The global mass functions of 35 Galactic globular clusters - II. Clues on the initial mass function and black hole retention fraction

In this paper, we compare the mass function slopes of Galactic globular clusters recently determined by Sollima & Baumgardt with a set of dedicated N-body simulations of star clusters containing between 65 000 and 200 000 stars. We study clusters starting with a range of initial mass functions (IMFs), black hole retention fractions and orbital parameters in the parent galaxy. We find that the present-day mass functions of globular clusters agree well with those expected for star clusters starting with Kroupa or Chabrier IMFs, and are incompatible with clusters starting with single power-law mass functions for the low-mass stars. The amount of mass segregation seen in the globular clusters studied by Sollima & Baumgardt can be fully explained by two-body relaxation driven mass segregation from initially unsegregated star clusters. Based on the present-day global mass functions, we expect that a typical globular cluster in our sample has lost about 75 per cent of its mass since formation, while the most evolved clusters have already lost more than 90 per cent of their initial mass and should dissolve within the next 1-2 Gyr. Most clusters studied by Sollima & Baumgardt also show a large difference between their central and global mass function (MF) slopes, implying that the majority of Galactic globular clusters are either near or already past core collapse. The strong mass segregation seen in most clusters also implies that only a small fraction of all black holes formed in globular clusters still reside in them.