Time Series Energy Production in Smoothed Particle Hydrodynamics Accretion Disks: Superhumps in the AM Canum Venaticorum Stars

The energy production time series of our purely hydrodynamic accretion disk simulations display remarkable similarities with the observed light curves of dwarf novae superhumps in general and the AM CVn stars in particular. The superhump period excess as a function of mass ratio agrees well with earlier theoretical and numerical results, and the amplitudes and relative phases of the harmonics in the power spectra agree well with the observations. The morphology of the mean pulse profile appears to be a useful predictor of system mass ratio. Our modified smoothed particle hydrodynamics code time symmetrizes the interparticle forces when individual time steps are used that differ from each other by a power of 2 and advances the internal energy using a very simple method based on fundamental principles that requires the calculation of only a single vector dot product per particle per time step instead of a separate pairwise internal energy equation. Both of these modifications act to increase the stability of the internal energy changes, resulting in a significant reduction in the noise in the energy production time series. The periodicities in our models are primarily the result of changes in the viscous energy production as the disks experience tidal stressing and oscillate between nearly circular and highly distorted shapes over a superhump period. We follow the system in an inertial frame of reference, and the symmetry axis of the disk during peak energy production is aligned roughly perpendicular to the line joining the center of the stars. This axis precesses slowly in the inertial frame on a timescale of ~35-75 orbital periods, where the precession period is a function of the system mass ratio. The disks are thickest in the quadrant undergoing the largest radial excursions. This feature is stationary in the slowly precessing frame. The particle trajectories also show quasi-periodic m ≈ 2 vertical oscillations that generally agree with published analytical predictions.