Linear polarization in gamma-ray burst prompt emission

Despite being hard to measure, GRB prompt gamma-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 ultrarelativistic 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 Bπ, 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 per cent ≲Π ≲ 45 per cent, 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 per cent with reasonably high fluences, but this requires steep gradients in Γ (θ). A polarization of 50 per cent ≲Π ≲ 65 per cent 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 favoured even by a single secure measurement within this range. We find that such a model would also be favoured if Π Γ 20 per cent is measured in most GRBs within a large enough sample, by deriving the polarization distribution for our different emission and jet models.