On the dynamical evolution of the brown dwarf population in open clusters

It is by now well established that open clusters contain a considerable fraction of brown dwarfs (BDs). This paper investigates the dynamical evolution of this substellar population by using simulations with Aarseth's (1994) NBODY5 code. A noticeable preferential escape of BDs is found, which may influence the determination of the IMF of substellar objects in dynamically evolved open clusters. This small dynamical-in-origin depletion may not explain, however, the scarcity of BDs observed in some evolved clusters, as the Hyades. On the other hand, BD cooling processes are able to reduce our ability to detect BDs in old clusters in a very significant way. Our results confirm that the probability of observing BDs in open clusters is almost the same over the whole cluster area because they are distributed quite uniformly even at late stages of the evolution of the cluster. This is expected to be a general feature as observed for low-mass stars in well studied open clusters (Pleiades, Praesepe). Our present calculations show that clusters as old as the Pleiades may have lost about 10% of their initial BD population but the number ratio of BDs to normal (not substellar) stars must remain almost unchanged. However, the long-term behavior of the relative percentage of BDs depends strongly on the initial mass function (IMF) assumed in the calculations. Clusters with a Salpeterian IMF evolve to reach relative percentages of BDs as low as 40% for a starting value around 70%. Our results suggest that BDs in clusters escape preferentially by evaporation.