4 Luminosity function

The V-band GCLF for NGC 5128 is compared to the ones of the MW and M 31 in Fig. 8. The actual shape of the luminosity function depends on the size of the bins and on the bin-centers. Statistically it is possible to compare them independently of binning using the Kolmogorov-Smirnov (KS) test. In Fig. 9 the cumulative distribution functions for the three GCLFs are shown. The thick line is used for NGC 5128, thin line for the MW and dotted line for M 31. Absolute magnitudes for NGC 5128 globular clusters were calculated using the distance modulus value of ( m-M)₀=27.8 (Soria et al.  1996) and reddening value of E(B-V)=0.1.

The KS statistic measures the maximum value of the absolute difference between two cumulative distribution functions from which a probability that the two distributions are drawn from a common distribution can be calculated. The probability that the GCLF of NGC 5128 matches the one of the MW is 89%, comparable to the probability that M 31 GCLF matches the MW one (85%). The difference is slightly bigger in the U-band distributions (Fig. 9 right panel), but it is also probable that the three luminosity functions are essentially similar for the three galaxies. I conclude that the NGC 5128 GCLF is as similar (or as different) to the MW GCLF as the M 31 one.

Figure 8: From top to bottom: V-band GCLF for M 31, NGC 5128 and MW

Usually the GCLF is fitted with a Gaussian or t₅ distribution function in order to determine its peak magnitude. It should be noted, however, that the reasonably complete luminosity functions are known only for the two spiral galaxies, the MW and M 31. Both of these GCLFs appear to depart from the Gaussian distribution (Ashman et al. 1995), while there is no complete GCLF for any elliptical galaxy. The dependence of the turn-over magnitude on the detection of the faint end of GCLF is discussed in Ashman et al. (1995). The determination of the turn-over magnitude for NGC 5128 is left for a subsequent paper where the complete analysis of WFI data will to be presented.

The detection of the faint end of the GCLF in an elliptical galaxy is also important from the dynamical point of view. The faint globular clusters are typically also the less massive ones and their presence in the deep potential of a giant elliptical puts strong constraints on the potential itself, as well as on the effects of tidal forces in the halo. Unfortunately, the faintest globular clusters, corresponding to the MW Pal 1, AM 4, Terzan 1 and Pal 13 are probably not detectable on FORS1 images (see Sect. 2.4).

The processes that destroy globular clusters can be divided into internal, such as two-body relaxation and mass loss during stellar evolution, and external. The external processes depend greatly on environment and therefore on the position of the clusters in the galaxy. While tidal shocks preferentially destroy less dense clusters, dynamical friction brings more massive clusters very close to the galactic centre. Both of these external processes are much stronger in the inner part of the galaxy. According to theoretical simulations (Vesperini 2000; Ostriker & Gnedin 1997) in a galaxy like NGC 5128, with the total mass of $\sim$4 10¹¹ $M_\odot$ (Israel 1998) and $R_{\rm e}=5.24$ kpc (Dufour et al. 1979), a strong disruption and mass loss are efficient only within a galactocentric distance of 1-2 $R_{\rm e}$, while at larger radii most of the mass loss is due to effects of stellar evolution. Field 1 is located at 2-3.5 $R_{\rm e}$ and Field 2 at 1.2-2.3 $R_{\rm e}$. While the dynamical effects may still be important for Field 2 clusters, they are probably completely negligible for clusters in the outer field. It is not possible to quantify these effects by simple comparison of the two subsamples, because of the small number statistics.

Figure 9: Kolmogorov-Smirnov statistic: the cumulative distribution function for NGC 5128 (thick line) is constructed from the V-band GCLF (left panel) and U-band GCLF (right panel) and compared with the ones of the MW (thin line) and M 31 (dotted line)

Figure 10: The color distribution for M 31, NGC 5128 and the MW. The line overplotted on the NGC 5128 histogram is the best nonparametric kernel estimate (Silverman 1986) of the color distribution