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

A sequence of AR Lac seasonal light curves covering the period 1967-1992 is analysed in the framework of the starspot hypothesis to derive the spot distribution and evolution on the component stars. The adopted approach makes use of the Maximum Entropy and Tikhonov principles to compute maps of the stellar photo-spheres exploiting also the eclipse scanning technique. Reliable results on the distribution of the spotted areas can be derived through a critical comparison of the maps obtained by the above quoted regularizing criteria. Satisfactory fits are computed assuming that spots are located on the photospheres of both components and that their unspotted luminosity ratio in the V band is: L(1)/L(2) = 0.59 +/- 0.03. The derived yearly spot distributions are analysed to infer general activity characteristics. The spot patterns appear to consist of two components, one uniformly and the other nonuniformly distributed in longitude, the latter suggesting the presence of preferential longitudes. Starspots at latitudes higher than similar to 50 degrees are not needed to reproduce the photometric modulation. On the less luminous primary we find evidence for quite compact spotted areas (similar to 30 degrees -40 degrees in diameter) which are occulted during primary eclipses. On the more luminous and larger secondary, spots cluster preferentially around longitudes similar to 60 degrees, similar to 180 degrees (i.e., around the substellar point) and similar to 300 degrees without showing evidence for a regular migration. The variation of the spotted area does not give a significant evidence for an activity cycle on the primary, whereas a possible modulation on a time scale of about 17 yr may be present on the secondary. The spatial association among photospheric spots and chromospheric and coronal plages (as detected in the UV and X-ray spectral domains) is significant for the large active region around the substellar point on the secondary and is suggested also for the smaller starspots on the secondary and primary components. A possible relationship between the orbital period modulation with a period of similar to 35 yr and an activity cycle on the secondary component is tentatively suggested and, if confirmed by future observations, can provide further support to recently proposed models for the connection between magnetic activity and orbital period variations.