The Mass Function of Main-Sequence Stars in NGC 6397 from Near-Infrared and Optical High-Resolution Hubble Space Telescope Observations

Abstract

We have investigated the properties of the stellar mass function in the globular cluster NGC 6397 through the use of a large set of Hubble Space Telescope (HST) observations. The latter include existing WFPC 2 images in the V and I bands, obtained at ~4.5‧ and 10' radial distances, as well as a series of deep images in the J and H bands obtained with the NIC 2 and NIC 3 cameras of the NICMOS instrument pointed, respectively, to regions located ~4.5‧ and ~3.2‧ from the center. These observations span the region from ~1 to ~3 times the cluster's half-light radius (r_hl~=3^') and have been subjected to the same, homogeneous data processing so as to guarantee that the ensuing results could be directly compared to one another. We have built color-magnitude diagrams that we use to measure the luminosity function of main-sequence stars extending from just below the turnoff all the way down to the hydrogen-burning limit. All luminosity functions derived in this way show the same, consistent behavior in that they all increase with decreasing luminosity up to a peak at M_I~=8.5 or M_H~=7 and then drop precipitously well before photometric incompleteness becomes significant. Within the observational uncertainties, at M_I~=12 or M_H~=10.5 (~0.09 M_solar) the luminosity functions are compatible with zero. The direct comparison of our NIC 2 field with previous WFPC 2 observations of the same area shows that down to M_H~=11 there are no more faint, red stars than those already detected by the WFPC 2, thus excluding a significant population of faint, low-mass stars at the bottom of the main sequence. By applying the best available mass-luminosity relation appropriate to the metallicity of NGC 6397 and consistent with our color-magnitude diagrams to both the optical and the IR data, we obtain a mass function that shows a break in slope at ~0.3 M_solar. No single-exponent power-law distribution is compatible with these data, regardless of the value of the exponent. We find that a dynamical model of the cluster can simultaneously reproduce the luminosity functions observed in the core, at ~3.2‧, 4.5‧, and 10' away from the center, as well as the surface brightness and velocity dispersion profiles of red giant stars, only if the model initial mass function (IMF) rises as m^-1.6+/-0.2 in the range 0.8-0.3 M_solar and then drops as m^0.2+/-0.1 below ~0.3 M_solar. Adopting a more physical lognormal distribution for the IMF, we find that all these data taken together imply a best-fit distribution with m_c~=0.3 and σ~=1.8. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555.