Radiation-mediated shocks in gamma-ray bursts: spectral evolution

TL;DR

Radiation-mediated shocks below the GRB photosphere can imprint the prompt emission. The authors develop a three-code pipeline combining 1D SRHD (GAMMA), the dynamical Kompaneets RMS approximation (Komrad dynamical), and a time-resolved observer-frame synthesis (Raylease) to predict the time-resolved signal from a single internal collision. They find a brief ∼0.1 s pulse with radiative efficiency around 23%, a spectrum that transitions from an early complex shape to a smooth curved form with a high-energy tail up to ∼5 MeV, and Ep that decreases as the pulse decays; the reverse shock primarily seeds the high-energy component. This work supports RMSs as viable candidates for GRB prompt emission and highlights how subphotospheric dissipation and two-shock geometry shape the observed spectral evolution and light curves, informing interpretation of time-resolved GRB data.

Abstract

Radiation-mediated shocks (RMS) occurring below the photosphere in a gamma-ray burst (GRB) jet could play a crucial role in shaping the prompt emission. In this paper, we study the time-resolved signal expected from such early shocks. An internal collision is modeled using a 1D special relativistic hydrodynamical simulation and the photon distributions in the resulting forward and reverse shocks, as well as in the common downstream region, are followed to well above the photosphere using a designated RMS simulation code. The light curve and time resolved spectrum of the resulting single pulse is computed taking into account the emission at different optical depths and angles to the line-of-sight. For the specific case considered, we find a light curve consisting of a short pulse lasting $\sim 0.1$ s for an assumed redshift of $z = 1$. The efficiency is large, with $\approx 23$% of the total burst energy being radiated. The spectrum has a complex shape at very early times, after which it settles into a more generic shape with a smooth curvature below the peak energy, $E_p$, and a clear high-energy power law that cuts off at $\sim 5$ MeV in the observer frame. The spectrum becomes narrower and softer at late times with $E_p$ steadily decreasing during the pulse decay from $E_p \approx 250~$keV to $E_p \approx 100$ keV. The low-energy index, $α$, decreases during the bright part of the pulse from $α\approx -0.5$ to $α\approx -1$, although the low-energy part is better fit with a broken power law when the signal-to-noise ratio is high. The high-energy power law is generated by the reverse shock at low optical depths ($τ< 30$) and has an index that decreases from $β\approx -2$ to $β\approx -2.4$. These results provide support for RMSs as potential candidates for the prompt emission in GRBs.

Figures (6)

• Figure 1: A flowchart showing the methodology of the paper. Each box shows one step of the chain, with the treated physics given in light blue and the simulation code used given in red. The final result is the time-resolved signal in the observer frame. The hydrodynamics are explained in Section \ref{['sec:hydro_implementation']}, the RMS modeling in Section \ref{['sec:KRA_dynamical']}, and the photon decoupling in Section \ref{['sec:time_resolved_signal']}. The observed time-resolved signal is shown in Section \ref{['sec:results']}.
• Figure 2: Top panel: Sketch of the Lorentz factor profile across the ejecta with the positions of the five different regions mentioned in subsection \ref{['subsec:H_geometry']} marked. The dashed vertical lines indicate the position of each region relative to the KRA zones given in the bottom panel. Bottom panel: Geometry of the KRA with both reverse and forward shocks included. Green, red, and purple color indicate the upstream zones, the RMS zones, and the common downstream zone, respectively. The zones are coupled via source terms as indicated in the figure. The RMS and downstream zones are evolved using the Kompaneets equation (Equation \ref{['eq:Kompaneets_sph']}) while the upstream zones are assumed to be in a thermal Wien distribution. The relevant temperature in each zone is given. This panel is adapted from Samuelsson2022, which shows the geometry of the KRA with three zones. In between the two panels, the subscripts used to refer to the different regions and zones are shown for clarity.
• Figure 3: The Lorentz factor (left) and the comoving density (right) at different optical depths as obtained from the hydrodynamical simulation. The dashed black line gives the corresponding profile at the start of the simulation. The comoving photon distributions in the five different zones of Komrad dynamical at the corresponding times are given in Figure \ref{['fig:KRA_comoving_photon_distribution']}. The simulation parameters are given in Table \ref{['tab:params']}.
• Figure 4: Comoving photon distribution in the five different zones as obtained by Komrad dynamical. The line coding is shown by the legend in the top left panel, where RS and FS stands for reverse shock and forward shock, respectively. The four different panels shows the distributions at different optical depths, corresponding to the optical depths in Figure \ref{['fig:hydro_evolution']}. The observed photon distribution will consist of a superposition of comoving spectra, leading to a smoothening and broadening effect on the observed spectrum. The simulation parameters are given in Table \ref{['tab:params']}.
• Figure 5: Observed spectral evolution (top left), light curve (top right), count spectrum of a Band fit to the time-integrated spectrum (bottom left), and the evolution of the best-fit Band parameters (bottom right). The gray dashed line in the top-left panel shows the time-integrated spectrum taken as the average over the first second of observations and purple shading shows the energy range of the GBM with darker color indicating the region with the highest effective area. The red dot-dashed line in the light curve shows the light curve in the BGO band scaled to the peak of the NaI light curve to highlight the difference between the two. The red, blue, cyan, and green data points in the count spectrum show the three NaI detectors and the one BGO detector used for the fit, respectively. The best-fit peak energy is given in units $E_{p,2} = E_p/100~{\rm keV}$ and the mock data set for the fit had a S/N $=50$. The best fit parameters with errors for the time-integrated spectrum are $\alpha = -0.90\pm 0.06$, $\beta = -2.65 \pm 0.2$, $E_p = 155\pm 12~$keV. All errors given represent $1\sigma$. The simulation parameters are given in Table \ref{['tab:params']}.