Spectroscopy of new brown dwarf members of ρ Ophiuchi and an updated initial mass function

International audience Aims: To investigate the universality hypothesis of the initial mass function in the substellar regime, the population of the ρ Ophiuchi molecular cloud is analysed by including a new sample of low-mass spectroscopically confirmed members. To that end, we have conducted a large spectroscopic follow-up of young substellar candidates uncovered in our previous photometric survey. Methods: The spectral types and extinction were derived for a newly found population of substellar objects, and its masses estimated by comparison to evolutionary models. A thoroughly literature search was conducted to provide an up-to-date census of the cluster, which was then used to derive the luminosity and mass functions, as well as the ratio of brown dwarfs to stars in the cluster. These results were then compared to other young clusters. Results: It is shown that the study of the substellar population of the ρ Ophiuchi molecular cloud is hampered only by the high extinction in the cluster ruling out an apparent paucity of brown dwarfs. The discovery of 16 new members of ρ Ophiuchi, 13 of them in the substellar regime, reveals the low-mass end of its population and shows the success of our photometric candidate selection with the WIRCam survey. The study of the brown dwarf population of the cluster reveals a high disk fraction of 76-8+5%. Conclusions: Taking the characteristic peak mass of the derived mass function and the ratio of brown dwarfs to stars into account, we conclude that the mass function of ρ Ophiuchi is similar to other nearby young clusters. Based on observations made at the ESO La Silla and Paranal Observatory under program 085.C-0960