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Appendix B: Flux density corrections for systematic effects

As already discussed in Sect. 4.2, two systematic effects are to be taken into account when dealing with ATESP flux densities, the clean bias and the bandwidth smearing effect.


 

 
Table B1: Mosaic parameters
Mosaic cc's $\sigma_{\rm fit}$ ($\mu$Jy) RA range
       
fld01to06 2033 78.7 22:32:35 - 22:39:24
fld05to11 1796 77.8 22:39:28 - 22:49:51
fld10to15 3104 88.1 22:49:54 - 22:56:46
fld20to25 2823 83.0 23:31:30 - 23:38:20
fld24to30 2716 82.8 23:38:27 - 23:48:51
fld29to35 2044 79.2 23:48:54 - 23:55:43
fld34to40 1616 76.3 23:55:51 - 00:06:15
fld39to45 2535 81.2 00:06:21 - 00:13:10
fld44to50 2377 78.0 00:13:20 - 00:23:35
fld49to55 2168 78.6 00:23:45 - 00:30:35
fld54to60 2504 77.3 00:30:40 - 00:41:01
fld59to65 2447 79.4 00:41:07 - 00:47:57
fld64to70 1899 75.1 00:48:03 - 00:58:29
fld69to75 3119 81.9 00:58:30 - 01:05:22
fld74to80 2558 77.1 01:05:26 - 01:15:50
fld79to84 1522 68.9 01:15:53 - 01:22:50


The flux densities reported in the ATESP source catalogue are not corrected for such systematic effects. The corrected flux densities ( $S^{\rm corr}$) can be computed as follows:

 \begin{displaymath}
S^{\rm corr}=\frac{S^{\rm meas}}{k \cdot [a \log{(S^{\rm corr}/\sigma)} + b]}
\end{displaymath} (B1)

where $S^{\rm meas}$ is the flux actually measured in the ATESP images (the one reported in the source catalogue). The parameter k represents the smearing correction. It is set equal to 1 (i.e. no correction) when the equation is applied to integrated flux densities and < 1 when dealing with peak flux densities. From the analysis reported in Sect. 4.2 we suggest to set k=0.95 ($5\%$ smearing effect).

The clean bias correction is taken into account by the term in the square brackets. As discussed in Paper I, Sect. 5.3, the importance of the clean bias effect varies from mosaic to mosaic depending on the average number of clean components (cc's). In particular we derived the values for the parameters a and b in three different mosaics representing the case of low (fld34to40, 1616 cc's), intermediate (fld44to50, 2377 cc's) and high (fld69to75, 3119 cc's) average number of cc's (see Table 4 of Paper I).

In correcting the source fluxes for the clean bias, we suggest to set (a,b)=(0.09,0.85) whenever the mosaic average number of cc's is < 2000 (low-cc's case); (a,b)=(0.13,0.75) whenever the mosaic cc's average number is between 2000 and 3000 (intermediate-cc's case); (a,b)=(0.16,0.67) whenever the mosaic cc's average number exceeds 3000 (high-cc's case). The average number of clean components for each mosaic is reported in Table B1. In order to trace back the sources to the original mosaics, Table B1 lists also the right ascension range covered by each mosaic (indicated by the RA of the first and the last source in that mosaic).

The clean bias is a function of the source signal-to-noise ratio $S^{\rm corr}/\sigma$. Since the noise level is fairly uniform within each mosaic, it is possible to assume $\sigma$ equal to the mosaic average noise value ( $\sigma_{\rm fit}$ in Table B1, we refer to Paper I for details on mosaic noise analysis and average noise value definition).


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