Chromatic activity window of periodic fast radio bursts: FRB 20121102A and FRB 20180916B

Two fast radio bursts, FRB 20121102A and FRB 20180916B, show periodic activity with cycles of 159.3 and 16.33 days, respectively. These cycles consist of active and inactive windows, with the peak activity centred within the active phase. For FRB 20180916B, studies reported a frequency-dependent or chromatic behaviour, for which the activity window starts earlier and becomes narrower at higher frequencies. The activity across frequencies is typically modelled with a power law. We developed a simple model that combines the phase and frequency dependence of the activity windows of FRB 20121102A and FRB 20180916B. Our goal was to perform a chromaticity study for FRB 20121102A that incorporates model improvements to account for the cyclic nature of its activity window and to compare the chromatic behaviour of the two periodic FRBs. We standardised the detections from the 425 observing epochs for FRB 20121102A and the 214 epochs for FRB20180916B to account for differences in the radio telescope sensitivity. To the normalised detection-rate phase distribution, we fitted a von Mises distribution and extracted the peak activity phase and activity width. These quantities as a function of frequency were then modelled as power laws to construct the chromatic model. The activity window starts earlier at higher frequencies for the two sources. The activity window of FRB 20121102A broadens at higher frequencies, however, and that of FRB 20180916B broadens at lower frequencies. Interestingly, it appears to remain active during at least 80% of the cycle at C band. The observed chromatic behaviour of FRB 20180916B is consistent with previous findings. For FRB 20121102A, a chromaticity in its activity window is also seen, but the source appears to be active for longer at higher frequencies, which is different from the behaviour of FRB 20180916B.