB or smoother jet edges (on angular scales ≳ 0.5/Γ) would significantly reduce Π. We construct a semi-analytic model for non-dissipative photospheric emission from structured jets. Such emission can produce up to Π 15% with reasonably high fluences, but this requires steep gradients in Γ(θ). A polarization of 50% Π 65% can robustly be produced only by synchrotron emission from a transverse magnetic field ordered on angles ≳ 1/Γ around our line of sight (like a global toroidal field, Btor, for 1/Γ < θobs < θj). Therefore, such a model would be strongly favored even by a single secure measurement within this range. We find that such a model would also be favored if Π 20% is measured in most GRBs within a large enough sample, by deriving the polarization distribution for our different emission and jet models.