next previous
Up: The ATESP radio survey


2 Survey design

The radio observations were carried out with two main goals in mind. The first aim was to detect the ESP galaxies in order to derive the "local'' ($z\sim 0.1$) bivariate luminosity function. We therefore tried to keep the sensitivity as uniform as possible over the whole ESP area, while at the same time reaching flux densities well below $\sim 1$ mJy (see Sect. 2.2).

The second aim was to have a complete catalogue of faint radio sources in order to study the sub-mJy population through a programme of optical identification of complete radio source samples extracted from the ATESP survey, exploiting the available data, i.e. deep CCD images.

As the survey is intended to achieve uniform sensitivity over a large area it is necessary to make use of the mosaicing technique.

2.1 Mosaicing technique

Mosaicing is the combination of regularly spaced multiple pointings of a radio telescope which are then linearly combined to produce an image larger than the radio telescope's primary beam. The linear mosaicing consists of a weighted average of the pixels in the individual pointings, with the weights determined by the primary beam response and the expected noise level (see equation in Sault & Killeen 1995). If the observing parameters and conditions are the same for every individual pointing, the expected noise variance in any observed field can be assumed to be equal for every observing field and the intensity distribution in the mosaiced final image, I(l,m), is modulated only by the primary beam response:

I(l,m) = \frac{ \sum_{i} P(l-l_i,m-m_i) I_i(l,m)}
{ \sum_{i} P^2(l-l_i,m-m_i)}
\end{displaymath} (1)

where the summation is over the set of pointing centres (li,mi). Ii(l,m) is the image formed from the i-th pointing (not corrected for the primary beam response) and P(l,m) is the primary beam pattern.

In planning a mosaicing experiment, the main issue to be decided is the pointing grid pattern, i.e. geometry and pointing spacings. For a detection experiment on a large area of sky (like the ATESP survey) the main requirement is uniform sensitivity over the entire region together with high observing efficiency. Such requirement can be satisfied by choosing opportunely the pointing grid pattern.

The mosaic noise standard deviation, $\sigma(I(l,m))$, can be obtained from the error propagation of Eq. (1) and the uniform sensitivity constraint is expressed by

\frac{\sigma (I(l,m))}{\sigma} = \frac{ 1}{ \sqrt{\sum_{i}
P_i^2(l-l_i,m-m_i)}} = {\rm constant}
\end{displaymath} (2)

for every position (l,m). In other words, the mosaic sensitivity, expressed in terms of $\sigma $s ($\sigma $ is the noise expected in the individual pointings) is modulated by the squared sum of the primary beam response.

The ATCA primary beam pattern can be approximated by a circular Gaussian function (Wieringa & Kesteven 1992)

P_i (r) = \mathrm{e}^{-4\ln 2 \left( \frac{r}{{FWHP}} \right)^2},
\end{displaymath} (3)

where $r=\sqrt{l^2+m^2}$ is the radial distance from the image phase center and FWHP is the full width at half power of the primary beam ($\sim$ 33 arcmin for ATCA observations at 1.4 GHz). Since the square of a Gaussian is still a Gaussian with FWHP reduced by a factor $\sqrt{2}$, the quadratic sum in Eq. (2) can be written as a linear sum of Gaussians with $FWHP \hbox{$^\prime$ }= {FWHP}/\sqrt{2}$ (corresponding to $s\simeq
33\hbox{$^\prime$ }/\sqrt{2} = 23.3\hbox{$^\prime$ }$ for ATCA 1.4 GHz observations).

To make the final choice for the ATESP survey grid pattern, we have performed a series of simulations of the bidimensional quantity

\sigma(I)/\sigma = \frac{1}{\sqrt{\sum_i \mbox{e}^{-4\ln 2
\left(\frac{(s_i-r)}{{FWHP}\hbox{$^\prime$ }}\right)^2}}}
\end{displaymath} (4)

where si=(li,mi), $r=\sqrt{(l-l_i)^2 + (m-m_i)^2}$ and $FWHP \hbox{$^\prime$ }=23.3\hbox{$^\prime$ }$, varying the pointing spacings s and the grid geometry (hexagonal and/or rectangular grids).

In general a very good compromise between uniform sensitivity and observing efficiency is represented by a grid pattern with pointing spacings of the order of $s\simeq {FWHP}\hbox{$^\prime$ }$. For our particular case, the best choice turned out to be a $20\hbox {$^\prime $ }$ spacing rectangular grid. The mosaic noise variations over a reference area of 1 sq. degr. for such a grid configuration are shown in Fig. 1. As expected, in the region of interest (central box) the noise is rather constant: variations are $\leq 5\%$, except at the region borders ($\leq 10\%$). We point out that hexagonal grids should be preferred when imaging wide areas of sky (like for the NVSS and FIRST radio surveys), but are not very efficient in the case of a narrow 1-degree wide strip of sky.

\par\includegraphics[width=8.8cm,clip]{}\end{figure} Figure 1: Noise variations expected over a 1 sq. degr. mosaic (central box, 1 pixel $= 1\hbox {$^\prime $ }$) for a $20\hbox {$^\prime $ }$ spacing rectangular grid. Filled circles indicate the pointing centres. At the center of the mosaic $\sigma (I)/\sigma \sim 1$. Contours refer to 5, 10, 20, 40, 80, 160, 320% noise increment from the center

2.2 Observing frequency, resolution and sensitivity

At 20 cm (the longest observing wavelength available at the ATCA) the field of view is largest (Gaussian primary beam $FWHP \simeq 33\hbox{$^\prime$ }$) and the system noise is lowest. Thus, observing at 20 cm allows minimization of both the number of fields (i.e. pointings) required to complete the survey and the observing time spent on each field. The ATCA can observe at two frequencies simultaneously (for instance 20 and 13 cm). However, we decided to optimize sensitivity at the expense of spectral information, by setting both receivers in the 20 cm band and observing in continuum mode ( $2\times 128$ MHz bandwidth, each divided into $32\times 4$ MHz channels in order to reduce the bandwidth smearing effect). This choice was also influenced by another consideration: since the field of view depends on the observing frequency, the grid pattern could not be optimized to get uniform sensitivity for both 13 and 20 cm bands simultaneously.

The observations were carried out at full resolution (ATCA 6 km configuration), since the identification follow up benefits from high spatial resolution, and the expected fraction of very extended sources (that could be resolved out and lost) is low at the ATESP resolution. Using the angular size distribution given by Windhorst et al. (1990) for radio sources, we estimate that $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... of the mJy and sub-mJy sources would appear point-like at the ATESP resolution, and $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... would have angular sizes twice the beam size or larger.

Since the ESP sample distance distribution peaks at $z\simeq 0.1$ and "normal'' galaxies are typically low-power radio sources, deep radio observations were needed to ensure detections of a statistically significant number of ESP galaxies. We considered satisfactory a point source radio limit of the order of $\sim 0.2$mJy ($3\sigma$), which corresponds to a detection threshold of $P \sim 3\; 10^{21}$ WHz-1at $z\sim 0.1$ (H0 =100 km s-1 Mpc-1). Furthermore a large sample of sub-mJy radio sources can be constructed at a $6\sigma$ detection limit, corresponding to a flux limit of $\sim 0.5$ mJy.

next previous
Up: The ATESP radio survey

Copyright The European Southern Observatory (ESO)