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ABSTRACT 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 σ ≳ 1 (i.e. the ratio of incoming Poynting flux to particle energy flux) and thermal spread Δγ ≡ kT/mc2 = 10−5−10−1. We measure the fraction fξ of total incoming energy that is converted into precursor waves, as computed in the post-shock frame. At fixed magnetization, we find that fξ is nearly independent of temperature as long as Δγ ≲ 10−1.5 (with only a modest decrease of a factor of 3 from Δγ = 10−5 to Δγ = 10−1.5), but it drops by nearly two orders of magnitude for Δγ ≳ 10−1. At fixed temperature, the scaling with magnetization $$f_\xi \sim 10^{-3}\, \sigma ^{-1}$$ is consistent with our earlier 1D results. For our reference σ = 1, the power spectrum of precursor waves is relatively broad (fractional width ∼1 − 3) for cold temperatures, whereas it shows pronounced line-like features with fractional width ∼0.2 for 10−3 ≲ Δγ ≲ 10−1.5. For σ ≳ 1, the precursor waves are beamed within an angle ≃σ−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.
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