2022ApJ...925..109L

We advance theoretical methods for studying propagation effects in 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. for the repeating FRB 20121102A (FRB 121102). In the data, we discover, first, a remarkable spectral structure of almost equidistant peaks separated by 95 ± 16 MHz. We suggest that it can originate from diffractive lensing of the FRB signals on a compact gravitating object of mass 10^–4M_☉ 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 ± 0.6 MHz at reference frequency 6 GHz. The third feature is a GHz-scale pattern that, as we find, linearly drifts with time and presumably represents a wideband 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 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 a narrow GHz bandwidth and variable central frequency. This confirms expectations from the previous observations. We discuss alternative interpretations of the above spectral features.