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 (positiv e) superhumps in close binary systems with numerical disc simulation result s and observed values. In the analytical expressions, we include both the d ynamical effects on the precession of the disc and effects caused by pressu re forces that have been theorized to provide a retrograde effect (i.e. slo wing) on the prograde disc precession. We establish new limits on density w ave pitch an-le to a normalized disc sound speed 60 greater than or equal t o Omega (orb) 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 numeri cal simulations and the analytical expression for the apsidal superhump per iod excess, which includes both the prograde and retrograde effects, for ma ss ratios of 0.025 less than or equal to 5 q less than or equal to 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.