Linear polarization in gamma-ray burst prompt emission

Abstract

Despite being hard to measure, GRB prompt ${\hat{I}}^3$-ray emission polarization is a valuable probe of the dominant emission mechanism and the outflow's composition and angular structure. During the prompt emission the outflow is ultra-relativistic with Lorentz factors $\hat{I}“\gg 1$. We describe in detail the linear polarization properties of various emission mechanisms: synchrotron radiation from different magnetic field structures (ordered: toroidal $B_{\mathrm{tor}}$ or radial $B_{\parallel }$, and random: normal to the radial direction $B_{\perp }$), 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 $\hat{I}{¸}_{\mathrm{obs}}$. Synchrotron with $B_{\perp }$ can produce large polarizations, up to $25\%\lesssim \hat{I}\lesssim 45\%$, for a top-hat jet but only for lines of sight just outside the jet's sharp edge. The same also holds for Compton drag, albeit with a slightly higher overall $\hat{I}$. Moreover, we demonstrate how $\hat{I}“$-variations during the GRB or smoother jet edges would significantly reduce $\hat{I}$. We construct a semi-analytic model for non-dissipative photospheric emission from structured jets. Such emission can produce up to $\hat{I}\lesssim 15\%$ with reasonably high fluences, but this requires steep gradients in $\hat{I}“(\hat{I}¸)$. A polarization of $50\%\lesssim \hat{I}\lesssim 65\%$ can robustly be produced only by synchrotron emission from a transverse magnetic field ordered on angles $\gtrsim 1/\hat{I}“$ around our line of sight (like a global toroidal field). 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 $\hat{I}\gtrsim 20\%$ is measured in most GRBs within a large enough sample, by deriving the polarization distribution for our different emission and jet models.

31 pages, 18 figures. Minor changes to the text; Accepted for publication in MNRAS