Long-term K$_S$-band photometric monitoring of L dwarfs

(abridged) We perform photometric time-series analysis of a sample of ten early to mid-L dwarfs in the field over three years of $K_s$-band observations with the OMEGA 2000 infrared camera of the 3.5m telescope on Calar Alto Observatory between January 2010 and December 2012. We perform $K_s$-band differential photometry of our targets (with typical errors of $\pm$15-30~mmag at the 1$σ$ level) by subtracting a reference flux from each photometric measurement. This reference flux is computed using three nearby, probably constant stars in the target's field-of-view. We then construct and visually inspect the light curves to search for variability, and use four different periodogram algorithms to look for possible periods in our photometric data. Our targets do not display long-term variability over 1$σ$ compared to other nearby stars of similar brightness, nor do the periodograms unveil any possible periodicity for these objects, with two exceptions: 2MASS~J02411151-0326587 and G196-3B. In the case of 2MASS~J02411151-0326587 (L0), our data suggest a tentative period of 307$\pm$21~days, at 40% confidence level, which seems to be associated with peak-to-peak variability of 44$\pm$10~mmag. This object may also display variability in timescales of years, as suggested by the comparison of our Ks-band photometry with 2MASS. For G196-3B (L3), we find peak-to-peak variations of 42$\pm$10~mmag, with a possible photometric period of 442$\pm$7~days, at 95% confidence level. This is roughly the double of the astrometric period reported by Zapatero Osorio (2014). Given the significance of these results, further photometric data are required to confirm the long-term variability.These results suggest that early- to mid-L dwarfs are fairly stable in the $K_s$-band within $\pm$90 mmag at the 3 $σ$ level over months to years, which covers hundreds to tens of thousands of rotation cycles.