Bunching Coherent Curvature Radiation in Three-Dimensional Magnetic Field Geometry: Application to Pulsars and Fast Radio Bursts

The extremely high brightness temperatures of pulsars and fast radio bursts (FRBs) require their radiation mechanisms to be coherent. Coherent curvature radiation by bunches has been long discussed as the mechanism for radio pulsars and recently for FRBs. Assuming that bunches are already generated in pulsar magnetospheres, we calculate the spectrum of coherent curvature radiation under a three-dimensional magnetic field geometry. Different from previous works assuming parallel trajectories and a mono-energetic energy distribution of electrons, we consider a bunch characterized by its length, curvature radius of the trajectory family, bunch opening angle, and electron energy distribution. We find that the curvature radiation spectra of the bunches are characterized by a multi-segment broken power law, with the break frequencies depending on bunch properties and trajectory configuration. We also emphasize that in a pulsar magnetosphere only the fluctuation of net charges with respect to the background (Goldreich-Julian) outflow can make a contribution to coherent radiation. We apply this model to constrain the observed spectra of pulsars and FRBs. For a typical pulsar ($B_p=10^{12}~{\rm G}$, $P=0.1~{\rm s}$), a small fluctuation of the net charge $\delta n_{\rm GJ}\sim 0.1 n_{\rm GJ}$ can provide the observable flux. For FRBs, the fluctuating net charge may be larger due to its abrupt nature. For $\delta n_{\rm GJ}\sim n_{\rm GJ}$, a neutron star with a strong magnetic field and fast rotation is required to power an FRB in the spindown-powered model. The requirement is less stringent in the cosmic comb model thanks to the larger cross section and compressed charge density of the bunch made by the external astrophysical stream that combs the magnetosphere.