Spectroscopy of very low-mass stars and brown dwarfs in the Lambda Orionis star-forming region II. Rotation, activity and other properties of spectroscopically confirmed members of Collinder 69

Context. Most observational studies conducted so far point toward brown dwarfs sharing a similar formation mechanism as the one that is accepted for low-mass stars. However, larger databases and more systematic studies are needed before strong conclusions can be reached. Aims. In this second paper of a series devoted to studying the spectroscopic properties of the Lambda Orionis star-forming region members, we study accretion, activity and rotation for a wide set of spectroscopically confirmed members of the central star cluster Collinder 69 to assess analogies and/or differences between the brown-dwarf and stellar populations of this cluster. Moreover, we present comparisons with other star-forming regions of similar and different ages to address environmental effects on our conclusions. Methods. We studied prominent photospheric lines to derive rotational velocities and emission lines to distinguish between accretion processes and chromospheric activity. In addition, we include information about disk presence and X-ray emission. Results. We report very strong differences in the disk fractions of low-mass stars and brown dwarfs (similar to 58%) when compared to higher mass stars (26(3)(+4)% ), with 0.6 M-circle dot being the critical mass we find for this dichotomy. As a byproduct, we address the implications of the spatial distribution of disk and diskless members in the formation scenario of the cluster itself. We used the Ha emission to distinguish among accreting and non-accreting sources, finding that 38(-7)(+8)% of sources harboring disks undergo active accretion and that his percentage stays similar in the substellar regime. For these sources we have estimated accretion rates. Finally, regarding rotational velocities, we find a high dispersion in nu sin(i) that is even higher among the diskless population.