Monte Carlo simulations of relativistic shock breakout from a stellar wind

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 $\Gamma_u = 2$, $3.5$, $6$, $10$, 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 ($f_\nu \propto \nu^{0}$) 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 $\Gamma_u = 2$, 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 $\Gamma_u \gtrsim 6$. 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 $\Gamma_{bo} \sim 6$. We also discuss limitations of our modelling assumptions and their implications for the predicted breakout observables.