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5 Mosaic analysis

Table 3 summarizes the main parameters for the final 16 mosaics: for each mosaic are listed the number of fields composing it (columns $\times$ rows), the tangent point (sky position used for geometry calculations) and the synthesized beam (size and position angle). The spatial resolution can vary from mosaic to mosaic depending on the particular array (6A, 6C or 6D) used in the observations. The mean value for the synthesized beam is $\sim 8\hbox{$^{\prime\prime}$ }\times 14\hbox{$^{\prime\prime}$ }$.

\par\includegraphics[width=8.8cm,clip]{}\end{figure} Figure 3: Histogram of the (residual) flux in one of the $6\times 4$ fields mosaiced images (fld01to06). As expected the flux is peaked at zero and the distribution is Gaussian

5.1 Noise

The last three columns of Table 3 show the results of the noise analysis. For each mosaic we report the minimum (negative) flux ( Smin) recorded on the image (typically |Smin| is of the order of 0.5 mJy, corresponding to the value at which we have stopped the cleaning) and the noise level. This has been evaluated either as the FWHMof the Gaussian fit to the flux distribution of the pixels (in the range $\pm~S_{\mathrm{min}}$), in order to check for correlated noise ( $\sigma_{\mathrm{fit}}$), or as the standard deviation of the average flux in several source-free sub-regions of the mosaics, in order to verify uniformity ( $<\sigma>$).

As expected, the noise distribution is fairly uniform within each mosaic and from mosaic to mosaic ($<10\%$ variations). Also, for each mosaic, the two noise values are consistent, that is the noise can be considered Gaussian (see also Fig. 3).

On average the noise level is $\sim 79 $ $\mu$Jy. The typical detection limits for the ATESP survey are thus $\sim 0.24$ mJy at $3\sigma$ and $\sim 0.47$ mJy at $6\sigma$. Dynamic range problems can cause slightly higher noise levels of $\sim 100$$\mu$Jy around strong sources ( Speak> 50-100 mJy). Such problems appear to be serious only in one mosaic (fld69to75): the region around the bright radio source PMNJ0104-3950 suffers from a very high noise level and a number of spurious sources are present. This was due to strong phase instabilities during the observations which could not be removed by self-calibration. This region (of size $\sim 20\hbox{$^\prime$ }\times 25\hbox{$^\prime$ }$) was masked and therefore excluded from further analysis. Excluding this region, the total unifom sensitivity area covered by the ATESP survey is 25.9 sq. degr. or $7.9 \; 10^{-3}$ sr.

5.2 Artefacts

Another problem we faced was the possible presence of artefacts in the images, like spurious sources ("ghosts'') at a level of 0.1 - 0.5% opposite to bright sources with respect to the phase center of the image and `holes' in the centre of the field. The first problem, caused by the Gibbs phenomenon, arises from the use of an XF correlator and can be serious in high dynamic range continuum observations (like ours). The second effect is a system error produced by the harmonics of the 128 MHz sampler clock at 1408 MHz. Both effects can be completely removed as long as the observing bands are centered appropriately (Killeen 1995; Sault 1995). Unfortunately, at the time of our first two observing runs these effects were not yet known. We therefore could apply the corrections only to the data taken in the last observing run.

We point out that the corrections, when applied, result in a larger bandwidth smearing effect, since only $13\times 8(10)$ MHz channels are used (instead of $32\times 4$ MHz).

Wherever not corrected for, the "ghosts'' problem is unlikely to be serious in our case, since "ghosts'' appear in different places for each field and so they tend to average out when mosaicing the fields. Moreover, only radio sources brighter than $\sim 100$ mJy can produce detectable "ghosts'' in the final mosaics and such bright sources are very few in the region surveyed ($\sim
30$) and therefore could be easily checked. No evident "ghosts'' have been found.

We have also tried to reduce the sampler clock self-interference effect as far as possible by flagging residual bad visibilities (that is correlated noise) after a first step of cleaning and self-calibration (see also Sect. 4.2), but some of our fields still show it to a small extent. On the other hand the area of sky affected by "holes'' is of the order of a few percents ( $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ...) of the total region observed.

5.3 Clean bias


Table 4: Clean bias average corrections (see text)
Mosaic cc's a b
fld34to40 1616 $0.09 \pm 0.04$ $0.85 \pm 0.08$
fld44to50 2377 $0.13 \pm 0.03$ $0.75 \pm 0.06$
fld69to75 3119 $0.16 \pm 0.05$ $0.67 \pm 0.09$

\par\includegraphics[width=8.8cm,clip]{}\end{figure} Figure 4: The source flux measured after the cleaning ( Soutput) normalized to the true source flux ( Sinput) as a function of the flux itself (expressed in terms of $\sigma $) is shown for three different cases: 1616 cc's mosaic (top panel), 2377 cc's mosaic (middle panel) and 3119 cc's mosaic (bottom panel). Also shown are the linear fits (see text)

\par\includegraphics[width=8.8cm,clip]{}\end{figure} Figure 5: We present Soutput/Sinputas a function of the average number of clean components. Each dotted line refers to a different source flux ($100\sigma $, $50\sigma $, $30\sigma $, etc.). Also shown is the average number of clean components for each of our 16 mosaics (full lines at the bottom of the figure)

As already mentioned in Sect. 4.2, when the UV coverage is incomplete, the cleaning process can "steal'' flux from real sources and redistribute it on top of noise peaks producing spurious ones.

To quantify the actual effect in our mosaics we performed a set of simulations by injecting point sources in the survey UV data at random positions. Then the whole cleaning process was started. The number of sources injected in a mosaic ($\sim 500$) was chosen in order to reduce the statistical uncertainty without changing significantly the components/image statistics. The source fluxes cover the entire range of the survey: 250 sources at 3$\sigma $, 100 at $5\sigma$, 50 at $7\sigma$, 50 at $10\sigma$, 25 at $20\sigma$, 10 at $30\sigma $, 10 at $50\sigma $, 10 at $100\sigma $.

Taking into account the time and frequency resolution and the baseline lenghts, we get about 1500-2500 indepentent UV points for each field observed. This means that with about 2000 independent (not too close together or on top of each other) clean components we could clean the image to zero flux. The average number of (not independent) clean components per mosaic ranges between 1500 and 3200. Since we used a clean loop gain factor g=0.1, the number of independent clean components per mosaic can be estimated as 1/10 of the numbers reported above. We thus expect a significant clean bias effect (10 - 20%), larger for mosaics with a higher number of cleaning components. We then decided to test three mosaics, with a low, an intermediate and a high average number of cleaning components (cc's) respectively: fld34to40 (1616 cc's), fld44to50 (2377 cc's) and fld69to75 (3119 cc's).

The results of the tests are presented in Figs. 4 and 5 and summarized in Table 4. Figure 4 shows, for each of the three mosaics, the average source flux measured after the cleaning ( Soutput) normalized to the true source flux ( Sinput) as a function of the flux itself (expressed in terms of $\sigma $). In general the clean bias increases going to fainter fluxes and, as expected, depends on the number of cleaning components. In the best case (1616 cc's) we get $\leq 10\%$flux underestimation for the faintest sources; in the worst case (3119 cc's) the effect rises up to $\sim 20\%$.

The dependency of the clean bias on the number of cleaning components is more clearly shown in Fig. 5. Here we present Soutput/Sinputas a function of the average number of clean components for different source fluxes ($100\sigma $, $50\sigma $, $30\sigma $, etc.). Again, the clean bias affects more seriously the faintest sources. Moreover it is evident that we are not dealing with a linear effect: a sudden worsening appears at fluxes of the order of $10-20 \sigma$ and when the number of cleaning components exceeds $\sim 2000$.

A first order fit of the clean bias effect for the three different mosaics has been obtained by applying the least squares method to the function $S_{\mathrm{output}}/S_{\mathrm{input}}=a\log(S_{\mathrm{input}}/\sigma)+b$. The values obtained for the parameters a and b are listed in Table 4 and the curves are shown in Fig. 4.

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