Pulse Structure of Hot Electromagnetic Outflows with Embedded Baryons

Abstract

Gamma-ray bursts (GRBs) show a dramatic pulse structure that requires bulk relativistic motion, but whose physical origin has remained murky. We focus on a hot, magnetized jet that is emitted by a black hole and interacts with a confining medium. Strongly relativistic expansion of the magnetic field, as limited by a corrugation instability, may commence only after it forms a thin shell. Then the observed $T_{90}$ burst duration is dominated by the curvature delay, and null periods arise from angular inhomogeneities, not the duty cycle of the engine. We associate the $O(1)$ s timescale observed in the pulse width distribution of long GRBs with the collapse of the central 2.5-3$M_\odot$ of a massive stellar core. A fraction of the baryons are shown to be embedded in the magnetized outflow by the hyper-Eddington radiation flux; they strongly disturb the magnetic field after the compactness drops below $\sim 4\times 10^3(Y_e/0.5)^{-1}$. The high-energy photons so created have a compressed pulse structure. Delayed breakout of magnetic field from heavier baryon shells is also a promising approach to X-ray flares. In the second part of the paper, we calculate the imprint of an expanding, scattering photosphere on pulse evolution. Two models for generating the high-energy spectral tail are contrasted: i) pair breakdown due to reheating of an optically thin pair plasma embedded in a thermal radiation field; and ii) continuous heating extending from large to small scattering depth. The second model is strongly inconsistent with the observed hard-to-soft evolution in GRB pulses. The first shows some quantitative differences if the emission is purely spherical, but we show that finite shell width, mild departures from spherical curvature, and latitudinal Lorentz factor gradients have interesting effects.