  We study mass loss from the outer Lagrange point (L2) in binary stellar
mergers and their luminous transients by means of radiative hydrodynamical
simulations. Previously, we showed that for binary mass ratios 0.06 < q < 0.8,
synchronous L2 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 = c_T/v_orb > 0.15. By contrast, for cold L2
mass-loss (\epsilon < 0.15) from binaries with q < 0.06 or q > 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 torqueing 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 disk, while for t_diff/t_adv > 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 ~0.01 to 0.1 of Mdot v_orb^2/2, where Mdot 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.
