Gaia Data Release 3. Rotational modulation and patterns of colour variations in solar-like variables

The Gaia third Data Release (DR3) presents a catalogue of 474\,026 stars with variability induced by magnetic activity. For each star, the catalogue provides a list of about 70 parameters among which the most important are the stellar rotation period $P$, the photometric amplitude $A$ of the rotational signal and the Pearson Correlation Coefficient $r_0$ between brightness and magnitude variations. The Specific Objects Study (SOS) pipeline, developed to characterise magnetically active stars with Gaia Data, has been described in the paper accompanying the Gaia second Data Release. Here we describe the changes made to the pipeline and a new method developed to analyze Gaia time-series and to reveal spurious signals induced by instrumental effects or by the peculiar nature of the investigated stellar source. The period-amplitude diagram obtained with the DR3 data confirms the bimodal distribution of fast rotating stars seen in the DR2 release. The DR3 data permitted, for the first time, to analyze the patterns of magnitude-color variations for thousands of magnetically active stars. The measured $r_0$ values are tightly correlated with the stars position in the period-amplitude diagram. The relationship between the $P$, $A$ and $r_0$ parameters inferred for thousands of stars could be very useful to improve the understanding of stellar magnetic fields and to improve theoretical models. The method developed to reveal the spurious signals can be applied to each of the released Gaia photometric time-series and can be exploited by anyone interested in working directly with Gaia time-series.