Persistent and occasional: searching for the variable population of the ZTF/4MOST sky using ZTF data release 11

We present a variability, color and morphology based classifier, designed to identify transients, persistently variable, and non-variable sources, from the Zwicky Transient Facility (ZTF) Data Release 11 (DR11) light curves of extended and point sources. The main motivation to develop this model was to identify active galactic nuclei (AGN) at different redshift ranges to be observed by the 4MOST ChANGES project. Still, it serves as a more general time-domain astronomy study. The model uses nine colors computed from CatWISE and PS1, a morphology score from PS1, and 61 single-band variability features computed from the ZTF DR11 g and r light curves. We trained two versions of the model, one for each ZTF band. We used a hierarchical local classifier per parent node approach, where each node was composed of a balanced random forest model. We adopted a 17-class taxonomy, including non-variable stars and galaxies, three transient classes, five classes of stochastic variables, and seven classes of periodic variables. The macro averaged precision, recall and F1-score are 0.61, 0.75, and 0.62 for the g-band model, and 0.60, 0.74, and 0.61, for the r-band model. When grouping the four AGN classes into one single class, its precision, recall, and F1-score are 1.00, 0.95, and 0.97, respectively, for both the g and r bands. We applied the model to all the sources in the ZTF/4MOST overlapping sky, avoiding ZTF fields covering the Galactic bulge, including 86,576,577 light curves in the g-band and 140,409,824 in the r-band. Only 0.73\% of the g-band light curves and 2.62\% of the r-band light curves were classified as stochastic, periodic, or transient with high probability ($P_{init}\geq0.9$). We found that, in general, more reliable results are obtained when using the g-band model. Using the latter, we identified 384,242 AGN candidates, 287,156 of which have $P_{init}\geq0.9$.