L1 Stream Deflection and Ballistic Launching at the Disk Bow Shock: An Absorption-line Velocity Analysis in Semi-detached Binaries

Observations of semi-detached interacting binaries reveal orbital modulation in the optical, UV, and X-ray bands, indicating the presence of absorbing material obscuring the disk and accreting primary star at specific orbital phases consistent with L1 stream material overflowing the disk edge. We simulate the L1 stream interaction with the disk using tests particles within the context of the Roche model in the restricted three-body problem. At the disk bow shock the L1 stream particles are deflected and launched onto ballistic trajectories above the disk (as would normally occurs at the front of a detached shock in the hypersonic flow past a blunt body). At a given scale height, the material is assumed to continue without being affected by the disk, while at lower altitude it is being launched at an increasing elevation, as well as gradually being dragged by the Keplerian flow. Near the disk midplane (z << H) the material is assumed to become part of the disk. We follow the stream material ballistic trajectories over the disk surface, where they reach a maximum height z/r at a binary phase Phi similar to 0.75 and land on the disk at a smaller radius around phase Phi similar to 0.5. The phase of the maximum height, the phase of the landing site, and the phase of the hot spot itself, all decrease significantly with decreasing radius. The radial velocity for each L1 stream ballistic trajectory along the line of sight (of the observer) to the hot inner parts of the disk is computed as a function of the orbital phase for a binary configuration matching the dwarf nova U Geminorum. The computed velocity amplitudes, phases, and pattern match the observed velocity offsets of the metal lines in the FUSE spectrum of U Gem during outburst. As ballistic trajectories are much easier to compute than realistic 3D hydrodynamical simulations, we propose the use of the L1 stream deflection and ballistic launching as a way to analyze the absorption-line orbital variability in semi-detached binaries and to assess or confirm, with some limitations, system parameters such as the mass ratio, inclination, and disk outer radius.