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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.