Near-infrared time-series photometry in the field of Cygnus OB2 association. I. Rotational scenario for candidate members

International audienceContext. In recent decades, the picture of early pre-main sequence stellar rotational evolution has been constrained by studies targeting different regions at a variety of ages with respect to young star formation. Observational studies suggest a dependence of rotation with mass, and for some mass ranges a connection between rotation and the presence of a circumstellar disk. The role of environmental conditions on the rotational regulation, however, has still not been fully explored. Aims: We investigate the rotational properties of candidate members of the young massive association Cygnus OB2. By evaluating their rotational properties, we address questions regarding the effect of environment properties on PMS rotational evolution. Methods: We studied JHK-band variability in 5083 candidate members (24% of them are disk-bearing stars). We selected variable stars with the Stetson variability index and performed the period search with the Lomb-Scargle periodogram for periods between 0.83-45 days. Period detections were verified using false alarm probability levels, Saunders statistics, the string and rope length method, and visual verification of folded light curves. Results: We identified 1224 periodic variable stars (24% of the candidate member sample, 8% of the disk-bearing sample, and 28% of the non-disk-bearing sample). Monte Carlo simulations were performed in order to evaluate completeness and contamination of the periodic sample, out of which 894 measured periods were considered reliable. Our study was considered reasonably complete for periods between 2 and 30 days. Conclusions: The general scenario for the rotational evolution of young stars seen in other regions is confirmed by Cygnus OB2 period distributions with disc-bearing stars rotating on average more slowly than non-disk-bearing stars. A mass-rotation dependence was also verified, but as in NGC 6530, very low mass stars (M ≤ 0.4 M⊙) are rotating on average slower than higher mass stars (0.4M⊙⊙). We observed an excess of slow rotators among the lower mass population. The disk and mass-rotation connection was also analyzed by taking into account the incident UV radiation arising from O stars in the association. Results compatible with the disk-locking scenario were verified for stars with low UV incidence, but no statistical significant relation between rotation and disk presence was verified for stars with high UV incidence suggesting that massive stars can have an important role in regulating the rotation of nearby low mass stars. The full Table 1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/603/A106