PART IV. SOME STATISTICAL PROPERTIES OF THE CATALOG

This REVISED SHAPLEY-AMES (RSA) Catalog provides a particularly useful sample for statistical studies because the velocity coverage is nearly complete and because the catalog completeness function f (m) is well determined (page 4). The luminosity and density functions of the nearby galaxies can be obtained from the RSA data from calculations of the bias (Sandage, Tammann, and Yahil, 1979; Tammann, Yahil, and Sandage, 1979; Yahil, Sandage, and Tammann, 1980) that start from the apparent distributions of velocities, apparent magnitudes, and absolute magnitudes. Because the distributions are of general interest in themselves, we summarize some of them in this section.

Histograms of the types are given in Figure 1, divided into the ordinary and the barred families. The types in the main catalog have a somewhat finer subdivision than shown in this figure, as we have combined the transition cases (such as E/S0, S0/a, Sab, Sbc) with the main groups. In those cases where the type is in doubt and where two possibilities are given [such as NGC 3390, listed as type S0₃(8) or (Sb)], the galaxy has been counted twice, once in each bin. Hence the sum of the numbers is greater than the 1246 entries in the catalog.

Figure 1. The distribution of types in the complete RSA. Intermediate and transitional types have been combined with the main types in these histograms.

Note the very few galaxies of types Sd, SBd, and later.This is due entirely to the observational bias in the apparent-magnitude-limited RSA caused by the fainter mean absolute magnitude of these types compared with Sc, SBc, and earlier galaxies. The density of Sd and later types per unit volume of space, in fact, dominates the true distribution (see Tammann et al., 1979).

The distribution of velocities v₀, i.e., reduced to the centroid of the Local Group, is shown in Figure 2, binned in 250 km/s intervals. Only nine galaxies of the 1245 listed have negative velocities, and these are either in the Local Group or are within 4° of the center of the Virgo Cluster. The Virgo cases are clearly in the tail of the virial velocity distribution of that cluster.

Figure 2. The distribution of reduced velocities v0 in the RSA (n = 1245), binned in 250 km/s intervals. (NGC 7119 with v0 = 9825 km/s is not plotted.)

Use of the (M), f (m), and D(v) functions determined from these data (Sandage et al., 1979; Tammann et al., 1979; Yahil et al., 1980) reproduces the histogram in Figure 2 by summing the separate calculations from this equation, providing that the sky is divided into coherent regions over which particular values of the density D(v) have relevance.

Note from Figure 2 the few numbers of RSA galaxies with v₀ > 4000 km s^-1. Hence, the grasp of the catalog is hardly further than ~ 80 Mpc with any statistical significance.

Figure 3 shows the distribution of B_T magnitudes, not corrected for Galactic absorption (A⁰ of Column 13) nor for internal absorption (Aⁱ of Column 14). A histogram (not shown) of corrected magnitudes B_T^0,i is similar, but is, of course, shifted toward brighter magnitudes. The expected count per magnitude interval A(B_T) can be calculated from the fundamental equation of stellar statistics with the adopted (M), f (m), and density functions. And because these functions were determined from the reverse analysis of Figures 2 and 3, the agreement of the prediction with the observed distribution of Figure 3 is of course good.

Figure 3. The number of galaxies in the RSA at magnitude BT (not corrected for Galactic or internal absorption) in the interval BT = 0m.2 mag.

The incompleteness of the RSA is shown in Figure 4, where the solid histogram represents counts in the RSA for galaxies with declinations north of -3°. The hatched histogram is for galaxies from the Table of Additional Bright Galaxies in Appendix A. These should have been included in the original Shapley-Ames but were not. The completeness function f (m) agrees well with the ratio of the hatched to the solid histograms at any given apparent magnitude.

Figure 4. Illustrates the incompleteness of the RSA as listed. The solid histogram is the distribution of apparent BT magnitudes for all galaxies in the RSA north of declination -3°. The hatched additions are the galaxies north of = -3° not listed in the RSA that are brighter than BT = 13m.4, found by reducing the Zwicky Catalogs to the BT system.

The incompleteness begins at about B_T 12^m and becomes severe by B_T = 12^m.5. Surprisingly, however, there are a number of galaxies even brighter than B_T = 12^m.0 that should also have been included. Ten of these are low-surface-brightness dwarfs (M_B - 17^m.0). Two additional galaxies (IC 342 and the Circinus system) lie at very low Galactic latitude. This shows the strong bias of the SA against low-surface-brightness galaxies. The brightest full-sized systems whose absence in the SA cannot be explained in this way are NGC 676, NGC 3507, and NGC 660.

For convenience we list the 20 known galaxies that are brighter than B_T = 12^m.0 missing from the RSA. The absolute magnitudes are from Kraan-Korteweg and Tammann (1979).

The distribution of absolute magnitudes for all galaxies in the catalog with redshifts is shown in Figure 5. The very few galaxies fainter than M_{BT^{0, i}} = - 18^m is a result of the intrinsic bias of the magnitude-limited catalog. The absolutely fainter galaxies are denied entry into the listing in appreciable numbers because the apparent magnitude limit is too bright for distances where the volume becomes sufficiently large. This natural bias is so severe that the true differential luminosity function rises monotonically from M_B -23^m to at least -16^m, whereas the apparent distribution in Figure 5 begins to fall already fainter than M_B -22^m. The method of calculating this apparent distribution from the luminosity and completeness functions is given elsewhere (Sandage, Tammann, and Yahil, 1979).

Figure 5. The distribution of absolute luminosities for all galaxies in the RSA that have redshifts, using maqgnitudes corrected for internal and Galactic absorption. The true luminosity function (i.e., the distribution per unit volume) rises monotonically. The fall of the apparent function fainter than -22 mag is due to the observational bias.

The comparison of the maximum luminosity of E and spiral galaxies depends, of course, on the adopted correction for intrinsic absorption. Without corrections, the brightest spiral is NGC 1961 with M_{BT^{0, i}} = - 23^m.04 which is ~ 0.3 fainter than the brightest elliptical.