The synchrotron maser emission from relativistic magnetized shocks: Dependence on the pre-shock temperature

Electromagnetic precursor waves generated by the synchrotron maser instability at relativistic magnetized shocks have been recently invoked to explain the coherent radio emission of Fast Radio Bursts. By means of two-dimensional particle-in-cell simulations, we explore the properties of the precursor waves in relativistic electron-positron perpendicular shocks as a function of the pre-shock magnetization $\sigma\gtrsim 1$ (i.e., the ratio of incoming Poynting flux to particle energy flux) and thermal spread $\Delta \gamma \equiv kT/mc^2=10^{-5}-10^{-1}$. We measure the fraction $f_\xi$ of total incoming energy that is converted into precursor waves, as computed in the post-shock frame. At fixed magnetization, we find that $f_{\xi}$ is nearly independent of temperature as long as $\Delta \gamma \lesssim 10^{-1.5}$ (with only a modest decrease of a factor of three from $\Delta\gamma =10^{-5}$ to $\Delta\gamma =10^{-1.5}$), but it drops by nearly two orders of magnitude for $\Delta \gamma \gtrsim 10^{-1}$. At fixed temperature, the scaling with magnetization $f_\xi\sim 10^{-3}\,\sigma^{-1}$ is consistent with our earlier one-dimensional results. For our reference $\sigma=1$, the power spectrum of precursor waves is relatively broad (fractional width $\sim 1-3$) for cold temperatures, whereas it shows pronounced line-like features with fractional width $\sim 0.2$ for $10^{-3} \lesssim \Delta \gamma \lesssim 10^{-1.5} $. For $\sigma\gtrsim 1$, the precursor waves are beamed within an angle $\simeq \sigma^{-1/2}$ from the shock normal (as measured in the post-shock frame), as required so they can outrun the shock. Our results can provide physically-grounded inputs for FRB emission models based on maser emission from relativistic shocks.