Cyclical period changes in the dwarf novae V2051 Oph and V4140 Sgr

We report on the identification of cyclical changes in the orbital period of the eclipsing dwarf novae V2051 Ophiuchi and V4140 Sagittarii. We used sets of white dwarf mid-eclipse timings to construct observed-minus-calculated diagrams covering, respectively, 25 and 16 yr of observations. The V2051 Oph data present cyclical variations that can be fitted by a linear plus sinusoidal function with period of  22 ± 2 yr  and amplitude of  17 ± 3 s  . The statistical significance of this period by an F-test is larger than 99.9 per cent. The V4140 Sgr data present cyclical variations of similar amplitude and period of  6.9 ± 0.3 yr  which are statistically significant at the 99.7 per cent level. We derive upper limits for secular period changes of     and     for V2051 Oph and V4140 Sgr, respectively.
We have combined our results with those in the literature to construct a diagram of the amplitude versus period of the modulation for a sample of 11 eclipsing cataclysmic variables (CVs). If the cyclical period changes are the consequence of a solar-type magnetic activity cycle in the secondary star, then magnetic activity is a widespread phenomenon in CVs, being equally common among long- and short-period systems. This gives independent evidence that the magnetic field (and activity) of the secondary stars of CVs do not disappear when they become fully convective. We also find that the fractional cycle period changes of the short-period CVs are systematically smaller than those of the long-period CVs.