We have investigated the properties of the stellar mass function in the globular cluster NGC 6397 through the use of a large set of HST observations .
The latter include existing WFPC 2 images in the V and I bands , obtained at \sim 4 \farcm 5 and 10 \arcmin 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 \sim 4 \farcm 5 and \sim 3 \farcm 2 from the center .
These observations span the region from \sim 1 to \sim 3 times the cluster ’ s half-light radius ( r _ { hl } \simeq 3 ^ { \prime } ) , 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 turn-off 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 } \simeq 8.5 or M _ { H } \simeq 7 and then drop precipitously well before photometric incompleteness becomes significant .
Within the observational uncertainties , at M _ { I } \simeq 12 or M _ { H } \simeq 10.5 ( \sim 0.09 M _ { \odot } ) 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 } \simeq 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 IR data , we obtain a mass function that shows a break in slope at \sim 0.3 M _ { \odot } .
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 \sim 3 \farcm 2 , 4 \farcm 5 , and 10 ^ { \prime } away from the center , as well as the surface brightness and velocity dispersion profiles of red giant stars only if the model IMF rises as m ^ { -1.6 \pm 0.2 } in the range 0.8 - 0.3 M _ { \odot } and then drops as m ^ { 0.2 \pm 0.1 } below \sim 0.3 M _ { \odot } .
Adopting a more physical log-normal distribution for the IMF , all these data taken together imply a best fit distribution with m _ { c } \simeq 0.3 and \sigma \simeq 1.8 .