On rapid binary mass transfer - I. Physical model

In some semidetached binary systems, the donor star may transfer mass to the companion at a very high rate. We propose that, at sufficiently high mass-transfer rates such that the accretion disc around the companion becomes geometrically thick (or advection-dominated) near the disc outer radius, a large fraction of the transferred mass may be lost through the outer Lagrangian (L2) point, as a result of the excessive energy generated by viscous heating that cannot be efficiently radiated away. A physical model is constructed where the L2 mass-loss fraction is given by the requirement that the remaining material in the disc has Bernoulli number equal to the L2 potential energy. Our model predicts significant L2 mass-loss at mass transfer rates exceeding $\mbox{a few}\, 10^{-4}\, {\mathrm{ M}_\odot \, \mathrm{yr}^{-1}}$. An equatorial circumbinary outflow (CBO) is formed in these systems. Implications for the orbital evolution and the observational appearance of the system are discussed. In particular, (1) rapid angular momentum loss from the system tends to shrink the orbit, and hence may increase the formation rate of mergers and gravitational-wave sources; and (2) photons from the hot disc wind are reprocessed by the CBO into longer wavelength emission in the infrared bands, consistent with Spitzer observations of some ultra-luminous X-ray sources.