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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 \gtrsim theta_j. In particular, the polarization degree of emission from narrow jets (theta_j \approx 1/Gamma_0) with steep Lorentz factor gradients (p \gtrsim 4) reaches \sim 40%. 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 percent 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.