Are there brown dwarfs in globular clusters?

Abstract

We present an analytical method for constraining the substellar initial mass function in globular clusters, based on the observed frequency of transit events. Globular clusters typically have very high stellar densities where close encounters are relatively common, and thus tidal capture can occur to form close binary systems. Encounters between main-sequence stars and lower-mass objects can result in tidal capture if the mass ratio is ≳10−2. If brown dwarfs exist in significant numbers, they too will be found in close binaries, and some fraction of their number should be revealed as they transit their stellar companions. We calculate the rate of tidal capture of brown dwarfs in both segregated and unsegregated clusters, and find that the tidal capture is more likely to occur over an initial relaxation time before equipartition occurs. The lack of any such transits in recent Hubble Space Telescope monitoring of 47 Tuc implies an upper limit on the frequency of brown dwarfs (≲15 per cent relative to stars) which is significantly below that measured in the galactic field and young clusters.