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 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 a 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 mid-plane (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 Φ ∼ 0.75, and land onto the disk at a smaller radius around phase Φ ∼ 0.5. The phase of the maximum height, phase of the landing site and phase of the hot spot itself, all decrease significantly with decreasing disk 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 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-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.

New Spectroscopy of U Gem

“…Stream material overshooting the disc edge and re-impacting at radii with lower velocity can create a second hot spot (Lubow 1989) which usually shows up in regions within the lower quadrants of the Doppler tomograms, as is the case in SW Sextantis systems (Schmidtobreick 2017). This scenario is further supported by the phase-dependent modulation of the FUV light curve and absorption lines velocity reported by Froning et al (2001), which can be explained by the stream overflowing the edge of the disc (Godon et al 2017;Godon 2019).…”