Binary stellar mergers with marginally bound ejecta: excretion discs, inflated envelopes, outflows, and their luminous transients

We study mass-loss from the outer Lagrange point (L-2) in binary stellar mergers and their luminous transients by means of radiative hydrodynamical simulations. Previously, we showed that for binary mass ratios 0.06 less than or similar to q less than or similar to 0.8, synchronous L-2 mass-loss results in a radiatively inefficient, dust-forming unbound equatorial outflow. A similar outflow exists irrespective of q if the ratio of the sound speed to the orbital speed at the injection point is sufficiently large, epsilon equivalent to c(T)/v(orb) greater than or similar to 0.15. By contrast, for cold L-2 mass-loss (epsilon less than or similar to 0.15) from binaries with q less than or similar to 0.06 or q greater than or similar to 0.8, the equatorial outflow instead remains marginally bound and falls back to the binary over tens to hundreds of binary orbits, where it experiences additional tidal torquing and shocking. As the bound gas becomes virialized with the binary, the luminosity of the system increases slowly at approximately constant photosphere radius, causing the temperature to rise. Subsequent evolution depends on the efficiency of radiative cooling. If the bound atmosphere is able to cool efficiently, as quantified by radiative diffusion time being shorter than the advection time (t(diff)/t(adv) << 1), then the virialized gas collapses to an excretion disc, while for t(diff)/t(adv) greater than or similar to 1 an isotropic wind is formed. Between these two extremes, an inflated envelope transports the heat generated near the binary to the surface by meridional flows. In all cases, the radiated luminosity reaches a fraction similar to 10 (2) to 10 (1) of (M) over dotv(orb)(2)/2, where (M) over dot is the mass outflow rate. We discuss the implications of our results for transients in the luminosity gap between classical novae and supernovae, such as V1309 Sco and V838 Mon.