Evolution of globular cluster systems in elliptical galaxies - I. Log-normal initial mass function

We study the evolution of globular cluster systems (GCS) in elliptical galaxies and explore the dependence of their main properties on the mass and the size of the host galaxy. We focus our attention on the evolution of the GCS mass function (GCMF), on the fraction of surviving clusters and on the ratio of the final to initial total mass in clusters; the dependence of these GCS properties on the structure of the host galaxy as well as their variation with the galactocentric distance inside individual host galaxies is thoroughly investigated. We adopt a log-normal initial GCMF with mean mass and dispersion (logM_i=5.25 and σ_i=0.6) similar to those observed in the external regions of elliptical galaxies where memory of initial conditions is likely to be well preserved. After a survey over a large number of different host galaxies we restrict our attention to a sample of galaxies with effective masses, M_e, and radii, R_e, equal to those observed for dwarf, normal and giant ellipticals. We show that, in spite of large differences in the fraction of surviving clusters, the final mean masses, logM_f, of the GCMF in massive galaxies (logM_e>~10.5) are very similar to each other (logM_f~=5.16, M_V=-7.3, assuming ML_V=2) with a small galaxy-to-galaxy dispersion; low-mass compact galaxies tend to have smaller values of logM_f and a larger galaxy-to-galaxy dispersion. These findings are in agreement with those of recent observational analyses. The fraction of surviving clusters, N_fN_i, increases with the mass of the host galaxy, ranging from N_fN_i~0.9 for the most massive galaxies to N_fN_i~0.1 for dwarf galaxies. We show that a small difference between the initial and the final mean mass and dispersion of the GCMF and the lack of a significant radial dependence of logM_f inside individual galaxies do not necessarily imply that evolutionary processes have been unimportant in the evolution of the initial population of clusters. For giant galaxies most disruption occurs within the effective radius, while for low-mass galaxies a significant disruption of clusters takes place also at larger galactocentric distances. The dependence of the results obtained on the initial mean mass of the GCMF is also investigated, and it is shown that outside the interval 4.7<~logM_i<~5.5 both the spread and the numerical values of logM_f are not consistent with those observed.