5. Results

Some data referring to the number of survey fields, and the number of galaxies examined, are summarized in Table 2. In the survey areas there are altogether 1273 galaxies with diameters larger than the above limits, and in the comparison areas 2084. The entire material thus comprises 3357 galaxies distributed over 518 fields.

Fig. 2 gives the statistical distribution of the 174 survey areas, the areas being grouped according to the number of galaxies (diameter 1.0 kpc). The number of companions, physical and optical, of the central spiral galaxies ranges from 0 to 13. The smooth curve represents the Poisson distribution corresponding to the same total number and the same arithmetical mean. As expected, the observed frequencies deviate from a random distribution. In order to reduce possible disturbances by distant clusters that may fall within the boundaries of the survey areas, it seemed advisable to exclude the 14 most populous areas-those with more than eight objects, or double the average number. The following analyses will be based on the 160 survey areas that have a maximum of eight galaxies. For the same reason, and as a compensation, the 28 most populous comparison areas have also been omitted. In the second part of the survey, down to a diameter of 0.61 kpc, we have excluded two additional survey areas with more than 15 galaxies, and the four most populous comparison areas.

Figure 2. Statistical distribution of 174 survey areas containing different number of galaxies. The smooth curve is the corresponding Poisson distribution.

The number of physical companions to the central spiral system in a survey area is, in a statistical sense, represented by the difference between the number of galaxies in this area and half the total number in the two comparison areas. However, the central systems, with a mean major diameter of 27 kpc, screen off parts of the survey areas, about 3% (class A) and 5% (class B). The comparison number is accordingly multiplied by 0.97 and 0.95, respectively (since for spirals of class A the physical companions are confined to position angles of 30° -90°, the factor will in reality be 0.65). For class C, comprising spiral systems of different inclinations which sometimes have large companions within the survey areas, the average factor is 0.95. It has been found that the accuracy is improved if the individual comparison number is replaced by the mean number derived from all the comparison areas as a function of the distance, the accidental fluctuations being reduced. The results listed in Table 7, as regards the number of physical companions (diam. 1.0 kpc), are based on these smoothed-out comparison numbers. The values of N_phys range from -2 to +7, the estimated mean error of an individual number being about 1.2. It should be remarked here that the statistical distribution derived later for position angles, separations, and absolute diameters are based on the total number of optical companions, corresponding to all the comparison areas.

There does not seem to be any systematic dependence of the tabulated N_phys on the galactic latitude, which may indicate that the surface-brightness gradients in the outer parts of the satellites are so steep that the measured diameters are not seriously affected by galactic absorption. On the other hand, the results obtained in the extended survey (diam. = 0.6 - 0.9 kpc) indicate a certain latitude effect, probably explained by the somewhat lower surface magnitude of these small satellites. For this reason, spiral systems with galactic latitudes below 29° (NGC 891, 925, 1023, 1560, 2835, 7640) will not be included when the results of the extended survey are used in the determination of the distribution of absolute diameters (sect. 10).

It was stated above that survey areas with more than eight galaxies (diam. 1.0 kpc) have been excluded, in order to reduce possible disturbances by background clusters. It is possible to make a check on the remaining part of the material by means of the charts of the distribution of distant clusters given in the catalogues by Zwicky et al. (1961, 1963, 1965, 1966, 1968). From the charts we estimate the fraction, f, of each survey area that is projected on a background cluster. If only clusters of a limited size are included, the very extended clouds being omitted, we find that f = 0 for about half the number of survey areas; on an average, f amounts to 0.22. It is not possible to establish a statistically significant relation between N_phys and f, the coefficient of correlation being as small as +0.10 ± 0.10 (m.e.).

For a reliable determination of the distribution of absolute diameters for galaxies in the physical groups it is important that the apparent diameter measures form a homogeneous system, that is, that the diameters are free from systematic errors that are a function of the diameter or of the distance modulus. All the diameters have been measured by the writer using the same eyepiece and taking care that the observing conditions were the same, for instance, as regards the illumination of the Atlas prints. A great part of the work has been repeated, with no indication of any serious changes in the diameter measures. The homogeneity is supported by the fact that N_phys, as listed in Table 7, shows no systematic dependence on the adopted distance modulus. Furthermore, an examination of the statistical distribution of the diameters of the galaxies in all the comparison areas shows that this distribution is compatible with the assumption of a constant space density of galaxies (cf. sect. 14). There is only a slight decrease in the number of galaxies with diameters less than 0'.35, which may be explained as a redshift effect in the diameters, since most of these small galaxies are at estimated distances of the order of 100-200 Mpc. It should be noted here that the diameters of the small physical satellites of the spiral systems do not suffer from any redshift effect; whereas most of the background objects are giant galaxies at very large distances, the satellites are dwarf systems with an average distance modulus of about 30.0.