Abstract
The results of studying manifestations of activity of the K8V dwarf FR Cnc according to the data from the TESS space telescope archive and other literary sources are presented. The TESS mission archive contains the results of observations of FR Cnc in three sectors: 44, 45, and 46 of a total duration of 78.3 days. The light curves of the star are characterized by the variability due to rotational modulation caused by the presence of cool spots on the surface. Based on the combined data from three observation sectors, the value of the star’s rotation period was estimated as \(P_{\rm{rot}}=0.8257\) days. Features of the amplitude changes of the stellar brightness variability, the shape of the phase light curve, and the position of the minima are highlighted. The fraction of the surface of FR Cnc occupied by spots varied in the range of 8.7–11.4 \(\%\) of the visible surface area of the star. The FR Cnc light curves are characterized by a large number of flares of different amplitudes. One of the flares is considered as an example; according to the estimate, its energy is \(E_{\textrm{TESS}}=1.9\times 10^{34}\) erg. To determine the long-term activity cycles of the star FR Cnc, the data from the Digital Access to a Sky Century @ Harvard (DASCH) project were used for the observation interval from 1886 to 1989 lasting 103 years in the photographic system close to the photometric one in the \(B\) filter. An independent estimate of \(P_{\textrm{cycl}}\) was made using the data from the long-term Kamogata Wide-field Survey (KWS) in the \(V\) filter. Analysis of the data from these surveys showed the long-term brightness variability of FR Cnc with a characteristic time of the order of 4500–4600 days (12.3–12.6 years).
