Polarization properties of photospheric emission from relativistic, collimated outflows

We consider the polarization properties of photospheric emission originating in jets consisting of a highly relativistic core of opening angle theta(j) and Lorentz factor Gamma(0), and a surrounding shear layer where the Lorentz factor is decreasing as a power law of index p with angle from the jet axis. We find significant degrees of linear polarization for observers located at viewing angles theta(v) greater than or similar to theta(j). In particular, the polarization degree of emission from narrow jets (theta(j) approximate to 1/Gamma(0)) with steep Lorentz factor gradients (p greater than or similar to 4) reaches similar to 40 per cent. The angle of polarization may shift by pi/2 for time-variable jets. The spectrum below the thermal peak of the polarized emission appears non-thermal due to aberration of light, without the need for additional radiative processes or energy dissipation. Furthermore, above the thermal peak a power law of photons forms due to Comptonization of photons that repeatedly scatter between regions of different Lorentz factor before escaping. We show that polarization degrees of a few tens of per cent and broken power-law spectra are natural in the context of photospheric emission from structured jets. Applying the model to gamma-ray bursts, we discuss expected correlations between the spectral shape and the polarization degree of the prompt emission.