Propagation effects in the FRB 20121102A spectra
  We advance theoretical methods for studying propagation effects in the Fast
Radio Burst (FRB) spectra. We derive their autocorrelation function in the
model with diffractive lensing and strong Kolmogorov-type scintillations and
analytically obtain the spectra lensed on different plasma density profiles.
With these tools, we reanalyze the highest frequency 4-8 GHz data of Gajjar et
al. (2018) for the repeating FRB 20121102A (FRB 121102). In the data we
discover, first, a remarkable spectral structure of almost equidistant peaks
separated by $95\pm 16$ MHz. We suggest that it can originate from diffractive
lensing of the FRB signals on a compact gravitating object of mass $10^{-4}\,
M_\odot$ or on a plasma underdensity near the source. Second, the spectra
include erratic interstellar, presumably Milky Way scintillations. We extract
their decorrelation bandwidth $3.3\pm 0.6$ MHz at reference frequency 6 GHz.
The third feature is a GHz-scale pattern which, as we find, linearly drifts
with time and presumably represents a wide-band propagation effect, e.g.
GHz-scale scintillations. Fourth, many spectra are dominated by a narrow peak
at 7.1 GHz. We suggest that it can be caused by a propagation through a plasma
lens, e.g., in the host galaxy. Fifth, separating the propagation effects, we
give strong arguments that the intrinsic progenitor spectrum has narrow GHz
bandwidth and variable central frequency. This confirms expectations from the
previous observations. We discuss alternative interpretations of the above
spectral features.
