Normalized vertical optical depth, at collisional and dynamical steady state, for four binary configurations; from top to bottom: e_B = 0, e_B = 0.2, e_B = 0.5, and e_B = 0.75. For each case, the disc profile is shown at periastron (left) and apoastron (right) passages of the companion star. The dotted circle is the theoretical outer radius for orbital stability r_crit. The rectangle in the upper right corner shows the orbit of the binary relative to the r_crit radius (dotted circle) and the current position of the companion on its orbit. (An animated version of these results, displaying disc profiles for ten different orbital positions of the companion, can be found at http://lesia.obspm.fr/perso/philippe-thebault/bindeb.html)