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Astron. Astrophys. 318, 405-415 (1997)

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3. Statistics

3.1. Photometric properties

In the following Figs. 1 and 2, all of our newly observed objects are considered jointly.

[FIGURE] Fig. 1. a Distribution of apparent B magnitude for 185 sample galaxies (bin size 0.5 magn.). b Distribution of mean [FORMULA] colours for 134 sample galaxies (bin size 0.5 magn.). c Distribution of mean angular diameters for 164 sample galaxies (bin size [FORMULA]). d Distribution of mean surface brightness for 164 sample galaxies (solid line) and for 1550 CfA galaxies in the northern hemisphere (dashed line) (bin size 0.5 magn.).
[FIGURE] Fig. 2. a Distribution of radial velocities for 193 sample galaxies (bin size 2500 km/s). b Distribution of absolute B magnitudes for 185 sample galaxies (solid line) and for 87 ZCAT galaxies from the same volume as our sample (dashed line) (bin size 0.5 magn.).

Their B magnitudes (Fig. 1a) lie between 15.5 and 20.5 (apart from the 7 Back-up galaxies with B [FORMULA] 15) thus being up to 5 magn. fainter than the galaxies of the CfA and other large scale surveys limited to [FORMULA].

Fig. 1b shows the [FORMULA] colours being spread from 0.5 to 2.0 magn. The distribution resembles that of irregular galaxies (Gallagher & Hunter 1987). Obviously the sample contains a considerable percentage of late type galaxies comprising young stellar populations.

The distribution of the mean angular diameters (corresponding to the arithmetic mean of the major and minor axes measured at the [FORMULA] / [FORMULA] isophote level) is shown in Fig. 1c. In accordance with our selection rules they are considerably smaller than those of recent diameter selected surveys. The SSRS I of da Costa et al. (1988), for instance, adopted a lower diameter limit of [FORMULA].

For the distribution of the mean surface brightness (SB) of our galaxies see Fig. 1d. About 76 [FORMULA] have fainter SBs than the mean of the CfA galaxies ([FORMULA] / [FORMULA], Bardelli et al. 1991). But only 2 [FORMULA] of our objects are classical LSB galaxies with [FORMULA] / [FORMULA] (Thuan et al. 1987). So they are not more abundant than in the CfA sample (Huchra et al. 1993).

Information about the morphological types of our objects is given in Table 3 of Paper I. Here we do not differentiate between the various groups.

3.2. Radial velocities [FORMULA]

The distribution peaks at 12500 km/s (Fig. 2a), see also Fig. 2 of Paper I. Almost 70 [FORMULA] of all galaxies are concentrated between 5000 km/s and 20000 km/s, whereas 44 [FORMULA] lie beyond 15000 km/s and therefore outside of the following cone diagrams. On the other hand, no galaxy with less than 4500 km/s was found, revealing that our sample does not contain objects within the nearest voids.

3.3. Absolute magnitudes ([FORMULA] km/s/Mpc)

Fig. 2b shows the absolute magnitude distributions of our complete sample (185 galaxies with known [FORMULA] and B magnitudes) as well as of all ZCAT galaxies with B [FORMULA] 15.5 towards the four regions VN2, VN8, VN4 and A2151 within the fields of our search (195 objects, field sizes 67, 83, 1 and 4 [FORMULA]). The ZCAT catalogue of Huchra et al. (1993) contains all galaxies with so far published redshifts. Although it is not a statistically-controlled data base we use it here and in Sect. 4 because of its greater quantity of data (cf. Fairall et al. 1991).

Compared to the ZCAT selection our sample is shifted towards lower luminosities by more than 1 magn.: The median brightness of our galaxies is -19.3, compared to -20.5 for ZCAT or -20.1 for CfA galaxies selected in the same way. 9.7 [FORMULA] of our galaxies are fainter than [FORMULA], compared with 1.0 [FORMULA] of the ZCAT sample. Thus, while a lot of our galaxies are rather luminous objects, our sample contains indeed more non-giant galaxies due to the fainter limiting magnitude of our survey and the morphological selection criteria. On the other hand we did not find any extreme dwarf beyond [FORMULA] although those should be detectable up to 9500 km/s for [FORMULA]

The absolute magnitude as a function of radial velocity for our galaxies is shown as Fig. 3. The shaded part emphasizes the known fact that at larger [FORMULA] the CfA sample includes only high luminosity objects (beyond 10000 km/s brighter than [FORMULA]). There is practically no overlap of the areas where the CfA galaxies and ours are located. In line with our intentions we found pretty many relatively nearby galaxies of lower luminosity as the diagram shows. But our sample still contains a lot of background objects as already mentioned in relation to Fig. 2b.

[FIGURE] Fig. 3. Absolute B magnitudes as a function of radial velocities. Empty circles indicate POSS galaxies, crossed circles K3/CCD objects and rhombs stand for Back-up galaxies. Dashed line: limit of the CfA extension with [FORMULA]. Solid lines: limits for surveys with [FORMULA] and [FORMULA].

3.4. Completeness

Rough information on the completeness of our search can be gained in this way: As a result of our fainter limits we should find additional galaxies in these regions where the CfA galaxies are concentrated. Their number can be estimated by means of the CfA luminosity function derived by de Lapparent et al. (1989). At [FORMULA] km/s, for instance, the limiting absolute magnitude of the CfA galaxies is -18.6, while for our survey it is either -15.1 (Sample 1, [FORMULA]) or -13.6 (Sample 2, [FORMULA]). Integration of the luminosity function up to these limits indicates that we should find about 5.5 (Sample 1) or 8.1 (Sample 2) times more galaxies within a fixed volume with this mean [FORMULA]. In a volume, defined by a field of 100 [FORMULA] around the observed directions and a depth of [FORMULA] [FORMULA] km/s, there are 10 to 30 galaxies in the CfA concentrations. So referring to similar field sizes the POSS Sample 1 should contain about 100 new galaxies around 5000 km/s for each field. This is not the case, as the cone diagrams (Fig. 4-7) immediately show.

[FIGURE] Fig. 4 a,b Cone diagrams for the void region VN2. Right ascension of 455 ZCAT galaxies (upper diagram) and declination for 510 ZCAT galaxies (lower diagram) as well as for 44 sample galaxies are plotted as a function of radial velocity up to a limit of 15000 km/s. All ZCAT and the sample galaxies with a distance of less than [FORMULA] from the coordinate planes are projected into these planes. The three voids I, II and III situated behind each other are indicated by the dashed lines. Dotted lines show the limits of the region surveyed by us. Symbols are the same as in Fig. 3.
[FIGURE] Fig. 5 a,b Cone diagrams for the void region VN8. Right ascension of 1439 ZCAT galaxies (upper diagram) and declination for 993 ZCAT galaxies (lower diagram) as well as for 30 sample galaxies are plotted as a function of radial velocity up to a limit of 15000 km/s. All ZCAT and the sample galaxies with a distance of less than [FORMULA] from the coordinate planes are projected into these planes. The two voids I and II situated behind each other are indicated by the dashed lines. Dotted lines show the limits of the region surveyed by us. Symbols are the same as in Fig. 3.
[FIGURE] Fig. 6 a,b Cone diagrams for the void region VN4. Right ascension of 701 ZCAT galaxies (upper diagram) and declination for 707 ZCAT galaxies (lower diagram) as well as for 11 sample galaxies are plotted as a function of radial velocity up to a limit of 15000 km/s. All ZCAT and the sample galaxies with a distance of less than [FORMULA] from the coordinate planes are projected into these planes. The void is indicated by the dashed line. Dotted lines show the limits of the region surveyed by us. Symbols are the same as in Fig. 3.
[FIGURE] Fig. 7 a,b Cone diagrams for the void region in front of A2151. Right ascension of 588 ZCAT galaxies (upper diagram) and declination for 517 ZCAT galaxies (lower diagram) as well as for 24 sample galaxies are plotted as a function of radial velocity up to a limit of 15000 km/s. All ZCAT and the sample galaxies with a distance of less than [FORMULA] from the coordinate planes are projected into these planes. The void is indicated by the dashed line. Dotted lines show the limits of the region surveyed by us. Symbols are the same as in Fig. 3.

In this context, however, one has to take into account that of the initially nearly 1000 newly identified objects on the POSS plates (Sample 1) redshifts have been derived from less than 10 [FORMULA] (see Sect. 2). Because of that, despite the considerably larger field surveyed, just half of our total 193 galaxies with known [FORMULA] come from the POSS sample. Therefore it is not surprising that this sample is incomplete in the sense that we caught by spectroscopy not more than a small percentage of the galaxies we are aiming at.

The case of the deeper K3/CCD sample is something different. On account of the much smaller fields of about 1 [FORMULA] we can expect at most a few objects, in agreement with the observational results. In these fields galaxies of smaller apparent diameter could be selected due to the 4.5 times larger scale of the K3/CCD images compared to the POSS plates (Sect. 2). Furthermore, nearly half of the finally selected objects have afterwards been observed spectroscopically. This means a far better portion than that for the POSS sample. Nevertheless it remains statistics of small numbers.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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