Narrow spectra of repeating fast radio bursts: A magnetospheric origin

Fast radio bursts (FRBs) can present a variety of polarization properties, and some of them have narrow spectra. We study spectral properties from perspectives of intrinsic radiation mechanisms and absorption during the waves propagating in the magnetosphere. The intrinsic radiation mechanisms are considered by invoking quasi-periodic bunch distribution and perturbations on charged bunches moving on curved trajectories. The narrow-band emission likely reflects some quasi-periodic structure on the bulk of bunches, which may be due to quasi-periodically sparking in a ``gap'' or quasi-monochromatic Langmuir waves. A sharp spike would appear at the spectrum if the perturbations can induce a monochromatic oscillation of bunches, however, it is hard to create a narrow spectrum because the Lorentz factor has large fluctuations so that the spike disappears. Both the bunching mechanism and perturbations scenarios share the same polarization properties with a uniformly distributed bulk of bunches. We investigate absorption effects including Landau damping and curvature self-absorption in the magnetosphere, which are significant at low frequencies. Subluminous O-mode photons can not escape from the magnetosphere due to the Landau damping, leading to a height-dependent lower frequency cut-off. Spectra can be narrow when the frequency cut-off is close to the characteristic frequency of curvature radiation, while such conditions can only be met sometimes. The spectral index is 5/3 at low-frequency bands due to the curvature self-absorption but not as steep as the observations. The intrinsic radiation mechanisms are more likely to generate the observed narrow spectra of FRBs rather than the absorption effects.