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Can brown dwarfs survive on close orbits around convective stars?

Brown dwarfs straddle the mass range transition from planetary to stellar objects. There is a relative paucity of brown dwarfs companions around FGKM stars compared to exoplanets for orbital periods less than a few years, but most of the short-period brown dwarf companions fully characterised by transits and radial velocities are found around F-type stars. We examine the hypothesis that brown dwarf companions could not survive on close orbit around stars with important convective envelopes because the tides and angular momentum loss through magnetic breaking should lead to a rapid orbital decay and quick engulfment of the companion. We use a classical Skumanich-type braking law, and constant time-lag tidal theory to assess the characteristic timescale for orbital decay for the brown dwarf mass range as a function of the host properties. We find that F-type stars may host massive companions for a significantly longer time than G-type stars for a given orbital period, which may explain the paucity of G-type hosts for brown dwarfs with orbital period less than 5 days. On the other hand, we show that the small radius of early M-type stars contributes to orbital decay timescales that are only half those of F-type stars, despite their more efficient tidal dissipation and magnetic braking. For fully convective later type M-dwarfs, orbital decay timescales could be orders of magnitude greater than for F-type stars. For orbital periods greater than 10 days, brown dwarf occurrence should largely be unaffected by tidal decay, whatever the mass of the host. On closer orbital periods, the rapid engulfment of massive companions could explain the lack of G and K-type hosts in the sample of known systems with transiting brown dwarfs. However, the paucity of M-type hosts can not be an effect of tidal decay alone, but may be the result of a selection effect in the sample and/or the formation mechanism.