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Subsections

5 Construction of the main catalogue

At this stage we have a catalogue of $3\ 222\ 414$ galaxy candidates. We now have to make the "auto-crossidentification'' to merge a same object seen on different plates. Because the information on the original plate will be lost in such a merging process we have to apply now the corrections which are plate-dependent, like the effects of the mean airmass extinction or the distance to the center of the chart (Rousseau et al. 1996; Garnier et al. 1996).

5.1 Astrophysical parameters

We use a Principal Component Analysis method applied on pixels positions (i,j)of the matrix associated to an object. So, we derive for each object a $2 \times 2$ covariance matrix from which we calculate its eigenvalues (v1 and v2) and corresponding eigenvectors. The position angle $\beta_{\rm DSS}$ of the major axis is determined from the direction of the first eigenvector (eigenvector associated with the highest eigenvalue). The major and minor axes are deduced from the square root of the first and second eigenvalues. The apparent magnitude is deduced from the sum of all pixel intensities. We thus obtain the following parameters:

In order to calibrate these equations we extracted from the LEDA database the apparent blue diameter D25, the major to minor axis ratio R25= D25/d25 (axes are defined at the isophote 25 mag arcsec-2) and the total $B_{\rm T}$ magnitude for the galaxies of the training sample. These quantities are in the system of the Third Reference Catalogue (RC3, de Vaucouleurs et al. 1991). We get the following results ($\sigma$ is the standard deviation, n is the number of remaining objects after 3-$\sigma$ rejection:

\begin{displaymath}%
\log D_{25} = \log D_{\rm DSS} + 0.09 \ \ \ \sigma=0.06 \ \ \ n=5619
\end{displaymath} (9)


\begin{displaymath}%
\log R_{25} = \log R_{\rm DSS} + 0.00 \ \ \ \sigma=0.07 \ \ \ n=5555
\end{displaymath} (10)


\begin{displaymath}%
B_{\rm T} = m_{\rm DSS} + 30.6 \ \ \ \sigma=0.34 \ \ \ n=5544.
\end{displaymath} (11)

It is worth noting, that the accuracy is reasonably good owing to the rather rough comparison. The standard errors should thus be considered as upper limits for galaxies up to $\approx 15$-th magnitude. These magnitudes will be re-analyzed in a future work in order to take into account local and secondary effects.

For stars, a comparison with SAO magnitudes gives a preliminary calibration:

\begin{displaymath}%
m({\rm stars}) = m_{\rm DSS} + 25.1 \ \ \ \sigma=0.46.
\end{displaymath} (12)

The difference of zero-points for stars and galaxies suggests that the dispersion of pixel optical densities intervenes in a refined calibration.

5.2 Auto-crossidentification

The catalogue of $3\ 222\ 414$ galaxies is sorted according to the declination (the search is easier and faster with such a sorting). Each galaxy is compared with all the others. This is done four times because one galaxy may only appear four times at the intersection of four charts. At each of these four iterations only the locally two closest galaxies are merged if their separation calculated along a great circle is smaller than a given limit. This procedure avoids the result depending on the order the galaxies are considered (in other words, the merging is done according to a physical measurement but not following an arbitrary order). The limit of the separation is calculated from the actual uncertainty on the position:

 \begin{displaymath}%
d_{\rm lim} = d_{\rm o} (1 + \cos ^2 \delta)^{1/2}
\end{displaymath} (13)

where $d_{\rm o}$ is the nominal uncertainty on coordinate measurement along one direction. We adopt $d_{\rm o}= 6\hbox{$^{\prime\prime}$ }$ (Paturel et al. 1999). In practice, the galaxies are not actually merged at this stage. They simply receive an internal numbering. A galaxy which appears several times receives the same internal number. The merging will be done later. Two reasons justify the postponement of the merging: 1) For each occurrence of a given object we have a matrix. It is not easy, without loss of information, to merge these matrixes in one mean matrix. 2) The crossidentification with LEDA will be done for each extracted object, even if it appears several times. This will give us a chance to detect possible inconsistency (e.g. a galaxy identified once with a given LEDA galaxy and then with another one when it is extracted from another plate).

Thus, we will still work with the catalogue of $3\ 222\ 414$ galaxy candidates (a direct merging would have lead to a catalogue of $2\ 876\ 111$ galaxies. No inconsistency is found).

5.3 Cross-identification with LEDA

In view of this cross-identification we carried out a campaign of measurement of accurate coordinates. More than 34000 positions of LEDA galaxies were measured (Paturel et al. 1999; Paturel et al. 2000) and we studied the accuracy of the coordinates provided to us by large catalogues (Paturel & Petit 1999). We added some recent accurate measurements (Cotton et al. 1999). After this work we have a list of 194544 galaxies from LEDA with accurate coordinates and the main astrophysical parameters (diameter, axis ratio, position angle and magnitude).

The cross-identification is based essentially on coordinates using a method similar to the one used for the auto-crossidentification. Nevertheless, two modifications are introduced: 1) The limit of the separation is calculated from the previous formula (Rel. 13) but the value of $d_{\rm o}$ is deduced from the weighted mean of the coordinate accuracy (Paturel & Petit 1999) and quadratically increased by the uncertainty of the DSS coordinates ( $6\hbox{$^{\prime\prime}$ }$), because the coordinates we are comparing have independent errors (this was not the case for auto-crossidentification). 2) When several galaxies match the position criterion we use astrophysical parameters to choose the best one. For this purpose we calculate a generalized separation between the objects according to

\begin{displaymath}%
t = \frac{1}{N} \sum_{i=1}^{N} w_i \frac{\vert\Delta X_i\vert}{ \sigma (X_i)}
\end{displaymath} (14)

where wi is the weight assigned to each parameter Xi(e.g., coordinates, diameter, axis ratio, position angle). $\Delta X_i$ is the difference of the parameter Xi for the two galaxies in test. After some trials we assigned a weight of 7 for coordinates, 1 for diameter, 2 for axis ratio $2 \log R$ for the position angle. After this step $144\ 721$ objects are identified in LEDA (corresponding to $107\ 991$ galaxies because some objects appear several times). Thus, $86\ 553$ galaxies known only in LEDA are added, leading to a catalogue of $3\ 308\ 967$ galaxies before the merging of repeated galaxies (or $2\ 962\ 664$ galaxies if the merging is done). The added objects are galaxies fainter than the magnitude limit of the DSS, or low surface brightness galaxies not detectable by our program, or a few very large objects (larger than individual frame).

At this stage we build the mean catalogue where a galaxy appearing several times is merged into one object. There is no practical difficulty because each object has its internal number from the auto-crossidentification step. Nevertheless, we must take into account that some periodical parameters (like the right ascension or the position angle) must be treated with special care. For instance, two measurements of the position angle of a galaxy elongated in the N-S direction may produce, e.g., $175 \deg$ and $5 \deg$. The mean of both measurements is not $90 \deg$ but $180 \deg$. After having merged all objects appearing on different plates we obtain a catalogue of $2\ 876\ 111$ objects.

5.4 Removal of non extragalactic extended objects

Automatic program of galaxy recognition cannot differentiate a true galaxy from, e.g. a planetary nebula or a globular cluster. Further, filaments in a bright nebula, in a HII region, in the neighborhood of a very large galaxy or in the halo of a very bright star can well be recognized as a galaxy. In order to remove such artefacts we constituted a catalogue by collecting objects prone to create them. This catalogue of "forbidden zones" is built from the following objects:

For stars the forbidden zone is the central circle (diameter $D_{\rm s}=1.1\hbox{$^\prime$ }$) and the branches of the diffraction cross. The total extension (with both arms) of one branch is estimated to B=-3 mv +25 (arcmin). For galaxies, the forbidden zone is the surface of the ellipse defined by its axes D25 and d25 (at the isophote 25 mag arcsec-2) and the position angle of the major axis $\beta$ (from North towards East). For all other objects the forbidden zone is the surface of the object assumed to be circular of diameter D. The forbidden zone catalogue gives for each object: the code (ST, GA, GC, OC, BN, H2, PN), the right ascension and declination for equinox 2000, and the parameters for the definition of the forbidden zone ($D_{\rm s}$ and B for stars, D25, d25and $\beta$ for galaxies and D for others). This catalogue is sorted according to declination and contains 21921 objects.

In Table 3 we give the number of rejected objects for the different classes of forbidden zones.

 

 
Table 3: Number of rejected galaxy candidates
Code Object Number of rejection
ST Stars (mv>7) 4028
GA Galaxies (>5') 34 017
H2 HII regions 25 560
GC Globular clusters 1906
OC Open clusters 12 578
BN Bright Nebulae 112 318
PN Planetary Nebulae 196
  Total 190 603


After these cleaning and merging steps $2\ 772\ 061$ galaxies remain. This catalogue constitutes the main catalogue from which we will start to work. A completeness curve made with these $2\ 772\ 061$ galaxies shows that the completeness limit is about 18.2 mag (see Fig. 13).


  \begin{figure}
\par\includegraphics[width=8cm,clip]{ds1851f13.eps}\end{figure} Figure 13: Completeness curve for the main catalogue of $2\ 772\ 061$ galaxies. The completeness is fulfilled up to 18.2 mag

The slope of the linear part is $0.56 \pm 0.01$. This is significantly less than the theoretical value (0.6). This result has been permanently found and has been interpreted in several ways (fractality, incompleteness, flat distribution of galaxies).


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