Astron. Astrophys. 325, 881-892 (1997)

3. The distribution of ELGs

3.1. The space densities

We calculate the space densities of our sample of ELGs using a method applied to the parameter , as defined in the previous section. Through this paper we used a Hubble constant km/s/Mpc. We computed a corresponding "absolute magnitude", which is the intrinsic flux of the emission-lines plus the continuum under the line, transformed in a magnitude scale, . We should once again mention that these so called absolute magnitudes do not have the meaning of the continuum absolute magnitudes and should be interpreted as the intrinsic strength of the emission-lines. The space density at is :

where is the solid angle covered by our survey, and the summation is over all galaxies in the absolute magnitude interval 0.5 mag. The absolute magnitudes were calculated considering a Galactic absorption given by .

In the computation of the we included all galaxies up to a , for which the completeness level is 49.1 . Thus we must increase the calculated space densities by a factor of 2.04 to allow for incompleteness. In Table 2 we listed the for each bin of absolute magnitude together with the number of galaxies included in each bin.

Table 2. Space Densities .

Table 2 shows that we found only a few extreme strong [OIII] 5007 line objects (5 ) and that most of our objects (57 ) have high and intermediate strengths of the emission-lines. Going to objects that have intrinsically faint [OIII] 5007 lines, our survey becomes less efficient, and some of these objects can be better detected by H surveys (see Zamorano et al. 1994).

The integration over the whole range of absolute magnitudes gives a space density of 0.046 . In order to calculate the corresponding error we considered different completeness limits and we estimated the spread around the assigned value. The integrated space density is nevertheless dominated by the last bin (at the faint end) of the luminosity function, which was calculated based only on three galaxies. This point is therefore very uncertain and we prefer to give a space density integrated only till . Then we obtain , which is a factor 3.5 lower then the previous value. The results for different completeness limits are now more stable, with the estimated error a factor 5 lower.

3.2. Cone-diagrams

A study of the spatial distribution of the ELGs requires a comparison with a catalogue of normal galaxies that would properly trace the main structures in the nearby Universe and would also properly define the nearby voids. We have already mentioned in the introduction that we selected our surveyed regions to contain well defined nearby voids in the distribution of the giant galaxies. For the comparison catalogue we used the latest electronic version of the ZCAT (April 1995) ² and we selected all galaxies brighter than B=15.5. The ZCAT contains only one strip that is complete to . This is the so called "Slice of the Universe", and . Our surveyed regions are outside the zone of the Slice, therefore the catalogue is not complete to . The incompleteness of the comparison catalogue do not affect the qualitative description of the large-scale structure, as given by the cone-diagrams, but could affect the results of some statistical tests, as mentioned in the next section.

The most common way to visualise the spatial distribution of galaxies is to use cone diagrams in both redshift-Right Ascension and in redshift-Declination plane. Since we give a qualitative description of the spatial distribution, we have plotted all ELGs, without respect to their completeness. Such a restriction is done only when we apply statistical tests (see subsection 3.3). The diagrams contain also the comparison catalogue (the ZCAT galaxies brighter than 15.5). In addition we have plotted the ZCAT galaxies fainter than 15.5, with the intention to have a first impression of how the fainter galaxies start to structure and how they correlate with the ELGs. In the following description we will use the term bright ZCAT for the ZCAT galaxies with apparent magnitudes brighter than B=15.5 and the term faint ZCAT for the ZCAT galaxies fainter than B=15.5. The terms bright and faint do not therefore refer to the intrinsic brightness of the comparison galaxies. As most of our galaxies are fainter than 15.5, there is practically no overlap in apparent magnitudes between our sample and the comparison (bright) catalogue.

All velocities are corrected for the Galaxy's motion with respect to the velocity centroid of the Local Group. We use a correction term of (Sandage 1975), where and are the galactic coordinates. We plotted all the galaxies with velocities out to km/s, which corresponds to a redshift of , including thus most of our sample. For velocities greater than 15000 km/s the comparison catalogue becomes essentially non-existent. Already for velocities greater than 10000 km/s the ZCAT quickly thins out, and therefore we refrain from drawing conclusions about the reality of voids beyond 10000 km/s.

In the cases where our surveyed region was too narrow in one dimension or not properly covering some main features of the large scale structures, a bigger area of sky is displayed. In these cones the surveyed region is either delimited with dotted lines or some specifications are given in the Captions. We should also mention that our cone diagrams do not completely cover all the surveyed region, and the strips are chosen to display the most relevant information.

The cones plotted in Fig. 2 a,b contain a larger angle in Right Ascension than our surveyed region, because we did not want to cut through the very well defined foreground voids and we wanted to have a better impression of the large scale structure in this region. The actual surveyed region is only between and .

Fig. 2. Wedge-plots of redshift (cz in km/s) - right Ascension out to a redshift of 15000 km/s. The ZCAT : small dots, the ZCAT : crosses, the ELGs: open circles. The wedge is a wide strip in Declination centred in a) , b) . The cones contain a larger angle in right Ascension than our surveyed region, which is only between (, ).

The strip plotted in Fig. 2 a is slightly to the North of the "Slice of the Universe". For this reason we can still see some of the prominent features of the Slice, remnants of the "Harvard Sticky Man" at velocities less than 7500 km/s, but without the Coma Cluster. The most remarkable feature of the diagram is the "Great Wall", which crosses our diagram from km/s at to km/s at . The structures of the Sticky Man define some foreground voids, of which that centred at , km/s is one of the best defined void in our surveyed region and we will call it Void 1. In the front of the Great Wall there is a very big void that opens to the western side of the cone and continues also outside our actual survey. We will call it Void 2. Void 1 and Void 2 will be used to draw our conclusions about the void population. Beyond the Great Wall there is another big void, but the size of the void is no more well defined by the ZCAT galaxies because at these distances the comparison catalogue becomes practically non-existent.

Our galaxies seem to follow the structures described above as well. At a closer inspection one can discover that there are some galaxies that lie very isolated in some of the foreground voids. In Void 1 there are two galaxies, HS1236+3821, km/s and HS1226+3719, km/s, that have the nearest bright ZCAT galaxy at a distance of Mpc and Mpc, respectively (for detailed description of the isolated galaxies see Table 3). At this distance the mean separations between galaxies is around Mpc, so these two galaxies are extremely isolated. They are among the best candidates we found in the voids. Two further faint ZCAT galaxies are also present in the void (see Table 4). In Void 2 we found an "Arch"of 7 ELGs (HS1236+3937, HS1232+3947, HS1240+3721, HS1332+3426, HS1328+3424, HS1310+3801), that seem to divide the void into three smaller voids. The galaxy HS1236+3937 has the largest isolation, of Mpc. The Arch is also populated by three faint ZCAT galaxies while a fourth one closes the Arch at lower redshifts (Table 4). In the background void beyond the Great Wall there are two HS galaxies, one at 8131 km/s, HS1306+3320, and one at km/s, HS1410+3446. However we have already mentioned that this background void is not delimited at the far distance edge by the bright ZCAT galaxies, but mainly by our ELGs and by some faint ZCAT galaxies. It is anyway remarkable the large number of ELGs we found at higher redshifts, where the ZCAT catalogue do not contains any galaxy.

Table 3. The main characteristics of the void galaxies.

Table 4. Void galaxies in the ZCAT sample fainter than B=15.0.

Fig. 2 b displays the same region in Right Ascension but shifted to the North and having an overlap with the previous diagram of in Declination. We chose a small overlap in order to see how the structures evolve when moving in one coordinate. The diagram no longer resemble the Slice, though one can still see some features of the Great Wall. There is an extra feature that appears at km/s, a filament that stretches from up to . The two voids in the front of the Great Wall seem to converge now in a unique void centred on km/s. The void still contains some galaxies from the Arch, but one can see now a chain of faint ZCAT galaxies that seem to associate with the ELGs and again divide the big void in two smaller voids. The region beyond km/s and east to contains the southwest boundary of the Bootes void (centred on , , km/s) (Kirshner et al. 1981).

In Fig. 3 a we plotted in a redshift-Declination diagram the galaxies from , the strip being chosen to cut through Void 1 and Void 2 (Fig. 2 a), containing thus some of the void galaxies. The "finger of God" that is the Coma Cluster is in fact at the border of the surveyed region, lying mainly outside it.

Fig. 3a and b. Wedge-plots of redshift (cz in km/s) - Declination out to a redshift of 15000 km/s. The ZCAT : small dots, the ZCAT : crosses, the ELGs: open circles. The wedge is a wide strip in Right Ascension.

Fig. 3 b contains the next strip between , plotted again in a redshift-Declination diagram. The cone contains now the easter side of the Arch and cuts through the filaments that we mentioned as remnants of the "Harvard Sticky Man".

In Fig. 3 c we plotted one more redshift-Declination cone, for the strip in Right-Ascension . The strip was chosen to cut through the filaments that runs in radial direction in our Fig. 2 a and therefore do not contain relevant nearby voids for our surveyed region.

In order to have a better impression of the whole surveyed region, we projected in a redshift-Right Ascension diagram (Fig. 4) a strip of in Declination, from . Projection effects would of course affect the cone but in this case we are interested only to which extent the voids are still defined in the diagram. Due to the crowding of the diagram we refrain from plotting the faint ZCAT galaxies, and we consider only the comparison catalogue (bright ZCAT galaxies). It is remarkable to see that despite the large strip in Declination that was projected in the cone, the two isolated galaxies in Void 1 are still clearly isolated and the void is still very well defined. This indicates that the void extends at least 15 degrees in Declination.

Fig. 4. Wedge-plots of redshift (cz in km/s) - Right-Ascension out to a redshift of 15000 km/s. The ZCAT : small dots, the ZCAT : crosses, the ELGs: open circles. The wedge is a wide strip in Declination.

Overall the wedge diagrams show that our ELGs follow the structures traced by the normal galaxies. However 17 ELGs (17 ) are very isolated, of which at least 8 () lie in some foreground voids. There are also some ELGs that lie at the rim of the voids and there seem to be a tendency for the ELGs to be more evenly distributed that the ZCAT galaxies.

3.3. The nearest neighbour test

In order to quantify the visual impression provided by Figures 2-4, we applied some statistical tests for differences in the distribution of HS and ZCAT samples. For the ELGs we consider only the galaxies from the complete sample derived in section 2, namely the galaxies that have ().

It is worth stressing that within the range of our surveyed regions we deal with a field sample. No rich Abell cluster is present, only some Zwicky clusters. In Region 3, the Coma Cluster neighbours the southern border of our region (see Fig. 3 a), with its main body outside. This implies that any differences that we could find will not be due to the fact that the emission-line galaxies have the tendency to avoid rich clusters.

We first applied a Kolmogorov-Smirnov test to the redshift distributions of the two samples out to a velocity of 10000 km/s. Since the velocity distribution of the ZCAT falls off rapidly beyond 10000 km/s, we limited our statistic to a subsample with velocities below this value. The comparison distribution was constructed by selecting at random from the ZCAT the same number of objects (N) and in the same volume of space as in the ELG sample. This randomly generated distribution was computed for 1000 samples of N ZCAT galaxies, and the results averaged to produce the final comparison. The results indicate that the two samples are drawn from the same parent population (KS=0.55).

To better address the question of whether or not the two samples have the same spatial distributions, we used a nearest neighbour (NN) test (Thompson 1983). The cone-diagrams give also an impression of the overall spatial structures, but as the plots are only two dimensional representations, the projection effects could affect some of the results. The nearest neighbour test calculates the real separation in the 3-dimensional space and also quantifies the results. Eder et al. (1989) showed that this test is particularly sensitive to the lack of clustering in a sample, and is therefore recommended for field samples. We limited again our statistic to subsamples with velocities less than 10000 km/s. We have computed two distributions. One gives the separation between each ELG galaxy of the sample (N objects) and the nearest ZCAT galaxy in the same field, but taken into consideration the edge effects. This means that the ZCAT galaxies were taken from a slightly larger field than that of the ELGs. For the second distribution we followed the same procedure as for the redshift distribution: a randomly selected sample of N galaxies was taken from the ZCAT catalogue. We calculated then the separation between each of the N ZCAT galaxies and its nearest ZCAT neighbour, again with edge effects considered.

The NN distributions are shown in Fig. 5. The overall impression is that the two distributions are quite similar. There seems to be an excess of ELGs at intermediate separations, around 2 h^-1 Mpc, but the errors in each bin are quite big, due to the pure number statistics. There are also some ELGs at higher separations, where the ZCAT do not contribute. But these differences cannot change the overall similarity between the two distributions. This is confirmed by a Kolmogorov-Smirnov test which gives a KS=0.59, which means that the two distributions are identical. We should notice that some of the very isolated galaxies are not contained in the complete sample and therefore were not included in the computation of the NN test. These galaxies produce a tail of high separations in the distribution of ELGs, which sharpen the difference between the two distributions and make the ELGs to be more uniformly distributed than the giant galaxies.

Fig. 5. The nearest neighbour distributions. The ELG/ZCAT separations are plotted with solid line and the comparison ZCAT/ZCAT distribution with dashed lines.

The results of our statistical tests should be considered with caution, since the comparison ZCAT is not complete up to 15.5. The incompleteness of the comparison catalogue could introduce some errors that cannot be controlled. Unfortunatelly, until the pulic release of the CfA2, the ZCAT is the only catalogue that samples the distribution of the normal galaxies on a large enough extent.

3.4. Discussion

In this section we discuss the significance of our findings in some of the nearby voids. We refer only to the two nearest and best defined voids presented in Figure 2a, Void 1 and Void 2. First we estimate how many normal galaxies brighter than 15.5 we expect to find in the voids if the galaxies would be uniformly distributed. We consider the ZCAT galaxies brighter than 15.5 because the voids were defined by the distribution of these galaxies. We calculate the volume of Void 1 considering for simplicity an elipsoid shape with the diameters of the main axis: 3500 km/s, and (in radial velocity, Righ Ascension and Declination). We took also into consideration that not all the volume of the void was surveyed. At a distance of z=0.01 this will give a volume of 1289 h . If we integrate the luminosity function derived by de Lapparent et al. (1989), over the magnitude range that includes galaxies brighter than 15.5, one would expect to find 106 galaxies brighter than 15.5. This result is obtained on the assumption that the galaxies were independently and randomly distributed, which is obviously not the case. One could of course correct for the fraction of galaxies that are not independent by using the autocorrelation function. For simplicity we consider only our rough estimates and we obtained an underdensity of 106. For Void 2 we obtain a volume of 1793 h and an underdensity of 57. This is the underdensity in the distribution of the normal galaxies.

The number of ELG one would expect in the voids was calculated using the space densities derived in subsection 3.1, . We then estimate to find 44 ELGs in Void 1 and 47 ELGs in Void 2. This would be the case if our sample would be 100 complete over the magnitude range for which the space densities were considered. We already mentioned that the incompleteness factor was 2.04, therefore we should expect only 22 galaxies in Void 1 and 23 galaxies in Void 2. We found one ELG in Void 1 (a second one is not an ELG, see 4) and 7 ELGs in Void 2 (of which 2 are at the rim of the void), which means we did not find a significant void population at the density that was tested (the density of the walls and filaments). Then the void population has either a density that is at least a factor 4.5 lower, or alternatively, that the void population is even fainter than the limits of our survey, and we reached only the brightest peaks of such population. One cannot reject the hypothesis that the few galaxies found in voids do not form a population, rather they represent fluctuations of the large scale structure. This would explain why some voids were found to contain a few galaxies and other voids to be empty (Rosenberg et al. 1994, Pustil'nik et al. 1995).

© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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