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Astron. Astrophys. 328, 83-94

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Determination of the globular cluster and halo stellar mass functions and stellar and brown dwarf densities*

Gilles Chabrier and Dominique Méra

C.R.A.L. (UMR 7455 CNRS), Ecole Normale Supérieure, F-69364 Lyon Cedex 07, France (chabrier, dmera @ens-lyon.fr)

Received 10 January 1997 / Accepted 28 April 1997


We use recent low-mass star models, which reproduce accurately the observed sequences of various globular clusters, to convert the observed luminosity functions into bolometric luminosity functions. These latter are shown to exhibit a similar behaviour with a rising slope up to $M_{\rm bol}\sim 9$, i.e. $m\sim 0.2-0.3 M_\odot$, and a decreasing behaviour beyond this limit. We then derive mass functions for globular star clusters down to the bottom of the main sequence. These mass functions are well described by a slowly rising power-law $dN/dm\propto m^{-\alpha}$, with 0.5 1.5, down to $\sim 0.1 M_\odot$, independently of the metallicity, suggesting a rather universal behaviour of the cluster initial mass functions. The effects of tidal stripping and mass segregation are illustrated by the overabundance of very low-mass stars in the outer parts of NGC6397 and their depletion in the central parts. This analysis confirms that the mass function determined near the half-mass radius has been weakly affected by external and internal dynamical effects and reflects relatively closely the initial mass function. We predict luminosity functions in the NICMOS filters in the stellar and in the brown dwarf domains for different mass functions and metallicities.

We apply these calculations to the determination of the mass function in the Galactic halo, including the DeVaucouleurs spheroid and the 1/r2 dark halo. We derive the slope and the normalization of the spheroid mass function which is well described by the afore-mentioned power-law function with $\alpha \sim 1.7\pm 0.2$ down to 0.1 $M_\odot$, although a slowly decreasing mass function below $\sim 0.15 M_\odot$ can not be excluded with the data presently available. Comparison with the Hubble Deep Field star counts is consistent with such a mass function and excludes a significant stellar population in the dark halo. This shows that essentially all the high-velocity subdwarfs observed in the solar neighborhood belong to the Galactic spheroid.

Consistent analysis with recent microlensing experiments towards the LMC shows that the spheroid and the dark-halo stellar+brown dwarf populations represent at most $\sim$ 1% of the Galactic dark matter density. This clearly excludes brown dwarfs and low-mass stars as significant dark matter candidates.

Key words: stars: Low-mass, brown dwarfs - stars: luminosity function, mass function - stars: Population II - Galaxy: globular clusters - Galaxy: stellar content - cosmology: dark matter

*The bolometric LF's displayed in Fig. 1 are available at CDS via anonymous ftp to cdsarc.u-strasbg.fr ( or via http://cdsweb.u-strasbg.fr/Abstract.html

© European Southern Observatory (ESO) 1997

Online publication: October 30, 1997
Last change: March 24, 1998