The mass function of main-sequence stars in NGC 6397 from near-infrared and optical high-resolution Hubble Space Telescope observations

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 similar to 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 similar to 4.'5 and similar to 3.'2 from the center. These observations span the region from similar to 1 to similar to 3 times the cluster's half-light radius (r(hl) similar or equal to 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 similar or equal to 8.5 or M-H similar or equal to 7 and then drop precipitously well before photometric incompleteness becomes significant. Within the observational uncertainties, at M-I similar or equal to 12 or M-H 2 10.5 (similar to 0.09 M.) the luminosity functions are compatible with zero. The direct comparison of our NIC 2 held with previous WFPC 2 observations of the same area shows that down to M-H similar or equal to 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 similar to 0.3 M.. No single-exponent power-law distribution is compatible with these data, regardless of the value of the exponent. We iind that a dynamical model of the cluster can simultaneously reproduce the luminosity functions observed in the core, at similar to 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. and then drops as m(0.2+/-0.1) below similar to 0.3 M.. 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) similar or equal to 0.3 and sigma similar or equal to 1.8.