An analytical expression for apsidal superhump precession and comparisons with numerical simulations and dwarf nova observations

We compare analytical expressions of precession rates from apsidal (positive) superhumps in close binary systems with numerical disc simulation results and observed values. In the analytical expressions, we include both the dynamical effects on the precession of the disc and effects caused by pressure forces that have been theorized to provide a retrograde effect (i.e. slowing) on the prograde disc precession. We establish new limits on density wave pitch angle to a normalized disc sound speed 60 $ Vorb d tan i/ c . 2:214. Using average values for the density wave pitch angle i and speed of sound c, we find good correlation between numerical simulations and the analytical expression for the apsidal superhump period excess, which includes both the prograde and retrograde effects, for mass ratios of 0:025 # q # 0:33. We also show good correlations with the four known eclipsing systems, OY Car, Z Cha, HT Cas, and WZ Sge. Our analytical expression for apsidal superhump period excess as a function of orbital period is consistent with the trend found in observed systems.