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Our aim is to investigate the nature and formation of brown dwarfs by addinga new well-characterised object to the small sample of less than 20 transitingbrown dwarfs. One brown dwarf candidate was found by the KESPRINT consortiumwhen searching for exoplanets in the K2 space mission Campaign 16 field. Wecombined the K2 photometric data with a series of multi-colour photometricobservations, imaging and radial velocity measurements to rule out falsepositive scenarios and to determine the fundamental properties of the system.We report the discovery and characterisation of a transiting brown dwarf in a5.17 day eccentric orbit around the slightly evolved F7V star EPIC 212036875.We find a stellar mass of 1.15+/-0.08 M$_\odot$, a stellar radius of1.41+/-0.05 R$_\odot$, and an age of 5.1+/-0.9 Gyr. The mass and radius of thecompanion brown dwarf are 51+/-2 MJ and 0.83+/-0.03 RJ, respectively,corresponding to a mean density of 108+15-13 g cm-3. EPIC 212036875 b is a rareobject that resides in the brown dwarf desert. In the mass-density diagram forplanets, brown dwarfs and stars, we find that all giant planets and browndwarfs follow the same trend from ~0.3 MJ to the turn-over to hydrogen burningstars at ~73 MJ. EPIC 212036875 b falls close to the theoretical model formature H/He dominated objects in this diagram as determined by interiorstructure models, as well as the empirical fit. We argue that EPIC 212036875 bformed via gravitational disc instabilities in the outer part of the disc,followed by a quick migration. Orbital tidal circularisation may have startedearly in its history for a brief period when the brown dwarf's radius waslarger. The lack of spin-orbit synchronisation points to a weak stellardissipation parameter which implies a circularisation timescale of >23 Gyr, orsuggests an interaction between the magnetic and tidal forces of the star andthe brown dwarf.

Greening of the Brown Dwarf Desert. EPIC 212036875 b -- a 51 M$_\mathrm{J}$ object in a 5 day orbit around an F7 V star