HIGH-RESOLUTION IMAGING OF THE ATLBS REGIONS: THE RADIO SOURCE COUNTS

Historically, radio source counts have been a key observational probe of cosmology, more specifically of the geometry of the universe. In an Euclidean universe the volume scales with distance as V∝r³ whereas the flux density scales as S∝r⁻², which means that the integral number of sources (for a population of non-evolving sources with constant comoving number density) above any flux density scales as n∝S^−3/2. Departures from this expectation were key evidence for non-Euclidean geometry. More recently, the geometry of the cosmos has been established with precision, and source counts represent a measure of cosmological evolution in radio source populations. The behavior of counts at sub-mJy flux density, the nature and evolution of these sources, and the question of whether they constitute a new population are unclear.

At flux densities of ⩽1.0 mJy, a "flattening" of normalized differential source counts has been widely reported in the literature (Windhorst et al. 1985, WMO85 henceforth; Hopkins et al. 2003; Huynh et al. 2005 and references therein). The rms noise level in the latter studies are 45 μJy for WMO85, varying between 12 to about 100 μJy for Hopkins et al. (2003; see Figure 9 from Hopkins et al. 2003), and approximately 10 μJy for Huynh et al. (2005). The flattenning is observed as an apparent change of slope from ∼0.7 at 5.0–100.0 mJy to about 0.4 in the range 0.25–5.0 mJy. WMO85 examined the optical identifications of faint radio sources and found that the sub-mJy radio source population is dominated by blue spiral galaxies. Later studies, however, have arrived at discordant results and identify the sub-mJy sources with different populations: starburst galaxies (Condon 1989; Benn et al. 1993; Huynh et al. 2005), early-type galaxies (Gruppioni et al. 1999), low (radio) luminosity active galactic nuclei (AGNs; Huynh et al. 2008), or a mixture of these. Since spectroscopically complete samples of sub-mJy sources are not available, the exact nature of the population observed as sub-mJy radio sources remains uncertain; however, it is widely agreed that flattening below 1.0 mJy requires an evolving population that is different from those that dominate counts at higher flux densities.

It may be noted here that the literature is not consistent in observing a flattening in counts at sub-mJy flux density; for example, the counts in Prandoni et al. (2001) and Subrahmanyan et al. (2010) are consistent with a continuation in the slope of the differential counts below mJy flux density. Potential causes for the discrepancy are that deep radio surveys often suffer from inadequate sky coverage that is necessary to average over clustering; wide-field surveys often do not go sufficiently deep and so biases arising from the proximity of the detection threshold to the image noise may distort measured counts. Additional uncertainly arises from the lack of understanding of the radio structures in sub-mJy radio sources, which may lead to biases related to the ability of the survey to catalog sources from detections of source components.

The ATLBS is a moderately wide-field radio survey, covering 8.42 deg² in the southern sky at 1.4 GHz. The survey has been carried out using the Australia Telescope Compact Array (ATCA), which is a Fourier imaging interferometer array. The radio observations for the low-brightness survey were designed for complete u − v coverage up to 750 m (for details of these observations, see Subrahmanyan et al. 2010). The work presented herein is based on the combination of the initial low-resolution survey and more recent radio observations with the ATCA in multiple expanded array configurations that extended the u − v coverage to 6 km, giving a synthesized beam with FWHM of 6'' and images with rms noise 72 μJy beam⁻¹. The high-resolution observations are critical in better estimation of the source structures and for removing the effects of blending (source confusion) in the low-resolution survey. See Saripalli et al. (2012) for details on a sample of extended sources and classification of sources from the ATLBS survey, which has been carried out using both the high-resolution and low-resolution images.

The improved imaging of the ATLBS survey regions has been used to revisit the 1.4 GHz source counts: the survey has sufficient sensitivity to probe the sub-mJy regime, and the relatively large sky coverage avoids clustering related uncertainties. A specific improvement in this work is the care taken to identify sources with low surface brightness by making use of low-resolution images and using multiple indicators to identify components of sources. The low-resolution images were used to make initial identifications so that the sources that might be resolved into multiple components at higher resolution are identified correctly. The blending issues inherent in using low-resolution images have been avoided using higher resolution images to identify blends. In addition, the use of low-resolution images (beam FWHM = 50'') almost completely removes effects of resolution bias (for a detailed discussion, see Section 4.1.4). These strategies, together with the use of optical images⁴ to locate candidate galaxy hosts and a careful visual examination of resolved and complex sources instead of automated classification ensures that the ATLBS catalog is a "source catalog" as opposed to a "component catalog." The distinction between "sources" (which are single sources) as opposed to components (which may be parts of a single source or unrelated sources which are close to each other due to projection effects) is crucial in estimating the true source counts.

The organization of the paper is as follows. In the next section, we give details of the new high-resolution radio observations of the ATLBS survey regions. In Section 3, we give details of the procedure adopted for source detection and the estimation of source flux densities. In Section 4, we present the source counts along with the corrections necessary to derive the true counts from the observations. Next, in Section 5, we compare the ATLBS source counts with previous work. Finally, in Section 6, the conclusions are presented.

The radio observations that form the ATLBS survey were made with the different array configurations of the ATCA. The observations were made in the 20 cm band, with a center frequency of 1388 MHz. These observations recorded visibilities in full polarization mode. The observations were made in two sub-bands with center frequencies of 1344 MHz and 1432 MHz, with bandwidths of 128 MHz. Each band was covered by 16 independent frequency channels of which multi-channel continuum visibilities in the 13 central channels were used.

The ATLBS survey covers two regions in the southern sky. These regions are designated as "A" and "B" having their centers at R.A. 00^h35^m00^s, decl. −67°00'00'' and R.A. 00^h59^m17^s, decl. −67°00'00'' (J2000 epoch), respectively. Together they cover an area of 8.42 deg². The two regions were specifically selected to be devoid of strong radio sources, low Galactic foreground emission, and at an optimum latitude that allowed for good visibility coverage for radio observations with the ATCA (see Subrahmanyan et al. 2010 for details). Each of the regions is covered in the interferometer observations as a mosaic of 19 pointings.

Earlier observations were made with the array configurations 750A, 750B, 750C, and 750D. These configurations provided complete u − v coverage up to 750 m, and low-resolution images made with these data were presented in Subrahmanyan et al. (2010). To obtain good u − v coverage up to 6 km antenna separations, new observations were made with the array configurations 6A, 6B, 6C, and 6D. The plan of the observations was as follows. The two regions A and B were observed for 12 hr with the array configured in each of the four layouts. The total observing time was 96 hr and this was spread over the mosaic pointings. Each pointing was observed for 20 s before switching to the next pointing and the pointings were thus cycled over every 19 × 20 s.

The reduction and imaging of the data was done with the radio interferometer data reduction software MIRIAD (Sault et al. 1995). The data were calibrated for amplitude and phase using the calibrator PKS B2353-686. The absolute flux scale was set using the calibrator PKS B1934-638. The visibility data were also examined for radio frequency interference and outliers and other obviously corrupted data were rejected. First, images were produced with the 6 km configuration visibilities. Deconvolution used the Clark algorithm (Clark 1980), which is faster for large images. After a phase-only self-calibration iteration, the clean components of sources exclusively within the primary beam main lobe were selected by masking the regions outside the primary beam main lobe in the images. Visibilities corresponding to these were subtracted from the data and the residual visibilities were imaged to model the sources outside the primary beam main lobe. The model was allowed to include both positive and negative intensity components since the source structures in these regions were unreal because of the significant azimuthal structure in the telescope primary beam sidelobes, which modulated the visibilities of sources outside the primary beam as the alt-azimuth antennas tracked the pointing centers over the observing session. Visibility domain subtraction of this model provided a data set containing essentially only sources inside the primary beam main lobe. Next, the visibilities from the array configurations of 750 m length were reduced in a similar way to get visibilities referring only to the sources within the primary beam main lobe. Following these steps, the visibilities were all concatenated for joint imaging, deconvolution, and iterative self-calibration.

The imaging was done with large sidelobe suppression area to obtain a good beam. Initial self-calibration iterations were of phase-only type. The multi-frequency deconvolution described in Sault & Wieringa (1994) was used to get the clean components from self-calibrated data. Because the u, v-coverage was not complete in the 750–6000 m range, deconvolution was assisted by masking areas of the image where no significant intensities were present. This was done by first smoothing the image to detect most of the diffuse emission and in the smoothed image regions below 4.5σ were masked. This process was repeated, iteratively, along with phase and amplitude self-calibration. The solution intervals for the successive iterations varied from 15 to 5 minutes. In a final step, the images of individual pointings were regridded and stitched together to obtain the combined mosaic image of region A and B separately. The sky area covered by these regions is depicted in Figure 1. Sample sub-images of these high-resolution images of these regions are presented in Figures 2 and 3. To better appreciate the difference between the high- and low-resolution images, we have presented a sky region in low and high resolutions in Figures 4 and 5. The linear combination of pointings was done with a weighting that maintained rms noise in the images nearly uniform; this value is 72 μJy beam⁻¹. Over the 8.42 deg² sky area where the gain in the mosaic images exceeds 0.5 (and hence the rms noise in primary-beam-corrected images does not exceed the above value by more than a factor of two) there are no image errors apparent above the thermal image noise. This exceptional quality in the wide-field images makes it a useful database for automated source finding and classifying algorithms as well as reliable studies of radio source properties. In addition, the range of source morphologies makes possible the validation and development of automated source finding algorithms, which may become crucial in the analysis of data from large surveys such as LOFAR and SKA.

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We have jointly used the low- and high-resolution ATLBS images in the strategy adopted for source detection and classification as well as for estimations of flux density. The former, with 50'' FWHM beam, was made using the 750 m arrays and the latter, with 6'' FWHM beam, was made using all of the visibilities up to 6 km baselines. The low-resolution images are used to identify sky regions in which to search for source components using the high-resolution images. The low-resolution images have a relatively lower chance of missing a source due to its being resolved: known in the literature as "resolution bias," resolved sources with same integrated flux density would have relatively lower peak flux density and hence may not have image pixels above the detection threshold; this would result in high-resolution images missing such sources that may be detected in lower resolution images. The high-resolution images have been used to detect source components, identify blends, and classify the sources. Various aspects that potentially introduce bias and errors in source detections such as the thermal noise in the images and the effects of blending confusion have been examined, as described below.

3.1. Thermal Noise Considerations

3.2. Source Blending Confusion

3.3. Bandwidth Smearing Correction

3.4. On the Classification of Radio Sources in the ATLBS Survey

3.5. The Identification of Sources with Complex Structures

In this section, we compute the ATLBS source counts and discuss the corrections necessary to estimate the true source counts from the distribution of ATLBS sources in flux density. First, the sources were binned in octave bins based on their integrated flux density. The effective bin centers need to be defined carefully because in a given bin the source counts are not expected to be uniformly distributed (in which case, the mean would suffice). The corrections that translate observed counts to true counts depend on this distribution within the bins and, hence, the effective bin center. The bin centers in our case have been calculated using the expression given by Windhorst et al. (1984):

$$\begin{equation} S_{{\rm bc}} = \left[(1-\gamma)\ \left(\frac{S_{l}-S_{u}}{S_{l}^{1-\gamma }-S_{u}^{1-\gamma }}\right)\right]^{1-\gamma }, \end{equation} \tag{ 1 }$$

where γ = 2.52 + 0.321 × log (S_gc) + 0.042 × log²(S_gc) and S_gc is the geometric center of the bin. The factor γ has been obtained by a fit to the source counts using a collection of data from Windhorst et al. (1984), therefore taking care of the source distribution within any bin. We have additionally estimated the value of γ from the source counts which we have derived; the value of the slope thus estimated is consistent with the above value of the slope over most of the flux density range.

The blending correction to the counts is negligible due to the high angular resolution in our images, and it has been discussed in detail in a previous section. To assure completeness of the source counts, we have applied resolution bias correction, effective area correction, and noise bias correction; these are discussed below.

4.1. Corrections to the Source Counts

4.1.1. Noise Bias Correction

Noise bias arises because the "true" source counts are modified by the noise in the image. This is true for estimations of any distribution affected by additive noise (Eddington 1913); noise bias corrections have been applied previously to radio source counts (Murdoch et al. 1973; Richards 2000; Bondi et al. 2008). Noise in the image effectively redistributes sources across neighboring bins, and the magnitude of the effect depends both on the image noise and the intrinsic source distribution. If a particular bin has nearby bins with nearly the same numbers of sources, then the number of sources migrating into the bin and out of the bin are the same, assuming symmetric noise distribution. Additionally, at high flux densities, the contribution of image noise to the source flux density is small and is usually a small fraction of the bin size, which most often increases in geometric progression. Therefore, the effects of noise bias are important for the lowest few bins.

We have simulated the effects of noise bias for our images. We have made use of the polynomial fit to the radio source counts given by Hopkins et al. (2003) as a model for the true source distribution. (It may be noted here that later in this paper in Section 5 we derive an improved estimate of noise bias and resultant source counts using Equation (9), which is derived from the ATLBS counts for self-consistency.) The polynomial fit is

$$\begin{equation} \log [(dN/dS)/S^{-2.5}] = \sum \limits _{i=0}^6 \ a_{i}[\log (S/{\rm mJy})]^{i}, \end{equation} \tag{ 2 }$$

with a₁ = 0.859, a₂ = 0.376, a₃ = −0.049, a₄ = −0.121, a₅ = 0.057, and a₆ = −0.008.

Noise of random amplitude, consistent with a Gaussian distribution with rms equal to that of the image noise, was added to the integrated flux density of the sources derived from the distribution, and the sources were rebinned. This gives an estimate of the noise bias correction required for each bin. The correction is significant only for the lowest two bins. For the first bin, 0.38–0.768 mJy, the correction to the source counts is 23.8% which drops to 3.6% for the second bin, and for the third bin the noise bias correction is only 0.69%. The derived corrections have been applied to the source counts for the above bins since for other bins the correction is negligible.

4.1.2. Effective Area Correction for Sources

Only sources that have peak flux densities (without gain correction) above the detection threshold and located in the area of the mosaic where the primary beam gain is above 0.5 are included in deriving the source counts. Approximately 17% sources above the detection threshold lie outside this area. Since the primary beam gain varies over the mosaic image, this leads to a bias in source detection because sources with higher peak flux densities are potentially detectable over a larger sky area. Sources with peak flux density above twice the detection threshold may be detected anywhere in the area mentioned above (since the maximum attenuation suffered would lower the peak flux densities above or at the detection threshold); whereas the sources with peak flux densities between the detection threshold and twice that value would be detectable only within a restricted area. The correction factor to account for the change in effective sky area with flux density may be estimated as the ratio of the effective area for a given peak flux density and the total detection area, assuming that sources are uniformly distributed on the sky.

4.1.3. Effective Area Correction for Blended Sources

For blended sources (or rather those sources that are blended in the low-resolution image and have been found to be multiple distinct sources at high resolution), the peak flux density as well as the integrated flux density have been determined using the high-resolution image. An effective area correction derived from the low-resolution peak flux density may be incorrect in these cases because in many such cases sources with a large difference in peak flux density are blended together. Blended sources with individual peak flux densities above the detection threshold would have all been detected irrespective of blending. For these sources, we use the high-resolution integrated flux density to derive the effective area correction. Blended sources with peak flux densities below the detection threshold but with integrated flux density above the detection threshold would also have been detected since at low resolution the peak flux density (in most cases) would have been equal to the integrated flux density in the high-resolution image. There are 37 sources with peak flux densities below the detection threshold but with the integrated flux density above the detection threshold. For these sources, therefore, we estimate the effective area correction using the high-resolution integrated flux density. Blended sources with integrated and peak flux densities below the detection threshold are not included in the derivation of source counts.

4.1.4. Resolution Bias Correction

Resolution bias is because extended sources that have integrated flux density above the threshold may have their peak flux density below the detection threshold; this would not happen in the case of an unresolved source of the same integrated flux density. Owing to this effect, a number of extended sources are lost in the source detection process, biasing the source counts to preferentially represent unresolved sources. We mitigate this effect by using low-resolution images for initial source detection. Below we estimate the resolution bias correction applicable to the source counts. We have used the expression given by Windhorst et al. (1990) to represent the angular size distribution of sources and thereby derive the resolution bias. The fraction of radio sources above an angular size ϕ is given by

$$\begin{equation} h(> \phi) = \exp [ -\ln 2 (\phi /\phi _{{\rm med}})^{0.62}], \end{equation} \tag{ 3 }$$

where the expression for ϕ_med (median angular size) is

$$\begin{equation} \phi _{{\rm med}} = 2\farcs 0 \ S_{1.4 \,{\rm GHz}}^{0.3}, \end{equation} \tag{ 4 }$$

with S_1.4 GHz in mJy.

The relationship between angular size and ratio of integrated to peak flux densities is

$$\begin{equation} 1 + (\phi /b_{s})^{2}= (S_{{\rm int}}/S_{{\rm peak}}). \end{equation} \tag{ 5 }$$

For a fixed integrated flux density, a source would be on the threshold of being missed if its peak flux density is equal to the detection threshold; such a source has an angular size

$$\begin{equation} \phi _{{\rm max}} = b_{s} \times [(S_{{\rm int}}/(S_{{\rm threshold}})) - 1]^{1/2}. \end{equation} \tag{ 6 }$$

Here b_s = 50'' is the angular size of the synthesized beam for the low-resolution images, S_threshold = 0.38 mJy is the detection threshold, and S_int is the mean flux density for the source bin.

Therefore, the fraction of sources missing due to being resolved is

$$\begin{equation} h(> \phi) = \exp [-\ln 2 (\phi _{{\rm max}}/\phi _{{\rm med}})^{0.62}]. \end{equation} \tag{ 7 }$$

Thus, the resolution bias correction for each bin is calculated as

$$\begin{equation} c = 1/(1-h(>\phi _{{\rm max}})). \end{equation} \tag{ 8 }$$

Since the beam FWHM in our case is 50'', the resolution bias is only a small correction to the source counts. The maximum effect of the resolution bias is seen in the lowest bin, where an estimated 1.25% of sources are lost due to the resolution bias. In higher flux density bins, the effect of resolution bias is negligible. For source counts generated solely with high-resolution images, however, the resolution bias corrections can be significant.

4.1.5. The ATLBS Source Counts

The total number of sources in the ATLBS survey above a threshold of 0.38 mJy is 1366; this is the final number of sources after using the high-resolution image to identify blended sources in the low-resolution image. The differential source counts, with all of the corrections discussed above, are shown in Figure 6. The fit to the source counts from the Australia Telescope Hubble Deep Field-South survey (ATHDFS) of Huynh et al. (2005) as well as the source counts for the Australia Telescope ESO Slice Project (ATESP) survey of Prandoni et al. (2001) are overlaid for comparison. Here the fit for ATHDFS is for a compilation of source counts of radio surveys including FIRST (Faint Images of Radio Sky at Twenty Centimeters; Becker et al. 1994), Phoenix Deep Field (PDF), ATHDFS, and ATESP. There is good agreement between the ATLBS source counts and ATESP source counts. Our source counts are, however, lower than the ATHDFS counts over most of the flux density range by about 10%. The ATLBS source counts derived herein based on high-resolution follow-up of the ATLBS survey is consistent with earlier derivations of ATLBS source counts (Subrahmanyan et al. 2010), which were based on the low-resolution images.

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The flattening in the normalized differential source counts widely reported in the literature is not obvious in the ATLBS source counts. To take a closer look at the behavior of the ATLBS counts below about 1 mJy, we have estimated the differential source counts using binning with smaller bin sizes; these are displayed in Figure 7. The ATLBS counts are consistent with the ATESP counts within the errors and continue the same trend to lower flux densities. However, the ATLBS counts appear not to follow the upturn of the ATHDFS counts and fall significantly short of the ATHDFS counts below about 1 mJy.

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The ATHDFS survey catalog is reported to have been constructed as a source catalog as opposed to a component catalog (Huynh et al. 2005). However, the specific forms of the corrections applied to the source counts from the ATLBS and ATHDFS differ, which may explain the difference in the source counts in the two cases. Specifically, we note that the corrections for noise bias are not applied to the source counts for ATHDFS as well as PDF survey (Hopkins et al. 2003). Since the sub-mJy counts are close to the detection threshold, the effect of noise bias is significant and needs to be applied to correctly estimate the source counts. In Figure 7, we have displayed the source counts for ATLBS, generated without applying the noise bias correction. It may be seen from the figure that in the absence of noise bias corrections, the differential source counts do exhibit a more pronounced flattening in the sub-mJy regime. Clearly, omitting noise bias corrections tends to generate flatter estimates for the source counts at levels close to the detection limit, and a factor responsible for the deficit in the ATLBS counts compared to those of the ATHDFS and PDF counts may be their having omitted the noise bias correction.

Source counts derived from "component" catalogs are expected to exhibit extra "sources" at low flux densities, as extended sources are decomposed into components with relatively lower flux densities. Additionally, in the case of surveys done with high resolution, it is possible for extended sources to break up into two or more compact components if the connecting diffuse emission is missed in the imaging. As a demonstration, we have constructed source counts from a component catalog generated from the ATLBS high-resolution images (with beam FWHM of 6''). The catalog was generated using the MIRIAD task IMSAD, with a detection threshold of 4σ, where σ = 72 μJy beam⁻¹ is the rms noise in the image, without any attempt at constructing a "source" catalog as we have done in this work. The source detection was restricted to regions with a primary beam gain of 0.9, so that corrections for the attenuation due to the primary beam, and the effective area correction, may be neglected. The noise bias correction as well as the resolution bias correction (which is important in the case of images with high resolution) were separately derived for these counts in the same manner as described in earlier sections. In Figure 8, we show the source counts generated from this component catalog. As may be expected, this results in a substantially flatter distribution for the source counts; additionally, the source counts are now greater than before as well as greater than the ATHDFS counts. In Figure 9, we display the ratio of component counts to source counts versus flux density. This ratio has an average value of 1.4, implying that on average the component counts are a factor 1.4 higher than the true source counts.

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The ATLBS counts are about 10% lower than the ATHDFS counts over the 0.4–10 mJy range. As seen in Figure 8, a component catalog may overestimate the counts in this flux density range by as much as 30%–50%; Hopkins et al. (2003) estimate that a component catalog may overestimate the counts by about 10%. The quantum of error would depend on the structures of radio sources at these flux densities and the quality of the imaging—the ability of the imaging to reproduce any connecting emission between components—and hence the correction factor necessary for deriving a source count from component counts may vary depending on the visibility coverage and imaging algorithms. Nevertheless, we conclude that the relatively lower source counts inferred in this work compared with, for example, PDS and ATHDFS counts are in part owing to the ATLBS counts having been carefully prepared to represent a source catalog rather than a component catalog. Note that catalogs such as NVSS are component and not source catalogs so any source count analysis based on these catalogs will have this problem. It is possible for this reason that no source count analysis is included in the NVSS publication (Condon et al. 1998).

The noise bias correction depends on the assumption of what are the true source counts: this prior assumption is used to determine the true number of sources in each bin so that the effect of noise bias may be estimated. As discussed earlier, we have adopted the PDF source counts for the determination of the noise bias. However, the PDF source counts show a more pronounced flattening compared to the ATLBS; therefore, we have carried out a second iteration of noise bias correction using the derived ATLBS source counts.

We fitted a second-order polynomial in flux density to the ATLBS source counts derived above, which appears sufficient to express the features seen in our source counts. The polynomial fit is given by

$$\begin{eqnarray} \log [(dN/dS)/S^{-2.5}] &=& 0.781 + 0.851\times \log (S/{\rm mJy})\nonumber \\ && -0.066\times \log ^{2}(S/{\rm mJy}). \end{eqnarray} \tag{ 9 }$$

Since the ATLBS source counts are relatively steeper compared to the PDF counts, the noise bias correction estimated from the ATLBS counts is smaller. For the lowest two bins, 0.38–0.54 and 0.54–0.77 mJy, the noise bias correction is now derived to be 11.18% and 5.22%, respectively, reduced from the previous values of 24.5% and 10%. This improved estimate of the source counts is shown in Figure 10 and Table 3. The ATLBS source counts are still systematically lower than the ATHDFS source counts; however, the difference between the two source counts is reduced.

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High-resolution radio images of the ATLBS survey regions are presented, with beam FWHM of 6''. The wide-field mosaic images covering 8.42 deg² sky area with rms noise 72 μJy beam⁻¹ are of exceptional quality in that there are no imaging errors or artifacts above the thermal noise over the entire field of view. The images have excellent surface brightness sensitivity—the visibility coverage is complete out to 750 m and hence provides good representation of extended emission components associated with radio sources. The images are, therefore, an excellent resource for examining with automated algorithms for source finding, parameter fitting, and morphological classification, and as a resource for testing such algorithms that would be used on upcoming all-sky continuum surveys with the LOFAR and ASKAP. We make the high-resolution ATLBS images available at the Web site www.rri.res.in/ ATLBS.

We have generated a source list from the ATLBS images. This is a carefully made source list as opposed to a component list. The images were initially examined using automated algorithms, which used representations with different resolutions, to identify sources and distinguish unresolved and single-component sources and complex sources. All complex sources were carefully examined by eye to recognize blends and classify appropriately. Optical surveys of the ATLBS fields were also examined for candidate host galaxies to aid in the classification of complex sources. The integrated flux densities of the sources were derived in a variety of methods—the method appropriate for the source structural classification was adopted in each case. We emphasize the use of multi-resolution images, which may complement each other, as well as the need to use data from other wavebands such as optical, infrared, etc. The source list is also presented online along with the integrated flux densities and classification.

The source list was used to estimate the radio source counts down to 0.4 mJy. The counts have been corrected for noise bias, resolution bias, and effective area. It may be noted that considerable care has been taken to ensure that the counts correspond to sources and not components. The counts presented in Figure 10 and Table 3 above have been self-calibrated for the noise bias in that the counts derived in a first iteration have been used to derive the noise bias correction.

Comparing the counts with previous work—the ATHDFS and PDS counts—shows that the ATLBS counts are systematically lower. This is attributed to our counts representing sources as opposed to components, as well as corrections for noise bias. We have demonstrated the substantial difference in counts that results from using component catalogs as opposed to source catalogs: at 1 mJy flux density component counts may be as much as 50% above true source counts. This implies that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources, which may require that source finding algorithms effectively work with multi-resolution and multi-wavelength data. The work presented herein underscores the importance of noise bias correction, in particular for deriving counts close to the limit of the survey sensitivity and for correctly estimating the faint-end slope and upturn in the source counts at sub-mJy flux density. Finally, the lack of an upturn in the source counts at faint flux densities implies that down to the faintest flux densities we have probed (approximately 0.4 mJy) there is no evidence for any new population. The upturn reported in the literature may be due to a combination of small survey areas and identification of radio sources as opposed to components, as well as effects of noise bias close to the detection limit.

The ATCA is part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. We thank Anant Tanna for his assistance with the initial processing of the visibility data.