7.1.2 Identification

As shown in Section 6.11, the astrometric accuracy of ELAIS 15 $\mu$m Final Analysis Catalogue was estimated by means of both simulations and optical identifications, the two methods providing results in good agreement.

The correlation between ELAIS 15 $\mu$m Final Analysis sources and optical objects has been carried out using a likelihood ratio method (Sutherland, 1992), similar to the one which has been successfully applied to the identification of 15 $\mu$m sources detected in ISO HDF-N survey by Mann (1997).

The probability that an optical object of magnitude $m$ is the true counterpart of a source with an error ellipse defined by its major axis, $\sigma_1$, and minor axis, $\sigma_2$, separated by a distance $r$, is given by

$${\cal L}=\frac{Q(m)\,\exp(-r^2/2)}{2\pi\,\sigma_1\sigma_2\,N(m)}$$ (7.1)

where $Q$ and $N$ are the magnitude distributions of sources and objects, respectively. The reliability of such identification is defined as

$${\cal R}_j=\frac{{\cal L}_j}{\Sigma_i\,{\cal L}_i+(1-Q)}$$ (7.2)

The identification process is carried out as follows. For each 15 $\mu$m source, all optical objects within a distance of 20 arcsec are selected. For each object in this candidate list the values of likelihood and reliability as given by Equations 7.1 and 7.2 are computed. Optical astrometric errors returned from the WFS pipeline and 15 $\mu$m astrometric errors as determined in Section 6.11 were adopted. The likelihood, estimated through Equation 7.1, gives the probability that a candidate is the true optical counterpart of the source, but it only provides information about the probability of each candidate being the correct counterpart. The reliability, estimated through Equation 7.2, provides information about the number of candidates with high likelihood values. A candidate will have large values of likelihood and reliability if it is the only probable counterpart of a source. In case where there are multiple probable counterparts (in the sense of high likelihood), they all will have low values of reliability. A candidate is selected to be the correct optical identification of a 15 $\mu$m source when ${\cal L} > 0.7$. Sources for which no candidate meets this requirement are flagged as blank fields and represent $\sim$ 8% of the sample. Sources with more than one candidate meeting this requirement and a low value of reliability are flagged as low-reliability identifications and represent $\sim$ 8% of the sample.

Optical identification of ELAIS radio sources detected in the N1 and N2 areas was carried out using a similar procedure, using the positional errors from the radio catalogue as inputs to the likelihood ratio algorithm. An optical counterpart is found for 389 out of the 691 sources, i.e. there is a 44% of blank fields.

Figure 7.3 shows the positional differences between 15 $\mu$m and radio sources and their optical identifications. Typical values are of 1 arcsec, a Gaussian curve of zero mean and unit dispersion providing a good fit both for 15 $\mu$m and radio sources. This provides a confirmation of the good astrometric accuracy of the the ELAIS 15 $\mu$m Final Analysis catalogue.

Figure 7.3: Positional Differences Between 15 $\mu$m (left) and Radio (right) Sources and their Optical Identifications.