Monte Carlo Simulations of Photospheric Emission in Relativistic Outflows

Abstract

We study the spectra of photospheric emission from highly relativistic gamma-ray burst outflows using a Monte Carlo (MC) code. We consider the Comptonization of photons with a fast cooled synchrotron spectrum in a relativistic jet with realistic photon to electron number ratio N γ /N e = 10 5 , using mono-energetic protons which interact with thermalised electrons through Coulomb interaction. The photons, electrons and protons are cooled adiabatically as the jet expands outwards. We find that the initial energy distribution of the protons and electrons do not have any appreciable effect on the photon peak energy E γ,peak and the power-law spectrum above E γ,peak . The Coulomb interaction between the electrons and the protons does not affect the output photon spectrum significantly as the energy of the electrons is elevated only marginally. E γ,peak and the spectral indices for the low and high energy power-law tails of the photon spectrum remain practically unchanged even with electron-proton coupling. Increasing the initial optical depth τ in results in slightly shallower photon spectrum below E γ,peak and fewer photons at the high-energy tail, although f ν ∝ ν −0.5 above E γ,peak and up to ∼ 1 MeV, independent of τ in . We find that E γ,peak determines the peak energy and the shape of the output photon spectrum. Lastly, we find that our simulation results are quite sensitive to N γ /N e , for N e = 3 × 10 3 . For almost all our simulations, we obtain an output photon spectrum with power-law tail above E γ,peak extending up to ∼ 1 MeV.

Explaining GRB prompt emission with sub-photospheric dissipation and Comptonization

“…• Electrons and protons: We consider a charge-neutral jet with particle number Ne = Np = 2 × 10 2 (Chhotray & Lazzati 2015;Bhattacharya et al 2018). We show that 2 × 10 2 electrons are sufficient in order to represent the outflow.…”

“…Furthermore, the observed spectrum is completely determined by the electron-photon interaction in the jet irrespective of the dissipation mechanism involved. While the high-energy non-thermal behaviour has been successfully explained by sub-photospheric dissipation (Giannios 2006;Lazzati & Begelman 2010;Vurm et al 2011;Chhotray & Lazzati 2015;Bhattacharya et al 2018), reproducing the low-energy non-thermal tails has turned out to be really challenging (Lazzati & Begelman 2010;Chhotray & Lazzati 2015;Bhattacharya et al 2018).…”

“…The bulk of the jet energy is contained as the kinetic energy of the protons with the average energy of the photons being much smaller compared to that of the electrons, thereby enabling significant energy transfer to the photons. In addition to the sub-photospheric episodic dissipation events, electrons are also accelerated continuously by the protons via Coulomb collisions (Bhattacharya et al 2018). While the outflow is optically thick, the photons continue to scatter electrons and gain energy until either the average photon energy matches that of the electrons or the outflow becomes optically thin so that the photons escape the photosphere.…”

“…While the outflow is optically thick, the photons continue to scatter electrons and gain energy until either the average photon energy matches that of the electrons or the outflow becomes optically thin so that the photons escape the photosphere. The photon spectrum can get significantly broadened due to both Comptonization with energetic electrons and geometrical effects (Begue et al 2013;Lundman et al 2013;Bhattacharya et al 2018). The shape of the photon spectrum changes considerably with the photon to electron number ratio Nγ/Ne as well (Bhattacharya et al 2018).…”

Diffusive photospheres in gamma-ray bursts

“…Most papers dealing with the photospheric emission, e.g. (Mészáros & Rees 2000;Pe'er 2008;Pe'er & Ryde 2011;Beloborodov 2011;Lundman et al 2013;Santana et al 2016;Bhattacharya et al 2018), for a review see Pe'er & Ryde (2017), adopt the hydrodynamic model of a steady and infinite wind. However, finite duration of GRBs implies finite width of the wind.…”