6 Cross-identification

To make a correct cross-identification we need coordinates, calibrated magnitudes and diameters, axis ratios and position angles. We will use the first calibration obtained from the preliminary cross-identification made for astrometric purposes (Sect. 4). This calibration will be refined in next section.

Because of frame overlap along the strip, many objects are measured twice (or even three or four times with adjacent strips). A first cross-identification is done for these galaxies measured several times. This will be called the "auto-cross-identification''. Then, the cross-identification with LEDA galaxies may start.

6.1 Auto-cross-identification

The "auto-cross-identification'' is performed using a hierarchical method in which we merge step by step the closest objects. The definition of the distance of two objects i and j is the following:  

$$d_{ij} = \frac{1}{n\rm _p} \sum_{k=1}^{n\rm _p} \frac {\vert p_{ik} - p_{jk}\vert}{2 \sigma_k}$$ (6)

where, $n\rm _p$ is the number of parameters (coordinates, diameters magnitudes...) for a given object, p_ik is the k-th parameter of object i, $\sigma_k$ is the standard error of the k-th parameter. When two objects are merged they are replaced by a single one, whose parameters are the means of both. The final result does not depend on the order the original file is read. Note that, special care must be taken for periodic parameters, Right ascension and position angle (e.g., PA $=0 \deg$ is identical to PA $=180 \deg$; thus, the mean of PA $=3 \deg$ and PA $=177 \deg$ is PA $=0 \deg$, not PA $=90 \deg$).

The adopted $\sigma_k$ are given in the following table:

The standard error of the position angle is taken as a function of $\log R$because its meaning vanishes for face-on galaxies.

Objects are merged for $d_{ij} < d_{\rm limit}$,$d_{\rm limit}$ beeing chosen from the distribution of all distances (Fig. 6). By its definition, d_ij has the meaning of a Student's t-test devided by 2 (it is thus dimensionless). A $1\sigma$ criterion corresponds roughly to $d_{\rm limit}=0.5$.However, the value of $\sigma$ attached to each parameter is somewhat arbitrary, so is the definition of $d_{\rm limit}$. We adopted $d_{\rm limit}=0.55$. This choice is guided by the minimum observed in the histogram of d_ij (Fig. 6).

  

Figure 6: Distribution of "distances'' dij between two DENIS objects (i and j). This graph is used to chose $d_{\rm limit}$in the auto-cross-identification phase (see text)

During "auto-cross-identification'' a provisional DENIS number (called RED) is given to each entry of the catalog. When a galaxy appears several times in the catalog, each original set of measurements is identified with the same RED number. Each entry will be cross-identified independently with LEDA galaxies, this will allow us to check the reliability of the cross-identification.

6.2 Cross-identification with LEDA galaxies

From the previous step we get an intermediate catalog in which each galaxy has a provisional number and all its astrophysical parameters ($\alpha_{2000}$, $\delta_{2000}$, $\log D\rm _I$, $\log R\rm _I$,$I\rm _T$ and $\beta$). Each entry of this catalog must now be cross-identified with LEDA galaxies in order to identify those already known.

LEDA galaxies have similar parameters $\alpha_{2000}$, $\delta_{2000}$, $\log D_{25}$, $\log R_{25}$, $B\rm _T$ and $\beta$, but diameters and magnitudes are defined in the photometric B-band. The cross-identification is done by calculating the distance (in the mathematical sense, as defined by Eq. (6)) between a DENIS and a LEDA galaxy. The coincidence is accepted if the distance is smaller than $d_{\rm limit}$.From a histogram of all distances between LEDA and DENIS measurements (Fig. 7), we adopted $d_{\rm limit}=1.0$ which corresponds to the first minimum of d_ij-histogram (a pure Student's t-test would have given $d_{\rm limit}=1.29$ at a 0.01 probability level). This limit is voluntarily conservative (i.e., small) because we prefer to miss a cross-identification than to merge two distinct galaxies.

Because a given galaxy is cross-identified each time it appears in the catalog, 15945 were cross-identified several times with their original parameters. We reject 1881 galaxies identified with more than one LEDA galaxy. The final catalog contains now 36247 galaxies.

  

Figure 7: Distribution of "distances'' dij between DENIS and LEDA galaxies (i and j). This graph is used to chose $d_{\rm limit}$in the cross-identification phase (see text)

6.3 Last cleaning

Many objects were kept in the catalog despite the fact that they were labelled "undefined objects'' by the DA. They were kept because a known galaxy was very close. In the present release we removed these objects which nature may be questionable without further inspection. Indeed, some very faint galaxies in LEDA have only a few parameters, so that the cross-identification is based mainly on coordinates. In some crowded field (clusters of galaxies or low galactic latitude) the accuracy of coordinates does not allow an identification secure enough. 10696 such objects were then rejected, leaving 25551 galaxies.

Finally, we rejected galaxies with uncertain coordinates so that only coordinates based on the GSC reference are used. So, 5291 galaxies are rejected in the present version, leading to the final catalog of 20260 galaxies. These drastic rejections aim at maintaining a high quality level for this first catalog. In order to judge the quality more quantitatively we will now compare with other sources of data.