A search for substellar members in the Praesepe and sigma Orionis clusters

(Abridged). We have conducted deep photometric searches for substellar members of the Praesepe (0.5-1 Gyr) and sigma Orionis (3 Myr) star clusters using the Sloan i' and z' filters, the 3.5-m and the 5-m Hale telescopes on the Calar Alto and Palomar Observatories, respectively. The total area surveyed was 1177 arcmin^2 (Praesepe) and 1122 arcmin^2 (sigma Orionis) down to 5-sigma detection limits of i'= 24.5 and z'= 24 mag, corresponding to masses of 50-55 M_Jup (Praesepe) and 6 M_Jup (sigma Orionis). Besides recovering previously known cluster members reported in the literature, we have identified new photometric candidates in both clusters whose masses expand the full range covered by our study. In sigma Orionis, follow-up NIR photometry has allowed us to confirm the likely cluster membership of three newly discovered planetary-mass objects. The substellar mass function of sigma Orionis, which is complete from the star-brown dwarf borderline down to 7 M_Jup, keeps rising smoothly with a slope of alpha = 0.6^{+0.5}_{-0.1}. Very interestingly, one of the faintest Praesepe candidates for which we have also obtained follow-up JHK photometry nicely fits the expected optical and infrared photometric sequence of the cluster. From its colors, we have estimated its spectral type in the L4-L6 range. If confirmed as a true Praesepe member, it would become the first L-type brown dwarf (50-60 M_Jup) identified in an intermediate-age star cluster. Our derivation of the Praesepe mass function depends strongly on the cluster age. For the youngest possible ages (500-700 Myr), our results suggest that there is a deficit of Praesepe brown dwarfs in the central regions of the cluster, while the similarity between the Praesepe and sigma Orionis mass functions increases qualitatively for models older than 800 Myr.