The change in the inclination angle of the non-eclipsing binary SS Lacertae: future eclipses

Eclipses in the 14.4 day period double-lined binary SS Lac were observed photographically and visually early in the 20 century, but stopped some 50 or 60 years ago. This has been explained by the presence of a distant third star in the system, which has now been detected spectroscopically with a period of 679 days. The plane of the orbit of the binary is changing relative to the line of sight in response to perturbations from this third object. A recent analysis by Milone et al. of all photometric material available for the system, including a re-measurement of original Harvard plates, has confirmed earlier reports of changes in the depth of the eclipses as a function of time, which are due to the third star. In this paper we discuss our detailed analysis of the eclipse amplitude measurements, and extract from them information on the change in the inclination angle of the binary over the last century. Our use of a much improved ephemeris for the system by Torres & Stefanik was found to be crucial, and prompted us to re-determine all the amplitudes from the historical data at our disposal, including the Harvard material used by M00. Systematically lower measurements on the branches of the minima were properly accounted for, and we made use of both a linear approximation to the time variation of the inclination angle and a more realistic model based on the theory of three-body interactions (“regression of the nodes” effect). The nodal cycle is found to be ∼600 yr, within which two eclipse “seasons” occur, each lasting about 100 yr. The non-eclipsing status of the system is expected to continue until the beginning of the 23 century. Subject headings: binaries: eclipsing — binaries: spectroscopic — stars: fundamental parameters — stars: individual (SS Lacertae)