Spectral and Polarization Properties of Coherent Radio Emission from Relativistic Magnetized Pair Plasma Shocks
Fast radio bursts (FRBs) are millisecond-duration radio transients whose emission mechanism remains an open question. The so-called synchrotron maser instability in relativistic magnetized shocks is a leading candidate for FRBs produced outside the compact object magnetosphere, yet its spectral and polarization predictions have not been systematically explored. We present three-dimensional particle-in-cell simulations of relativistic magnetized pair plasma shocks with upstream magnetization $σ> 1$ and bulk Lorentz factor $γ_0 = 10$, assuming a plane-parallel shock geometry and neglecting radiative cooling, and compute the spectra and polarization of the precursor maser emission for an arbitrary line of sight. For on-axis observers aligned with the shock-propagation direction, the X-mode dominates the emission. The O-mode power increases at off-axis viewing angles and is primarily associated with currents parallel to the upstream background magnetic field. Assuming a spherical shock, we find full-width-at-half-maximum fractional bandwidths of $Δν/ν_0\simeq0.57$ and $0.82$ for $σ=3$ and $6$, respectively. For highly magnetized shocks, the intrinsic emission bandwidth accounts for most of the spectral width, while high-latitude contributions provide additional broadening. The integrated emission remains highly linearly polarized near the spectral peak, with a nearly constant polarization angle due to the dominance of the X-mode. Our results suggest that synchrotron maser emission can produce spectra with bandwidths and high linear polarization degrees compatible with observations of some non-repeating FRBs, and may provide testable signatures for distinguishing shock-powered FRBs from other emission mechanisms.