Is the β Pictoris member GJ 3039AB a physical binary? What the rotation periods tell us?

We have carried out a multi-band photometric monitoring of the close visual binary GJ 3039, consisting of a M4 primary and a fainter secondary component, and likely member of the young stellar association β Pictoris (24-Myr old). From our analysis we found that both components are photometric variables and, for the first time, we detected two micro-flare events. We measured from periodogram analysis of the photometric time series two rotation periods P = 3.355 d and P = 0.925 d, that we could attribute to the brighter GJ 3039A and the fainter GJ 3039B components, respectively. A comparison of these rotation periods with the period distribution of other β Pictoris members further supports that GJ 3039A is a member of this association. We find that also GJ 3039B could be a member, but the infrared magnitude differences between the two components taken from the literature and the photometric variability, which is found to be comparable in both stars, suggest that GJ 3039B could be a foreground star physically unbound to the primary A component.