Search for the sub-stellar lithium depletion boundary in the open star cluster Coma Berenices

We mainly aim to search for the lithium depletion boundary (LDB) among the sub-stellar population of the open star cluster Coma Berenices. We carried out a search for brown dwarf (BD) candidates using colour-magnitude diagrams combining optical and infrared photometry from the latest public releases of the following large-scale surveys: UKIRT/UKIDSS, Pan-STARRS, SDSS, and AllWISE. We checked astrometric consistency with cluster membership using $Gaia$ DR2. A couple dozen new candidate BDs located inside the tidal radius of Coma Ber are reported, but none of these are significantly fainter and cooler than previously known members. A search for Li in three new and five previously known BD candidate cluster members was performed via spectroscopic observations using the OSIRIS instrument at the 10.4-m GTC. No LiI resonance doublet at 6707.8 A was detected in any of eight Coma Ber targets in the magnitude range J=15--19 and G=20--23 observed with the GTC. Spectral types and radial velocities were derived from the GTC spectra. These values confirm the cluster membership of four L2--L2.5 dwarfs, two of which are new in the literature. The large Li depletion factors found among the four bona fide BD members in Coma Ber implies that the LDB must be located at spectral type later than L2.5 in this cluster. Using the latest evolutionary models for BDs, a lower limit of 550 Myr on the cluster age is set. This constraint has been combined with other dating methods to obtain an updated age estimate of 780$\pm$230 Myr for the Coma Ber open cluster. Identification of significantly cooler sub-stellar cluster members in Coma Ber awaits the advent of the Euclid wide survey, which should reach a depth of about J=23; this superb sensitivity will make it possible to determine the precise location of the sub-stellar LDB in this cluster and to carry out a complete census of its sub-stellar population.