We explore the photospheric emission from a relativistic jet breaking out from a massive stellar envelope based on relativistic hydrodynamical simulations and post-process radiation transfer calculations in three dimensions. To investigate the impact of three-dimensional (3D) dynamics on the emission, two models of injection conditions are considered for the jet at the center of the progenitor star: one with periodic precession and another without precession. We show that structures developed within the jet due to the interaction with the stellar envelope, as well as due to the precession, have a significant imprint on the resulting emission. Particularly, we find that the signature of precession activity by the central engine is not smeared out and can be directly observed in the light curve as a periodic signal. We also show that non-thermal features, which can account for observations of gamma-ray bursts, are produced in the resulting spectra even though only thermal photons are injected initially and the effect of non-thermal particles is not considered.

We study the stability of a non-rotating single-component jet using two-dimensional special relativistic hydrodynamic simulations. By assuming translational invariance along the jet axis, we exclude the destabilization effect by Kelvin-Helmholtz mode. The nonlinear evolution of the transverse structure of the jet with a normal jet velocity is highlighted. An intriguing finding in our study is that Rayleigh-Taylor and Richtmeier-Meshkov type instabilities can destroy cylindrical jet configuration as a result of spontaneously induced radial oscillating motion. This is powered by in-situ energy conversion between the thermal and bulk kinetic energies. The effective inertia ratio of the jet to the surrounding medium η determines a threshold for the onset of instabilities. The condition η < 1 should be satisfied for the transverse structure of the jet being persisted.

Long duration gamma-ray bursts (GRBs), the brightest events since the Big Bang itself, are believed to originate in an ultra-relativistic jet breaking out from a massive stellar envelope. Despite decades of study, there is still no consensus on their emission mechanism. One unresolved question is the origin of the tight correlation between the spectral peak energy and peak luminosity discovered in observations. This Yonetoku relation is the tightest correlation found in the properties of the prompt phase of GRB emission, providing the best diagnostic for the radiation mechanism. Here we present three-dimensional hydrodynamical simulations, and post-process radiation transfer calculations, of photospheric emission from a relativistic jet. Our simulations reproduce the Yonetoku relation as a natural consequence of viewing angle. Although jet dynamics depend sensitively on luminosity, the correlation holds regardless. This result strongly suggests that photospheric emission is the dominant component in the prompt phase of GRBs.

We explore the spectral and polarization properties of photospheric emissions from stratified jets in which multiple components, separated by sharp velocity shear regions, are distributed in lateral directions. Propagation of thermal photons injected at a high optical depth region are calculated until they escape from the photosphere. It is found that the presence of the lateral structure within the jet leads to the nonthermal feature of the spectra and significant polarization signal in the resulting emission. The deviation from thermal spectra, as well as the polarization degree, tends to be enhanced as the velocity gradient in the shear region increases. In particular, we show that emissions from multicomponent jet can reproduce the typical observed spectra of gamma-ray bursts irrespective of the position of the observer when a velocity shear region is closely spaced in various lateral (θ ) positions. The degree of polarization associated with the emission is significant (>few percent) at a wide range of observer angles and can be higher than 30%.

We address the linear stability of a discontinuous surface of a relativistic flow in the context of a jet that oscillates radially as it propagates. The restoring force of the oscillation is expected to drive a Rayleigh-Taylor instability (RTI) at the interface between the jet and its cocoon. We perform a linear analysis and numerical simulations of the growth of the RTI in the transverse plane to the jet flow with a uniform acceleration. In this system, an inertia force due to the uniform acceleration acts as the restoring force for the oscillation. We find that not only the difference in the inertia between the two fluids separated by the interface but also the pressure at the interface helps to drive the RTI because of a difference in the Lorenz factor across the discontinuous surface of the jet. The dispersion relation indicates that the linear growth rate of each mode becomes maximum when the Lorentz factor of the jet is much larger than that of the cocoon and the pressure at the jet interface is relativistic. By comparing the linear growth rates of the RTI in the analytical model and the numerical simulations, the validity of our analytically derived dispersion relation for the relativistic RTI is confirmed.