Long-term starspot evolution, activity cycle and orbital period variation of RT Lacertae

A sequence of V-band light curves of the active close binary RT Lacertae (G5+G9 IV), extending from 1965 to 2000, is presented and analysed to derive the spot distribution and evolution on the component stars. In our modelling approach, the Roche geometry and Kurucz's atmospheric models were adopted. The resulting maps of the spot surface distribution were regularized by means of the Maximum Entropy and Tikhonov criteria to take full advantage of the increased geometrical resolution during eclipses. By comparing the maps obtained with these two criteria, it was possible to discriminate between surface features actually required by the data and artifacts introduced by the regularization process. Satisfactory fits were obtained assuming spots on both components and the unspotted V-band luminosity ratio: $L_{\rm G5}/L_{\rm G9\,IV} = 0.65 \pm 0.05$. The more massive G5 primary appears to be the most active star in the system and its spotted areas are mainly responsible for the light curve distortions. The yearly spot distributions on both components indicate that their spot patterns consist of two components, one uniformly and the other non-uniformly distributed in longitude, the latter suggesting the presence of preferential longitudes. In particular, spots are concentrated around the substellar points and their antipodes on both stars. The eclipse scanning reveals spots with diameters of ~$40^{\circ}$, or possibly smaller, on the hemisphere of the primary star being occulted. The primary shows clear evidence for a short-term activity cycle with a period of ~8.5 yr and a possible long-term cycle with a period of approximately 35 yr. The variation of the spot migration rate may be related with surface differential rotation, with a lower limit of $\Delta\Omega/\Omega \sim 3.2\times 10^{-3}$. The G9 IV secondary does not show evidence for an activity cycle, its spot coverage appearing rather constant at ~$15{-}20$% of its surface. The relative amplitude of its surface differential rotation, as indicated by the variation of the spot migration rate, is $\Delta\Omega/\Omega \sim 2.7\times 10^{-3}$. The variation of the orbital period shows a correlation with the activity level of the primary component. Specifically, the decreases of the orbital period appear to be associated with minimum spottedness and sizeable changes of the surface spot distribution that may be related to increases of the rotation rate of the spot pattern. Conversely, an episode of increase of the orbital period was related to an increase of the spotted area on the primary star. Such results support the recently proposed models that connect the perturbations of the orbital dynamics with the variation of the figure of equilibrium of the active components, due to the operation of non-linear hydromagnetic dynamos in their extended convective envelopes