Spatial dependence of 2MASS luminosity and mass functions in the old open cluster NGC 188

Luminosity and mass functions in the old open cluster NGC 188 are analysed by means of J and H 2MASS photometry. Within the uncertainties, the observed projected radial density profile of NGC 188 departs from the two-parameter King model in two inner regions, which reflects the non-virialized dynamical state and possibly, some degree of non-sphericity in the spatial shape of this old open cluster. Fits with two and three-parameter King models to the radial distribution of stars resulted in a core radius of 1.3 pc and a tidal radius of 21 pc. The present 2MASS analysis resulted in significant slope variations with distance in the mass function $\varphi (m)\propto m^{-(1+\chi )}$, being flat in the central parts ($\chi =0.6\pm 0.7$) and steep in the cluster outskirts ($\chi =7.2\pm 0.6$). The overall mass function has a slope $\chi =1.9\pm 0.7$, slightly steeper than a standard Salpeter mass function. Solar metallicity Padova isochrone fits to the near-infrared colour-magnitude diagram of NGC 188 resulted in an age of $7.0\pm 1.0$ Gyr. The best fit, obtained with the 7.1 Gyr isochrone, produced a distance modulus $\text{mM}=11.1\pm 0.1$, $\text{ebv}=0.0$, and a distance to the Sun $\text{ds}=1.66\pm 0.08$ kpc. The observed stellar mass (in the range $0.98\text{ms}-1.08\text{ms}$) in NGC 188 is $\text{mobs}=380\pm 12\text{ms}$. A simple extrapolation of the observed overall mass function to stars with $0.08\text{ms}$ resulted in a total present mass of $\text{mtot}\sim (1.8\pm 0.7)\times {10}^4\text{ms}$. On the other hand, for a more realistic initial mass function which flattens in the low-mass range, the total mass in NGC 188 drops to $\text{mtot}\sim (3.8\pm 1.6)\times {10}^3\text{ms}$.