  Our aim is to investigate the nature and formation of brown dwarfs by adding
a new well-characterised object to the small sample of less than 20 transiting
brown dwarfs. One brown dwarf candidate was found by the KESPRINT consortium
when searching for exoplanets in the K2 space mission Campaign 16 field. We
combined the K2 photometric data with a series of multi-colour photometric
observations, imaging and radial velocity measurements to rule out false
positive scenarios and to determine the fundamental properties of the system.
We report the discovery and characterisation of a transiting brown dwarf in a
5.17 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 of
1.41+/-0.05 R$_\odot$, and an age of 5.1+/-0.9 Gyr. The mass and radius of the
companion 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 rare
object that resides in the brown dwarf desert. In the mass-density diagram for
planets, brown dwarfs and stars, we find that all giant planets and brown
dwarfs follow the same trend from ~0.3 MJ to the turn-over to hydrogen burning
stars at ~73 MJ. EPIC 212036875 b falls close to the theoretical model for
mature H/He dominated objects in this diagram as determined by interior
structure models, as well as the empirical fit. We argue that EPIC 212036875 b
formed via gravitational disc instabilities in the outer part of the disc,
followed by a quick migration. Orbital tidal circularisation may have started
early in its history for a brief period when the brown dwarf's radius was
larger. The lack of spin-orbit synchronisation points to a weak stellar
dissipation parameter which implies a circularisation timescale of >23 Gyr, or
suggests an interaction between the magnetic and tidal forces of the star and
the brown dwarf.
