  We discuss constraints that the observed brightness temperatures impose on
coherent processes in pulsars and Fast Radio Bursts (FRBs), and in particular
on the hypothesis of coherent curvature emission by bunches. We estimate the
peak brightness temperature that a bunch of charge $Ze$ can produce via
synchrotron 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's
electrostatic energy required to produce observed brightness temperature is
prohibitively high, of the order of the total {\it bulk } energy. We compare
corresponding requirements for the Free Electron Laser mechanism (Lyutikov
2021) and find that in that case the constraints are much easier satisfied.

High Energy Astrophysical Phenomena