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, which provides uniformity and spatial coverage for a proper background subtraction. With an age of about 6–8 Gyr, NGC 188 is expected to be suffering the effects of advanced dynamical evolution. Indeed, previous works in optical bands have suggested the presence of mass segregation. 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 R core pc and a tidal radius R tidal pc, about twice as large as the visual limiting radius. The concentration parameter $c=1.2\pm0.1$ of NGC 188 makes this open cluster structurally comparable to the loose globular clusters. The present 2MASS analysis resulted in significant slope variations with distance in the mass function $\phi(m)\propto m^{-(1+\chi)}$, being flat in the central parts ($\chi=0.6\pm0.7$) and steep in the cluster outskirts ($\chi=7.2\pm0.6$). The overall mass function has a slope $\chi=1.9\pm0.7$, slightly steeper than a standard Salpeter mass function. In this context, NGC 188 is similar to the 3.2 Gyr, dynamically evolved open cluster M 67. Solar metallicity Padova isochrone fits to the near-infrared colour-magnitude diagram of NGC 188 resulted in an age of $7.0\pm1.0$ Gyr. The best fit, obtained with the 7.1 Gyr isochrone, produced a distance modulus $\mbox{$(m-M)_0$}=11.1\pm0.1$, $\mbox{$E(B-V)$}=0.0$, and a distance to the Sun $\mbox{$d_\odot$}=1.66\pm0.08$ kpc. The observed stellar mass (in the range $0.98\,\mbox{$M_\odot$}{-} 1.08\,\mbox{$M_\odot$}$) in NGC 188 is m obs. A simple extrapolation of the observed overall mass function to stars with $0.08\,\mbox{$M_\odot$}$ resulted in a total present mass of m tot. 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 m tot. Since mass-loss processes such as evaporation and tidal stripping have been occurring in this old open cluster for about 7 Gyr, the primordial mass in NGC 188 must have been significantly larger than ${\sim}4\times10^3\,\mbox{$M_\odot$}$. We also examined the consequences of the presence of unresolved binaries and concluded that, even if dominant in the CMD, binaries alone are not responsible for the flat central mass function, which supports the mass-segregation scenario.