Question

What is the mean numerical density of stars in a spherical globular cluster that contains 1 million stars ?how can we express it in stars/parsec-cube?

Answer 1

Globular star clusters have had time to relax so their radial density distribution of stars is approximately Gaussian.  The mean density will be a function of radius with larger radii showing lower average density.  Using  cluster diameters measured at FWHM will give values that can be easily compared to each other.  If a  typical globular cluster has a radius of 10 pc, and if 67% of its stars are within that radius, then the mean density will be about 160 stars per pc^3,  much higher than the solar neighborhood!  Other distributions will give somewhat different values, especially at larger radii.hope this answer is useful,