Radial distribution of stars in globular clusters inferred from the Monte Carlo approach

Abstract

In this paper we try to reconstruct the spatial distribution of stars in globular clusters (GCs) from heuristic statistical ideas. Such 3D radial distributions are important for understanding physical conditions across the clusters. Our method is based on converting spherically symmetrical functions such as exp(-r2/s2), exp(-r/s), 1/(1 + r2/s2) 2 and 1/(1 + r2/s2)m, (s and m are parameters) to 2D star distributions in a GCs by the Monte Carlo method. By comparing the obtained 2D profiles with observational ones we demonstrate that Gaussian or exponential distribution functions yield too short extensions of periph-eral parts of the GCs profiles. The best candidate for fitting GCs profiles has been found to be the generalized Schuster density law: C/ (1 + r2/s2)m, where C is the normalization constant and s and m are adjustable parameters. These parameters display a nonlinear correlation with s varying from 0.1 to 10 pc, whilst m is close to 2. Using this law the radiation temperatures across M 13 and 47 Tucane were estimated.