Time-dependent photospheric radiative transfer in structured GRB jets: spectral evolution and polarization diagnostics

Abstract

Photospheric emission from relativistic gamma-ray burst (GRB) jets is a promising mechanism for producing the Band-like spectra observed in the prompt phase, yet the connections between jet structure, dissipation location, and polarization signatures remain unclear. We investigate time-dependent photospheric radiation transfer in structured relativistic jets by coupling two-dimensional axisymmetric special relativistic hydrodynamic (SRHD) simulations with Monte Carlo photon propagation. Photon escape and subphotospheric dissipation are characterized using the residual line-of-sight optical depth tau_out evaluated along each photon trajectory, allowing a direction-dependent treatment of photon decoupling in structured jets. The radiative transfer includes Klein-Nishina Compton scattering and polarization evolution using the Mueller matrix formalism. We perform a systematic parameter study exploring the effects of viewing angle, electron-positron pair loading (Z_pm), and the optical-depth window of subphotospheric dissipation. The model produces time-resolved spectra, peak-energy evolution E_pk(t), Band parameters, polarization degree Pi(E,t), and last-scattering statistics. We find that jet angular structure and the geometry of the line-of-sight optical depth strongly regulate spectral evolution and polarization signatures. The dissipation depth and pair loading jointly control the stability of E_pk, the formation of high-energy spectral tails, and the energy dependence of polarization. These results provide quantitative predictions for GRB prompt-emission spectra and polarization that can be tested with current and upcoming high-energy polarimeters.

Figures (9)

• Figure 1: Schematic illustration of a multi-zone dissipative photosphere and the concept of the line-of-sight optical-depth coordinate. The horizontal axis denotes radius $r$, indicating the Planck, Wien, and unsaturated Comptonization zones. In structured jets, photon decoupling is more naturally characterised by the residual optical depth along the true propagation direction, $\tau_{\rm out}(\hat{\Omega})$, rather than by a single radial optical-depth profile $\tau(r)$.
• Figure 2: Lorentz factor distribution $\Gamma(r,z)$ of the two-dimensional axisymmetric SRHD jet background. The high-$\Gamma$ jet core extends along the symmetry axis, with shear and boundary structures clearly visible at the interface with the surrounding medium. This structured flow field provides the dynamical background for the subsequent photospheric radiative transfer calculations.
• Figure 3: Density distribution at representative output times, shown as $\log_{10}\rho(r,z)$ to emphasise the strong contrast between the jet and the ambient medium. The density gradients and envelope structure determine the local electron number density and the effective scattering optical depth, thereby influencing the spatial distribution of photon decoupling.
• Figure 4: Pressure distribution at representative times, displayed as $\log_{10}p(r,z)$. The pressure structure reflects the internal thermal content of the jet and the confinement imposed by the ambient medium, and provides the background scaling for the parameterised heating prescriptions adopted in the radiative transfer calculations.
• Figure 5: Baseline model comparison between two injection depths. Left and right columns correspond to $z=64$ and $z=74$, respectively. Top panels: normalized light curve (black line) and time-resolved peak energy $E_{\rm pk}(t)$ (symbols; right axis). Bottom panels: spectral width $W(t)=\log_{10}(E_{90}/E_{10})$, where $E_{10}$ and $E_{90}$ enclose 10% and 90% of the cumulative $\nu F_\nu$ distribution. In the absence of subphotospheric dissipation and pair loading, both the pulse morphology and the spectral-width evolution are highly consistent across injection depths, indicating a weak dependence on the initial optical depth.