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 Gamma >> 1. We describe in detail the linear polarization properties of various emission mechanisms: synchrotron radiation from different magnetic field structures (ordered: toroidal B-tor or radial B-parallel to, and random: normal to the radial direction B-perpendicular to), 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 theta(obs). Synchrotron with B-perpendicular to can produce large polarizations, up to 25 per cent less than or similar to Pi less than or similar to 45 per cent, for a top-hat jet but only for lines of sight just outside (theta(obs) - theta(j) similar to 1/Gamma) the jet's sharp edge at theta = theta(j). The same also holds for Compton drag, albeit with a slightly higher overall Pi. Moreover, we demonstrate how Gamma-variations during the GRB or smoother jet edges (on angular scales greater than or similar to 0.5/Gamma) would significantly reduce Pi. We construct a semi-analytic model for non-dissipative photospheric emission from structured jets. Such emission can produce up to Pi less than or similar to 15 per cent with reasonably high fluences, but this requires steep gradients in Gamma(theta). A polarization of 50 per cent less than or similar to Pi less than or similar to 65 per cent can robustly be produced only by synchrotron emission from a transverse magnetic field ordered on angles greater than or similar to 1/Gamma around our line of sight (like a global toroidal field, B-tor, for 1/Gamma < theta(obs) < theta(j)). 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 Pi greater than or similar to 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.