The Luminosity Functions of Young Stellar Clusters
Session 12 -- Stars and Variable Stars
Oral presentation, Monday, June 12, 1995, 10:00am - 11:30am

## [12.01] The Luminosity Functions of Young Stellar Clusters

A.B. Fletcher (MIT), S.W. Stahler (UC Berkeley)

We describe a new theoretical framework for computing the evolution of both the mass function (MF) and luminosity function (LF) of a young stellar cluster that is forming within a molecular cloud core. Our method utilizes detailed results from stellar evolution theory, and assumes that young clusters arise from the continual collapse of dense cloud cores over an extended period of time. By further demanding that the stars reaching the main sequence conform to a prescribed Initial Mass Function (IMF), we are able to explicitly solve for the separate contributions, to the cluster MF \& LF, from each of the evolving populations of protostars, pre-main-sequence (PMS) stars and main sequence (MS) stars. Among the many detailed results generally predicted by our calculations, we find that the protostellar LF is peaked at a characteristic luminosity throughout the time of cluster formation, and that the time-averaged number fraction in protostars is typically just a few percent. At most times, the vast majority of cluster members are PMS stars, but the cluster light is dominated in the first $\, Myr$ by the intrinsically brighter protostars. After about $10 \, Myr$, the higher mass MS stars provide most of the light. In the intervening period, a pronounced step in the cluster LF is seen at about $10 \, L_{\sun}$.

A preliminary application of our models to the $\rho$ Ophiuchus embedded cluster indicates that it is reaching the end of its early evolution; we estimate its age to be about $1 \, Myr$, to within a factor of two. A corollary of this result is our theoretical expectation that there should be $> 160$ stars with bolometric $L > 0.01 L_{\sun}$ in this cluster, a significant fraction of which would be below the brown dwarf hydrogen burning limit of $0.08 \, M_{\sun}$. This interesting prediction suggests the idea that a good place to look for brown dwarfs is in star forming regions, where they are presumably born in elevated numbers. This, however, runs counter to the current state of observational affairs in regard to the search for baryonic dark matter in the form of brown dwarfs. One possible way out of this dichotomy between theory and observation would be to find a physical mechanism for severely attenuating the low mass end of the IMF. This research was supported by NSF Grants AST-90-14479 \& AST-90-22501.