4 Cluster survey in the NGP region

In Sect. 3, we have examined the performance of this method with a well-behaved model cluster. Further tests with real galaxy data are needed for putting the method to practical use. Here we perform a cluster survey with 5.3 deg² data of the North Galactic Pole region in the B band, which were obtained with our Mosaic CCD Camera 1 (hereafter MCCD1) attached to 1.05 m Schmidt telescope at Kiso Observatory, Japan.

4.1 Observation

The observation was made from March 16th to 18th in 1994 at Kiso Observatory. MCCD1, consisting of $2\times 8$ TC215 CCDs, was attached to 1.05 m Schmidt telescope. The CCDs have 1000$\times$1018 pixels and the pixel size is $12\ \rm \mu m\times 12 \ \mu m$. This corresponds to the scale of 0.75 arcsec/pixel at the prime focus of Kiso Schmidt telescope (see Sekiguchi et al. 1992 for more details). In MCCD1, CCD chips are placed with large intervals between them. Therefore we have to take 15 exposures to obtain data for a contiguous region on the sky.

The data are centered at ($\alpha$,$\delta$) = (13$^{\rm h}09{\hbox{$.\!\!^{\rm m}$}}$ 1, +29$\hbox{$^\circ$}$ 48.3$\hbox{$^\prime$}$) (J2000.0), covering $1.7\times 3.4$ deg² with 15 exposures. Unfortunately, seeing was poor amounting up to 6.0 arcseconds. A chip is out of work and the data lack in the south-eastern corner of about 0.3 deg², hence the actual observed area is 5.3 deg².

4.2 Galaxy catalog construction

4.2.1 Data reduction

The data reduction is executed in a usual way for optical CCD imaging data. After bias subtraction, flat-fielding and sky subtraction, we measure relative positions and relative gains between all pairs of neighboring frames taken either with the same CCD or with the adjacent CCDs at different exposures, using stars common in both frames, to construct a mosaicked image. When matching the images, we made positional and flux errors uniformly spread over the whole data. Typical seeing size is 3.5-4.0 arcseconds, but among the 15 exposures, there are some data with large seeing ($\sim$ 6.0 arcseconds). To keep homogeneity in detecting objects in the whole combined data with the same threshold, we convolved all frames with two-dimensional Gaussian with appropriate $\sigma$ so that FWHMs of PSF at any place in the mosaicked image become the same (namely, the largest value of $\sim$ 6.0 arcseconds). The detection threshold is set to 25.5 magarcsec^-2 in the B band. This corresponds to $1.5-3 \,\sigma _{\rm sky}$ above the sky level. If more than 10 pixels at which the counts exceed the threshold are connected, we regard them as an object. Altogether 6822 objects were detected. They consist of stars, galaxies, sky noises, and junks. All the above procedures are performed almost automatically by the data reduction software system developed by our group (Doi et al. 1995).

The error in astrometry is 0.9 arcsecond in rms (with 2$\sigma$ rejection), the magnitude zero-point error is 0.02 mag in rms, and the random error in magnitude is 0.2 mag in rms (Akiyama 1996). The large random error in magnitude is due to bad weather conditions, namely large fluctuation of seeing size. However, as described in the last section, these errors are within tolerance for our cluster-finding technique.

4.2.2 Star/galaxy discrimination

The detected objects consist of stars, galaxies, sky noises, and junks. We extract galaxies from the objects using the photometrical information, namely "sharpness'' of the image and magnitude.

Figure 8 shows the distribution of all objects in the "sharpness''-magnitude diagram. "Sharpness'' is defined by $I_{\rm peak}/\sqrt{N_{\rm pix}}$, where $I_{\rm peak}$ means the peak count of an object and $N_{\rm pix}$ means the number of pixels belonging to the object. In Fig. 8, we can recognize a tight sequence, which corresponds to stars. The bending of the sequence at the bright end reflects the saturation of CCDs. Galaxies, having flatter profile than stars with the same magnitude, are widely distributed in the region below the star sequence. Most of sky noises occupy faint and unsharp end of the diagram (often in several short sequences) and we can eliminate them by simply setting a cut-off magnitude. Other brighter unquestionable junks with quite flat profiles, due to bad pixel columns, haloes around bright stars, and sometimes loci of artificial satellites, often mingle galaxies. These junks must be carefully checked and removed.

  

Figure 8: Star/galaxy discrimination diagram for the 6822 "object''s in the B band MCCD data in the NGP region. The border between "star region'' and "galaxy region'' is shown as a solid line

We separate galaxies from the other objects with the following boundaries. The first one is a line corresponding to Gaussian profiles with $\sigma$=1.1$\sigma_{\rm PSF}$, where $\sigma_{\rm PSF}$ is the standard deviation of the best-fit Gaussian to the PSF that was composed of stellar images. PSFs have usually longer tails than that of Gaussian and are never well-fitted with a single Gaussian profile. However, for fainter magnitudes, outskirts of PSFs become negligible, and an approximation with single Gaussian is good enough. The second boundary is $I_{\rm peak}/\sqrt{N_{\rm pix}} = 300$. Actually, some objects above this boundary and below the star sequence are blended objects; in most cases, they are galaxies overlapping with stars. As magnitude goes fainter, the star sequence falls and eventually merges into the galaxy territory. And so do sky noises.

  

Figure 9: The distribution of 996 galaxies in the $1.7\times2.9\ {\rm deg}^2$ region. Symbol size changes with apparent magnitude. The largest symbol corresponds to mB = 14.2 and the smallest to mB = 21.0. The field center is at ($\alpha , \delta$) = ($13^{\rm h}08^{\rm m}55\hbox{$.\!\!^{\rm s}$}3, +30^{\circ}00'47\hbox{$.\!\!^{\prime\prime}$}2$) (J2000.0). North is up and east is to the left

It is no longer possible to discriminate between stars and galaxies. Therefore, our galaxy sample must also be restricted by the limit of star/galaxy discrimination. We fix the limit to be $m_{\rm limit}$ = 21.0, which is the third boundary.

  

Figure 10: "Richness image'' of the NGP galaxy sample of Fig. 9 for $z_{\rm fil}$ = 0.20. Solid line shows the contour of the threshold richness $N_{\rm th}$ = 180. Plus signs indicate positions of cluster candidates

Finally, we cut off the uneven edge region due to the dead CCD chip and select the central 1.7$\times$2.9 deg² rectangular region which contains 996 galaxies. The two-dimensional distribution of these galaxies are shown in Fig. 9. North is up and east is to the left.

4.3 Results

Figure 10 shows the "richness image'' of the NGP region for $z_{\rm fil}=0.20$. We can find some cluster candidates as peaks. Table 1 lists 18 significant peaks with $N_{\rm p} \gt 180$ at $z_{\rm fil}=0.20$, and their ${\cal L}_{\rm p}-z_{\rm fil}$ curves are shown in Fig. 11. In Fig. 11, only Nos. 3 and 7 have a prominent single peak in their ${\cal L}_{\rm p}-z_{\rm fil}$ curves. The ${\cal L}_{\rm p}-z_{\rm fil}$ curves for the other cluster candidates are almost flat and featureless (Nos. 4, 5, 8, 13, and 18) or monotonically descends as the filter redshift increases (the others).

 

Table 1: All detected cluster candidates in the NGP region

$\dagger$ - may be junk (edge of Coma)
$\ddagger$ - may be junk
$\ast$ - II Zw 1305.4+2941.

An ${\cal L}_{\rm p}-z_{\rm fil}$ curve which monotonically descends with increasing filter redshift does not always mean that the redshift of the corresponding cluster candidate is less than 0.1; in the most cases, ${\cal L}_{\rm p}-z_{\rm fil}$ curves just keep increasing and have no peak, or become noisy, as filter redshift becomes even smaller. These behaviors are similar for the case of monotonically ascending ${\cal L}_{\rm p}-z_{\rm fil}$ curve. Thus, most of the cluster candidates with flat or monotonically descending/ascending ${\cal L}_{\rm p}-z_{\rm fil}$ curves are spurious.

  

Figure 11: Peak logarithmic likelihood as a function of filter redshift for the 18 cluster candidates shown in Fig. 10

We can recognize many cluster candidates gathered in the bottom-right region in Fig. 10. However, the area includes the north-eastern outskirts of the Coma cluster, which correspond to the concentration of bright galaxies in the bottom-right region in Fig. 9. No cluster candidates in this region have a single peak in their ${\cal L}_{\rm p}-z_{\rm fil}$ curves, implying that most of them may be spurious. The ${\cal L}_{\rm p}-z_{\rm fil}$ curves of the candidates Nos. 16-18 do not show a single peak and their $N_{\rm p}$ values are too small (less than 100). They may also be spurious.

The most significant cluster candidates are Nos. 3 and 7. These candidates both correspond to a single Abell cluster A1677. Splitting into two peaks may be either due to the poor quality (for example, the bright limiting magnitude or the inhomogeneity) of the data or due to a possible substructure. The measured redshift of A1677 is 0.183 (ACO) and the Abell richness c is 112, which corresponds to $N\sim$ 3000. Our estimates of (z, N) are (0.26, 697.1) for No. 3 and (0.16, 673.5) for No. 7. There is another cataloged cluster, No. 14. This cluster is II Zw 1305.4+2941 (Koo et al. 1986 and references therein). It has also been detected with X-ray satellites such as Einstein (MS 1305.4+2941 in Gioia et al. 1990), ROSAT (1RXS J130749.3+292536 in Voges et al. 1996), and ASCA (Ueda 1996). The measured redshift of this cluster is 0.241, while our redshift estimation for this cluster gives 0.10. Taking into account the poor quality of the data and the brighter limiting magnitude than that of the simulations in Sect. 3, we conclude that redshift and richness estimations for these two clusters are consistent with the cataloged values.

Let us compare this result with that of intuitive eye selection. A glance of the galaxy distribution in Fig. 9 can find some other "somewhat conspicuous'' galaxy concentrations. They are, for example, at $(X,Y) = (35,\,110)$, (40, 90), and (60, 80). These three clumps seem to be more plausible "clusters'' at a glance than the fainter one, for example, No.  14 in Table 1 at $(X,Y) = (55,\,55)$. However, when we examine a "richness image'' (Fig. 10), these three appear to have much less remarkable peaks than No. 14, which is a real cluster.

Searching for clusters with a simultaneous use of magnitudes and positions can produce a quite different, and more objective result than that by conventional techniques using surface density of galaxies only.