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We discuss constraints that the observed brightness temperatures impose oncoherent processes in pulsars and Fast Radio Bursts (FRBs), and in particularon the hypothesis of coherent curvature emission by bunches. We estimate thepeak brightness temperature that a bunch of charge $Ze$ can produce viasynchrotron and/or curvature emission as $k_B T \sim (Z e)^2/\lambda$, where$\lambda$ is the typical emitted wavelength. We demonstrate that the bunch'selectrostatic energy required to produce observed brightness temperature isprohibitively high, of the order of the total {\it bulk } energy. We comparecorresponding requirements for the Free Electron Laser mechanism (Lyutikov2021) and find that in that case the constraints are much easier satisfied.

Brightness temperature constraints on coherent processes in magnetospheres of neutron stars