Monte Carlo simulations of relativistic shock breakout from a stellar wind

Abstract

We present Monte Carlo simulations of relativistic radiation-mediated shocks (RRMS) in the photon-starved regime, incorporating photon escape from the upstream region--characterized by the escape fraction, $f_{\rm esc}$--under a steady-state assumption. These simulations, performed for shock Lorentz factors $Γ_u = 2$, $3.5$, $6$, $10$, and $15$, are applicable to RRMS breakouts in shallowly declining density profiles such as stellar winds. We find that vigorous pair production acts as a thermostat, regulating the downstream temperature to $\sim 100$-$200~{\rm keV}$, largely independent of $f_{\rm esc}$. A subshock forms and strengthens with increasing $f_{\rm esc}$. The escaping spectra peak at $E_p \approx 300$-$600~{\rm keV}$ in the shock frame and deviate from a Wien distribution, exhibiting low-energy flattening ($f_ν\propto ν^{0}$) due to free-free emission and high-energy extensions caused by inverse Compton scattering from subshock-heated pairs. While an earlier analytical model reproduces the velocity structure well at $Γ_u = 2$, it significantly overestimates the shock width at higher Lorentz factors, particularly for $f_{\rm esc} \gtrsim$ a few $\%$. Based on this finding, we provide updated predictions for breakout observables in wind environments for $Γ_u \gtrsim 6$. Notably, the duration of the relativistic breakout becomes largely insensitive to the explosion energy and ejecta mass, typically exceeding analytical predictions by orders of magnitude and capable of producing a $\sim$300 s flash of MeV photons with a radiated energy of $\sim 10^{50}$ erg for an energetic explosion yielding $Γ_{bo} \sim 6$. We also discuss limitations of our modelling assumptions and their implications for the predicted breakout observables.

Figures (13)

• Figure 1: Profiles of 4-velocity ( top), temperature ( middle), and pair-to-baryon ratio ( bottom) as functions of the pair-loaded Thomson optical depth $\tau_* = \int \Gamma (n + n_{\pm})\sigma_T dz$ for the simulations with an upstream Lorentz factor of $\Gamma_u = 2$. The profiles are represented by solid lines in green, orange, purple, blue, and red, each indicating the results from finite shocks with different escape fractions as detailed in the legend. For comparative purposes, the structure of an infinite shock is depicted with a black line. It is noted that for infinite shocks, the upstream boundary extends beyond the left edge of the figure, whereas the leftmost points of the finite shock profiles mark their respective upstream boundaries. A discontinuous jump in both the 4-velocity and temperature profiles at $\tau_{*}=0$ reflects the presence of a subshock.
• Figure 2: Same as Figure \ref{['fig:profileGu2']}, but for $\Gamma_u = 3.5$.
• Figure 3: Same as Figure \ref{['fig:profileGu2']}, but for $\Gamma_u = 6$.
• Figure 4: Same as Figure \ref{['fig:profileGu2']}, but for $\Gamma_u = 10$.
• Figure 5: Shock-frame, $\nu f_\nu$ flux of escaping photons normalized by the total kinetic energy flux of baryons at the upstream boundary, $F_b = \Gamma_{u} (\Gamma_{u}-1) n_{u} m_p c^3 \beta_{u}$. Each panel shows results for $\Gamma_{u}=2$ (top left), $3.5$ (top right), $6$ (bottom left), and $10$ (bottom right).