Loss or gain in surface temperature and brightness of a binary system due to appearance of a third body from infinity in hyperbolic/parabolic orbit

Abstract

Based on Roche equipotential surface, a theoretical model of a binary system has been constructed where the system is disturbed by a third body which comes from infinity in hyperbolic/parabolic orbit towards the binary, closes to it and finally goes away to infinity. Using this model, system's loss or gain in surface temperature and brightness have been calculated over the entire cycle of the system as a function of parameters like: (i) mass - ratio q between masses of the third body and the primary, (ii) eccentricity of the wide orbit, (iii) length of the semi - transverse axis a2 of the wide orbit which is hyperbolic and (iv)distance d between the common centre of gravity and the focus of wide orbit for different angle alpha (see Fig. 1a). These calculations show an anomalous behaviour of loss or gain in surface temperature and brightness where phase of the cycle plays a very important role. At high mass - ratio q' anomaly is higher and at higher eccentricity e it is still higher.