A theory of photospheric emission from relativistic, collimated outflows

TL;DR

This paper develops a theoretical model for photospheric emission from relativistic, collimated jets, revealing how jet structure and viewing angle influence observed spectra, with implications for gamma-ray burst prompt emission.

Contribution

It introduces a new Lorentz factor profile model for jets and analyzes how jet collimation and viewing angle affect the observed photospheric spectra.

Findings

Low energy photon index is approximately -1 for narrow jets, independent of viewing angle.

Wide jets observed at small angles produce multicolor blackbody spectra.

Results resemble the observed spectra in gamma-ray bursts.

Abstract

Relativistic outflows in the form of jets are common in many astrophysical objects. By their very nature, jets have angle dependent velocity profiles, Gamma = Gamma(r, theta, phi), where Gamma is the outflow Lorentz factor. In this work we consider photospheric emission from non-dissipative jets with various Lorentz factor profiles, of the approximate form Gamma \approx Gamma_0/[(theta/theta_j)^p + 1], were theta_j is the characteristic jet opening angle. In collimated jets, the observed spectrum depends on the viewing angle, theta_v. We show that for narrow jets (theta_j Gamma_0 \lesssim few), the obtained low energy photon index is alpha \approx -1 (dN/dE \propto E^alpha), independent of viewing angle, and weakly dependent on the Lorentz factor gradient (p). A similar result is obtained for wider jets observed at theta_v \approx theta_j. This result is surprisingly similar to the average low energy photon index seen in gamma-ray bursts. For wide jets (theta_j Gamma_0 \gtrsim few) observed at theta_v \ll theta_j, a multicolor blackbody spectrum is obtained. We discuss the consequences of this theory on our understanding of the prompt emission in gamma-ray bursts.