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

Abstract

Observations of semi-detached interacting binaries reveal orbital modulation 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. We follow the stream material ballistic trajectories over the disk surface, where they reach a maximum height z/r at a binary phase $\Phi \sim 0.75$, and land onto the disk at a smaller radius around phase $\Phi \sim 0.5$. 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 three-dimensional hydrodynamical simulations, we propose the use of the L1 stream deflection and ballistic launching as a means for the analysis of the absorption lines orbital variability in semi-detached binaries and to assess or confirm, with some limitations, the system parameters such as the mass ratio, inclination, and disk outer radius.