It seems natural to assume that the number of physical satellites must be a function of the size of the central galaxy or of some other parameter that is related to the size. In this section, the dependence of Nphys on total mass, hydrogen mass, and other absolute characteristics will be examined.
The total mass, and the HI mass, can be estimated from the absolute luminosity and the integrated color index (or the morphological type); in the present case, certain relations previously derived by the writer (1964) have been used. For a number of nearby galaxies direct observational results are available. The total masses for the majority of the spiral systems of Table 7 have already been listed Ill the above-mentioned paper. For the 38 spirals included from the Reference Catalogue the apparent magnitudes needed have been assembled from various sources, in the first place from the catalogue by Humason et al. (1956).
In the upper part of Fig. 7 the number of physical companions has been plotted against the log. total mass (solar units), the material comprising 113 spiral systems of classes A - B in Table 7 (two objects omitted on account of missing data). The log. mass ranges from 8.7 (NGC 4236) to 12.1 (NGC 4594). Quite unexpectedly, the plot does not indicate any correlation between the two parameters. The negative result may possibly be due to the fact that the separations of the satellites are limited to 5.0 kpc. It seems possible that the more massive spiral galaxies have satellite clouds of larger extensions than the less massive ones.
Figure 7. Variation in number of satellites with total mass and Hi mass of central galaxy (in the bottom part spirals with nuclear color excess > +0m.06 are omitted). The square represents the mean result referring to 8 central galaxies of type Ir I.
In the middle part of the figure, Nphys for the same material is plotted against the log. HI mass (solar units); the hydrogen mass ranges from 8.3 to 10.3 in the logarithmic scale. In this case a correlation is indicated, as represented by the straight regression line. The number of satellites approaches zero as the log. mass decreases below 9.0.
As was mentioned in the preceding section, spiral systems with nuclear color excesses larger than +0m.06 have a mean number of satellites = 0.0. The correlation found above is naturally reduced by the presence of these systems in the material. If the 26 spirals with high color excesses are left out, we arrive at the diagram in the lower part of Fig. 7. The coefficient of correlation now amounts to +0.28 ± 0.10 ; since the result is about three times the mean error, it is presumably significant.
The open circle introduced in the three diagrams shows the position of the Milky Way (two nearby companions). The square gives the mean position referring to eight galaxies of type Ir I (NGC 1156 - 2366 - 3109 - 4532 - 6822, IC 1613, Ho II, WLM). In circular survey areas with a radius of 50 kpc around these galaxies a total number of three physical satellites have been found by applying the same procedure as that used for the spiral systems. Since the number does not significantly differ from zero, it seems likely that Ir I galaxies do not possess any physical satellites.
As regards other absolute characteristics of the spiral systems, there are weak correlations between Nphys , on the one hand, and absolute magnitude, absolute diameter, and morphological type, on the other. All these correlations are very likely reflections of the relation between Nphys and hydrogen mass.
To summarize the results of this chapter, it is recollected that physical satellites of spiral galaxies are apparently concentrated in high local latitudes, and that they seem to favor systems which have nuclear color excesses below a certain limit and which contain large amounts of gas. The results seemingly point to one interpretation: that the satellites have been formed from gas ejected from the central galaxies. This interpretation must be considered as, a hypothesis, since the statistical evidence presented is not of a conclusive nature.
As regards possible ejections of matter, definitive results have been obtained from direct observations of explosive events in the nuclei of a number of systems, in the first place, some well-known Seyfert galaxies. In M82 (Lynds and Sandage 1963; Solinger 1969), and in NGC 1275 (Burbidge and Burbidge 1965), observational evidence shows that material has been ejected to great distances from the nuclei. In NGC 1068 (Walker 1968a) nuclear clouds are being expelled at velocities that are probably in. excess of the escape velocity; similar processes are apparently also taking place in NGC 4151 and NGC 7469. Nuclear clouds of the same type appear in the central region of the elliptical galaxy M87 (Walker 1968b), indicating that the cloud-ejection process is not confined to spiral galaxies. Several attempts have been made to show that the ejected matter condenses into galaxies; references may be made to Arp (1967, 1968a, 1968b), and to Sérsic (1968). So far these attempts, which are based on statistical analyses of available data, have not yielded any results that appear to be conclusive. From a theoretical point of view, the construction of a model for the condensation process seems to encounter serious difficulties. In any case, if the velocity of the ejected gas is larger than the escape velocity, which often seems to be the case, possible condensations cannot give birth to gravitationally bound satellites.
While awaiting the accumulation of further observational data that may eventually lead to a settlement of the question, the conservative position to adopt for the present is naturally to assume that all the members of a physical group of galaxies have been formed more or less simultaneously from different parts of the same gas cloud. The formation of galaxies would thus be a parallel to the formation of stars in associations. In a previous investigation on the evolution of galaxies the writer (1964) has presented some arguments in favor of the assumption that all galaxies have approximately the same actual age.