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 2D 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 greater than or similar to 1 (i.e. the ratio of incoming Poynting flux to particle energy flux) and thermal spread Delta gamma = kT/mc(2) = 10(-5)-10(-1). We measure the fraction f. of total incoming energy that is converted into precursor waves, as computed in the post-shock frame. At fixed magnetization, we find that f. is nearly independent of temperature as long as Delta gamma less than or similar to 10(-1.5) (with only a modest decrease of a factor of 3 from Delta gamma = 10(-5) to Delta gamma = 10(-1.5)), but it drops by nearly two orders of magnitude for Delta gamma greater than or similar to 10(-1). At fixed temperature, the scaling with magnetization f(xi) similar to 10(-3) sigma(-1) is consistent with our earlier 1D results. For our reference sigma = 1, the power spectrum of precursor waves is relatively broad (fractional width similar to 1 - 3) for cold temperatures, whereas it shows pronounced line-like features with fractional width similar to 0.2 for 10(-3) less than or similar to Delta gamma less than or similar to 10(-1.5). For sigma greater than or similar to 1, the precursor waves are beamed within an angle similar or equal to 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.