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 \lesssim q \lesssim 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 , \varepsilon \equiv c _ { T } / v _ { orb } \gtrsim 0.15 .
By contrast , for cold L _ { 2 } mass-loss ( \varepsilon \lesssim 0.15 ) from binaries with q \lesssim 0.06 or q \gtrsim 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 } \ll 1 ) , then the virialized gas collapses to an excretion disk , while for t _ { diff } / t _ { adv } \gtrsim 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 \sim 10 ^ { -2 } to 10 ^ { -1 } of \dot { M } v _ { orb } ^ { 2 } / 2 , where \dot { M } 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 .