2.1. Observations

RACS-low2 largely follows the footprint layout of the original RACS-low1, using the regular square_6x6 layout of the Phased Array Feed (PAF) beams with a central frequency of 887.5 MHz and 288-MHz bandwidth. It was carried out in 2022 based on a specification of 947 pointings.

The RACS-low2 observing strategy matches the later RACS epochs like RACS-mid and RACS-high, executed by the dynamic scheduler SAURONFootnote ^e as part of the autonomous science operations of ASKAP (Moss et al. in prep). Each pointing is observed within an individual scheduling block with a unique ID (SBID). We note that the initial RACS-low survey observations in 2019/2020 preceded the late-2020 shift to this autonomous mode of operations, and provided key input to optimise the transition from semi-automated to autonomous observing. In the case of RACS, we optimise each of the 15-min pointings based on specific constraints in addition to other global constraints and weightings that apply to all surveys being carried out. For RACS, these include restricting observations to $\pm 1$ h angle off meridian to maintain then best possible angular resolution at any given declination, ensuring the presence of all six outer antennas to also maximise angular resolution, and limiting both solar and lunar proximity to $\gt$ 10 deg.

Figure 1 in Paper IV shows the difference in the PAF beam arrangement for the square_6x6 and closepack36 footprints, the latter of which is used for RACS-mid, RACS-high, and RACS-low3. For RACS-low2, pointings were also conducted up to $\delta_{\text{J2000}} = +43^{\circ}$ following the later epochs to provide survey coverage up to $\delta_{\text{J2000}} \approx +48^{\circ}$ compared to the $\approx+41^{\circ}$ declination limit of RACS-low1.

Figure 1.

Example giant radio galaxy associated with ESO 505 $-$ G014 (van Velzen et al. Reference van Velzen, Falcke, Schellart, Nierstenhöfer and Kampert2012; Dabhade et al. Reference Dabhade2020) viewed in RACS-low1 and RACS-low2 (original images, full-sensitivity mosaics, and at $25^{\prime\prime} \times 25^{\prime\prime}$ angular resolution). The colour scales are linear between $-3 \sigma_{\text{rms}}$ and $50\sigma_{\text{rms}}$ with $\sigma_{\text{rms}}$ reported at the bottom of each panel. Note that RACS-low1 full-sensitivity mosaics were all produced at $25^{\prime\prime} \times 25^{\prime\prime}$ angular resolution.

RACS-low2 was observed after RACS-high, with data taken between 2022-03-18 and 2022-06-21. Observations were initially processed to check data quality, with poor observations due to miscellaneous system issues flagged to be reobserved. The total number of observations performed was 1 079, of which 132 were duplicates of the same field.

As with RACS-high and subsequent RACS epochs, RACS-low2 was observed alongside contemporaneous holography observations of PKS B0407 $-$ 658 to allow us to model the PAF beam responses over the course of the observations. The PAF beams are measured after every major beam weight update, and for RACS-low2 there were four separate holography-derived primary beam models used. Table 2 reports the SBID range for each holography observation and derived beam model. Note that unlike RACS-high, widefield leakage models derived from those holography observations are available for all of the holography observations, though for the work here we did not make use of the widefield leakage models.

Table 2.

Holography observation details and associated science SBIDs for RACS-low2.

Table 2. Long description

The table presents holography observation details and associated science SBIDs for RACS-low2. It contains four rows and four columns. The columns are labeled Holography SBID, Science SBID range, Date range for science SBIDs, and Number of SBIDs. Row 1: Holography SBID, 38585; Science SBID range, 38307-38528; Date range for science SBIDs, 2022-03-18 11:40:00-2022-03-24 22:09:39; Number of SBIDs, 108. Row 2: Holography SBID, 38709; Science SBID range, 38545-39385; Date range for science SBIDs, 2022-03-25 12:20:02-2022-04-14 01:54:49; Number of SBIDs, 605. Row 3: Holography SBID, 39549; Science SBID range, 39400-40878; Date range for science SBIDs, 2022-04-14 10:00:00-2022-05-22 19:23:53; Number of SBIDs, 356. Row 4: Holography SBID, 41055; Science SBID range, 40989-41829; Date range for science SBIDs, 2022-05-26 17:39:29-2022-06-21 13:31:14; Number of SBIDs, 10.

^a Inclusive.

^b Observation start times.

2.2. Processing

The RACS-low2 data were processed using the ASKAP pipeline (version 2.9.11)Footnote ^f built around the ASKAPsoft software packages (Guzman et al. Reference Guzman2019). Processing took place on the Pawsey Supercomputing Centre cluster Setonix.Footnote ^g We obtained 7.4M CPU hours as part of the Pawsey Partner Scheme (PPS) under project pawsey1014 (PI Duchesne). Some additional reprocessing (described in Section 3.2.2) made use of a separate PPS project, ja3 (PI Whiting), allocated for extra post-processing and related work for ASKAP surveys. Data processing for RACS-low2 is largely identical to previous RACS epochs, including initial bandpass and complex gain calibration and on-axis leakage correction based on observations of PKS B1934 $-$ 638 (assuming it is unpolarised), two rounds of phase-only self-calibration, and final imaging with the ASKAPsoft cimager Footnote ^h for each PAF beam dataset.

We make both Stokes I and Stokes V images, making use of multi-term, multi-scale deconvolution using the BasisfunctionMFS CLEAN deconvolution algorithm.Footnote ⁱ Two Taylor terms are used to represent the apparent sky brightness distribution. Widefield gridding is performed with the W-projection algorithm (Cornwell et al. Reference Cornwell, Golap and Bhatnagar2008), and image weighting uses Wiener preconditioning (Rau Reference Rau2010) with a robust parameter of 0.0 (similar to ‘Briggs’ robust 0.0, Briggs Reference Briggs1995) providing a good trade-off between sensitivity and angular resolution. Stokes I images go through up to ten major cycles of CLEAN deconvolution, down to a final depth of 0.5 mJy. Stokes V images only use up to three major iterations due to the comparatively empty circularly polarised sky.

A subset of the data also go through a bespoke off-axis source subtraction process prior to self-calibration, where bright sources (and observations they affect) are manually selected. This process is not part of the official ASKAP pipeline, though the ASKAPsoft off-axis source subtraction implementation has recently been enabled in the ASKAP operation pipeline. The bespoke workflowFootnote ^j is described in Paper IV and Paper VI, and involves imaging a small region around the offending source and either directly subtracting the CLEAN component model or first deriving complex gain amplitudes and phases in the direction of the source and then subtracting the model. This process is similar to peeling (see Noordam Reference Noordam and Oschmann Jacobus2004; Smirnov Reference Smirnov2011), though gain solutions are not directly applied to the data and only operates on XX and YY instrumental polarisations. This process uses WSClean (Offringa et al. Reference Offringa2014; Offringa & Smirnov Reference Offringa and Smirnov2017) for imaging the regions around sources and CASAFootnote ^k (CASA Team et al. Reference Team2022) for deriving gain solutions. The list of subtracted sources is included in Appendix A, though we note sources are only subtracted from a PAF beam dataset if they are not within 1.2 deg of the beam centre. This choice of radius resulted in over-subtraction in some images – see Section 3.2.2 for further details.

After imaging, the individual PAF beam images are then mosaicked using the ASKAPsoft linear mosaicking package linmos, which applies the primary beam models and also provides Stokes I leakage removal for the Stokes V images based on the leakage models derived from holography. We use a primary beam attenuation cutoff of 12% during linear mosaicking so the mosaic images do not extend beyond this cutoff. Individual PAF beam images are convolved to a common resolution for that specific set of PAF beams prior to mosaicking, and mosaics are weighted with a combination of primary beam attenuation and the total number of gridded visibilities. An output mosaic weight map is also produced.

Unlike RACS-mid, we do not apply any post-image brightness scale corrections. See Section 4.7 for an assessment of the resultant brightness scale for the RACS-low2 data.

3.1. Stokes I mosaics

To reduce sensitivity roll-off at the edge of the individual images due to the primary beam attenuation, we mosaic neighbouring observations following Paper II. Mosaicking and subsequent source-finding made use of the internal CSIRO supercomputer, petrichor. As the spacing between fields is equivalent to the spacing of the PAF beams, there is significant overlap between each individual image allowing us to create a ‘full-sensitivity’ image for each field as a linear mosaic. These mosaics make use of the weight maps generated earlier so that the mosaicking is functionally a continuation of the mosaicking of individual PAF beams. In this case, we make use of SWarp Footnote ^l (Bertin et al. Reference Bertin, Mellier, Radovich, Missonnier, Didelon, Morin, Bohlender, Durand and Handley2002) for regridding and co-adding the images. For each full-sensitivity mosaic, we also convolve all individual images to a common resolution for that mosaic, following Paper V, using beamcon_2D from RACS-tools.Footnote ^m This allows us to retain an angular resolution that is close to the original resolution of the images while ensuring flux density measurements will be accurate in the full-sensitivity images.

In Figure 1 we show example cutouts of a giant radio galaxy (associated ESO 505 $-$ G014; van Velzen et al. Reference van Velzen, Falcke, Schellart, Nierstenhöfer and Kampert2012; Dabhade et al. Reference Dabhade2020) to highlight the differences in the available RACS-low1 and RACS-low2 images. The left and centre-left panels show the original RACS-low1 images (before and after mosaicking and convolution to $25^{\prime\prime} \times 25^{\prime\prime}$ angular resolution) and the remaining three images show cutouts from the same field from RACS-low2 (original image, full-sensitivity mosaic image, and the full-sensitivity mosaic image convolved to $25^{\prime\prime} \times 25^{\prime\prime}$ angular resolution). This particular field saw a dramatic improvement to the angular resolution and root-mean-square (rms) noise in the RACS-low2 observation, going from $18.3^{\prime\prime} \times 17.3^{\prime\prime}$ (with an rms noise of $\sigma_{\text{rms}} = 342$ $\unicode{x03BC}$ Jy PSF $^{-1}$ ) in the RACS-low1 observation to $13.1^{\prime\prime} \times 11.1^{\prime\prime}$ ( $\sigma_{\text{rms}} = 214$ $\unicode{x03BC}$ Jy PSF $^{-1}$ ) in the equivalent RACS-low2 field. Part of the improvement in rms noise follows from the improvement in angular resolution, though we also see reduction in the rms noise for the full-sensitivity mosaic $25^{\prime\prime}$ images as well, highlighting the general data quality improvement with this second RACS-low epoch.

3.2. Stokes I catalogue

3.3. Initial Stokes V catalogue

Circular polarisation affords a unique opportunity to search for sources such as pulsars and radio stars due to the overall lower density of circularly polarised sources in the radio sky (e.g. Gaensler et al. Reference Gaensler, Manchester and Green1998). As many sources of strong circularly polarised emission tend to be time-varying (e.g. Pritchard et al. Reference Pritchard2021; Rose et al. Reference Rose2023, including long-period radio transients; Lee et al. Reference Lee2025), performing a similar mosaicking process with the Stokes V images would potentially result in averaging a time-dependent signal between observations that might be separated by up to a few months.

To generate a catalogue of Stokes V sources, we instead use the individual Stokes I and V images prior to constructing the full-sensitivity mosaics described in Section 3.1. For individual SBIDs, we first run PyBDSF on the Stokes I images and make measurements on the corresponding Stokes V images using the positions from Stokes I source lists. This ensures that each Stokes I and V measurement are taken from the exact same observation, and that each Stokes I measurement has a corresponding Stokes V measurement. We use the whole image for source-finding, which has been constructed with a primary beam cutoff of 12% during mosaicking. The Stokes V measurements are made as an absolute peak Stokes V flux density within a $3\times3$ pixel box at the Stokes I source position reported by PyBDSF. We take a local measurement of the Stokes V rms noise as the uncertainty on the Stokes V flux density measurement. The resulting Stokes V source lists are then concatenated, retaining the relevant Stokes I and Stokes V information for each entry in the resultant table. For each measurement, we also record the direction cosines, l and m, relative to the image centre to provide information about where on a particular image the measurement was made. We note that the construction of the Stokes I portion of this catalogue is identical to the ‘time-domain’ catalogue produced for RACS-mid (Paper V) and no de-duplication is done so sources may have multiple entries and measurements corresponding to measurements in adjacent or overlapping observations.

Note that we do not patch this catalogue with fixed measurements for bright sources as described in Section 3.2.2. While the off-axis source-subtraction does not operate on XY and YX correlations, the underestimated Stokes I flux (formed from XX and YY correlations) may boost the fractional polarisation reported for those sources. For this reason, they are removed from the raw Stokes V catalogue. Similarly, the extended sources that were originally missed are not added.

In total, we report 5 727 958 Stokes I measurements in this concatenated catalogue which includes multiple measurements of sources in regions that overlap between images. From this, we obtain 32 098 Stokes V measurements with absolute peak flux density above $5\sigma_{V, {\rm rms}}$ . These Stokes V measurements includes sources of Stokes I leakage into Stokes V. In Section 5.1 we will assess the leakage and appropriate thresholds to help remove sources of leakage.

Figure 2.

The HEALPix-binned rms noise across the full-sensitivity mosaics as reported in the catalogue. We use $N_{\text{side}}=64$ for HEALPix binning, corresponding to an area of $\approx55 \times 55$ arcmin $^2$ . The dashed black lines are drawn at Galactic latitudes of $|b| \pm 5^{\circ}$ .

4.1. Noise and reliability

As a measure of image and catalogue fidelity, we report the general rms noise properties and reliability of our source finding process. Figure 2 shows the position-dependent rms noise across the survey as reported in the catalogue with $N_{\text{side}} = 64$ HEALPix binning (corresponding to bins of $\approx55 \times 55$ arcmin $^2$ ). This highlights regions of higher noise like the Galactic Plane, around Cygnus A and other bright sources, and generally above $\delta_{\text{J2000}} \approx +0^{\circ}$ , common with other RACS data products. Due to the overlap in SBIDs where the sky tiling changes to cover the South Celestial Pole (SCP), the rms noise is also lower around $\delta_{\text{J2000}} \approx -70^{\circ}$ , also a feature of the common tiling pattern used across RACS epochs. The median rms noise across the whole survey is $195_{-32}^{+48}$ $\unicode{x03BC}$ Jy PSF $^{-1}$ (when measured at the locations of sources in the catalogue). This is an overall improvement from RACS-low1 which reports $314_{-72}^{+123}$ $\unicode{x03BC}$ Jy PSF $^{-1}$ when obtained from catalogue rms noise values, though note a fixed resolution of $25^{\prime\prime} \times 25^{\prime\prime}$ is used in that case. For comparison, median noise across the individual SBID images prior to the additional mosaicking of neighbouring images is $\approx225$ $\unicode{x03BC}$ Jy PSF $^{-1}$ .

As with other RACS data releases (Paper II; Paper V; Paper VI), we define an estimate of the catalogue reliability based on the number of negative components found with identical source-finding parameters below $-5\sigma_{\text{rms}}$ . We assume that noise is Gaussian and that for all negative components found an equal number of positive components would be found and should be considered artefacts/false detections (e.g. Intema et al. Reference Intema, Jagannathan, Mooley and Frail2017). Repeating source-finding after multiplying the images by $-1$ yields an overall 15 834 negative Stokes I sources with $|S_{\text{peak}}| \geq 5\sigma_{\text{rms}}$ after merging source lists. For comparison, we take the source catalogue prior to patching (Section 3.2.2, with 3 922 159 sources) and report a total reliability of 99.60%. Figure 3 shows how this reliability metric varies as a function of declination (top panel), SNR (middle panel), and angular resolution (bottom panel). As with other RACS catalogue at varied angular resolutions, we find the reliability varies as a function of declination, decreasing in regions of finer angular resolution (and as, as expected, a function of SNR). We note that overall reliability increases to 99.94% for sources above $7\sigma_{\text{rms}}$ .

Figure 3.

Estimates of the reliability of the catalogue, binned as a function of declination (top), SNR (middle), and angular resolution (bottom). In the top panel, we also show the declination-dependent reliability at three separate SNR limits, with medians for each limit shown as a horizontal line. In the centre and bottom panels, a dashed horizontal line is drawn at 100% reliability.

4.2. Angular resolution and unresolved sources

As the catalogue is constructed by combining source lists from images with their own angular resolution, it has a variable angular resolution, in contrast to the fixed angular resolution of the RACS-low1 catalogue. This variation is largely a function of declination, and Figure 4 shows how the angular resolution varies as a function of position. The median PSF is $15.2^{\prime\prime} \times 13.0^{\prime\prime}$ , and the major and minor axes range from $12.5^{\prime\prime}$ – $69.2^{\prime\prime}$ and $11.3^{\prime\prime}$ – $22.9^{\prime\prime}$ , respectively. For comparison, the original SBID images prior to additional mosaicking have a median PSF of $14.3^{\prime\prime} \times 11.8^{\prime\prime}$ with a range in major and minor axes of $11.8^{\prime\prime}$ – $50.8^{\prime\prime}$ and $10.6^{\prime\prime}$ – $21.0^{\prime\prime}$ , respectively, so in general there is only a small decrease in angular resolution when making the full-sensitivity images.

Figure 4.

The HEALPix-binned FWHM of the PSF major (top) and minor (bottom) axes as a function of position across the sky, as reported at catalogue positions. The binning is the same as in Figure 2.

Figure 4. Long description

A heat map showing the distribution of PSF major and minor axes across the sky. Panel A: The top heat map displays the PSF major axis in arcseconds. The x-axis ranges from 180 degrees to 225 degrees, and the y-axis ranges from -60 degrees to +60 degrees. The color scale ranges from 12 to 60 arcseconds, with darker colors indicating larger values. Notable regions of higher values are observed near the equator. Panel B: The bottom heat map displays the PSF minor axis in arcseconds. The x-axis ranges from 180 degrees to 225 degrees, and the y-axis ranges from -60 degrees to +60 degrees. The color scale ranges from 10 to 30 arcseconds, with darker colors indicating larger values. Notable regions of higher values are observed near the equator.

For comparisons against other surveys in later sections, it is important to consider whether all sources or just unresolved sources should be compared. For the RACS-low2 catalogues, we follow the method described in Paper II where we assume that the ratio of total flux density to peak flux density, $S_{\text{total}} / S_{\text{peak}}$ should be approximately 1 for an unresolved source, but will deviate away from 1 for faint sources (due to scatter in the measurements of the Gaussian component parameters) and will have a bulk shift above 1 for all sources due to blurring from astrometric offsets between images when mosaicking.

Figure 5 shows the distribution of $S_{\text{total}} / S_{\text{peak}}$ as a function of SNR for single component sources, highlighting the spread at low SNR and the overall marginal increase above 1. Following Paper II, we create bins in SNR and take the lower 95-th percentile of the logarithmic distribution for each bin to consider as a lower envelope fit with $S_{\text{total}} / S_{\text{peak}} = A\sigma^{B} + \text{med}(S_{\text{total}} / S_{\text{peak}})$ . The reflected upper enveloped (shown on Figure 5) is used to define an unresolved source, and includes an additional offset to account for blurring that is not accounted for with the lower envelope. Sources below that line are considered unresolved. Overall, we find $\approx66$ % of sources can be considered unresolved. In the FITS tables we use Flag = 0 to define unresolved sources and Flag = 1 for resolved sources.

Figure 5.

$S_{\text{total}}/S_{\text{peak}}$ distribution for single component sources as a function of SNR to define sources that are unresolved. We show the lower fitted envelope and the reflected upper envelope used to define an unresolved source, along with the binned medians used for fitting. The horizontal solid line is drawn at $S_{\text{total}}/S_{\text{peak}} = 1$ , and the horizontal dotted line is drawn at the sample median.

4.3. Source-finding completeness

To check how complete the catalogue is at different flux density limits, we follow a process is similar to previous RACS epochs (Paper II; Paper V). This takes simulated models of the sky and injects sources onto residual images after removing the 2D Gaussian components modelled by PyBSDF during source-finding. As a change from RACS-low1 and RACS-mid, we make use of a model generated by the Tiered Radio Extragalactic Continuum Simulation (T-RECS; Bonaldi et al. Reference Bonaldi, Bonato, Galluzzi, Harrison, Massardi, Kay, De Zotti and Brown2019), which includes star-forming galaxies and AGN. We use the ‘medium’ tier, 25-deg $^2$ catalogue with a 1.4-GHz flux density limit of 10 nJy.

After source-finding is done for each full-sensitivity image, we obtain an image of the residuals after subtraction of the 2D Gaussian components. To inject sources onto the residual image, we randomise positions of each simulated source within a $5^{\circ} \times 5^{\circ}$ region within the image boundaries, and take sources in range of $3\sigma_{\text{rms}} \leq S_{\text{simulated}} \lt 2\times\text{max}(S_{\text{image}})$ , where $S_{\text{image}}$ is the maximum brightness in the original image and $S_{\text{simulated}}$ is the peak brightness of the simulated source, assuming it is a point source. Simulated flux densities are scaled to 887.5 MHz from the 780-MHz simulated value assuming a spectral index of $\alpha=-0.83$ . Sources in the T-RECS catalogue are reported with a projected angular size in one dimension and we assume both AGN and star-forming galaxies will have some varied ellipticity, e. We take a random value of e from a uniform distribution in the range $1 \leq e \leq 4$ to model the sources as 2D Gaussians. These are convolved to the angular resolution of the image and injected onto the residual images. PyBDSF is then re-run to generate a simulated source list. This process is run five times for each image, with the source positions and $5^{\circ} \times 5^{\circ}$ box placement randomised for each iteration to provide a range of samples across each full-sensitivity image. Each output source list is then matched to the input simulated catalogue independently and finally all source-lists and matched source-lists are concatenated.

We estimate the flux densities above which the RACS-low2 catalogue is complete to 50% and 95% as the ratio of sources in the input T-RECS simulated source lists to the output PyBDSF source lists after matching to the respective input lists. Figure 6 shows the flux density limits for 50% and 95% completeness in 9-deg declination bins, covering $-90^{\circ} \leq \delta_{\text{J2000}} \leq +45^{\circ}$ . Completeness generally decreases as declination increases, likely corresponding to a similar increase in rms noise as a function of declination (Figure 2). The lower flux density limit around $ \delta_{\text{J2000}} \approx -70^{\circ}$ also corresponds to the higher sensitivity in the region where the observation tiling changes to cover the SCP. We estimate the mean 50% and 95% flux density limits as $1.2\pm0.4$ and $2.1\pm0.8$ mJy, respectively (shown as horizontal lines on Figure 6).

Figure 6.

Estimated RACS-low2 catalogue 50% (blue circles) and 95% (red squares) completeness as a function of declination in equally-spaced 9-deg bins between $-90 \leq \delta_{\text{J2000}} \leq +45^{\circ}$ . The horizontal lines indicate the median flux density completeness limits.

Figure 7.

The RACS-low2 Euclidean normalised source counts, before (red filled circles) and after correction for source-finding incompleteness (red empty circles). We also show the equivalent corrected source counts from RACS-low1 (blue diamonds Paper II), the MeerKAT DEEP2 images (black squares Matthews et al. Reference Matthews, Condon, Cotton and Mauch2021), and the source counts compilation from (grey crosses de Zotti et al. Reference de Zotti, Massardi, Negrello and Wall2010), highlighting the RACS-low2 catalogue follows the expected source-count distribution when incompleteness is modelled and corrected for. Note that RACS-low1 and RACS-low2 source counts are scaled to 1.4 GHz for comparison with other work assuming $\alpha=-0.83$ .

4.4. Source counts

To check the accuracy of our source-finding completeness assessment, we produce the Euclidean normalised source counts (e.g. Heywood et al. Reference Heywood, Jarvis and Condon2013) for the RACS-low2 catalogue. For each declination band described in the previous section, sources are counted in 51 logarithmically-spaced flux density bins in the range $0.82$ mJy (corresponding to approximately five times the 16-th percentile of the rms noise distribution) to $\approx3\,100$ Jy (ensuring we include the brightest source in our survey, Cygnus A). The raw counts per declination band are corrected for incompleteness using the T-RECS simulated models, and are then summed and normalised by the total area of 32 362 deg $^2$ between $-90^{\circ} \leq \delta_{\text{J2000}} \leq +45^{\circ}$ , excluding the Galactic latitudes of $|b| \lt 5^{\circ}$ .

Figure 7 shows the Euclidean normalised source counts for RACS-low2, both before and after correction of source-finding incompleteness, and scaled to 1.4 GHz assuming $\alpha=-0.83$ . We also show the equivalent corrected source counts from RACS-low1 (Paper II), the faint source counts from the MeerKAT DEEP2 image (Matthews et al. Reference Matthews, Condon, Cotton and Mauch2021), and the source counts from the compilation of de Zotti et al. (Reference de Zotti, Massardi, Negrello and Wall2010). At the high flux density end of the distribution, we see significant scatter and uncertainties due to very low numbers of extragalactic sources this bright, with most flux density bins above $\approx100$ Jy only featuring a single source at most, consistent with other widefield surveys including RACS-low1. A decrease in counts at $\approx50$ Jy is present in the RACS-low2 catalogue compared to RACS-low1, which may be the result of a small number of bright extended sources being decomposed into multiple Gaussian components by PyBDSF that were not patched as in the case of PKS J0133 $-$ 3629 (see Sections 3.2.2 and 4.7). The comparatively low angular resolution of the RACS-low1 catalogue is better suited to modelling extended sources with simple Gaussian components. At low flux densities the RACS-low2 corrected counts agree well with Matthews et al. (Reference Matthews, Condon, Cotton and Mauch2021) and de Zotti et al. (Reference de Zotti, Massardi, Negrello and Wall2010), though tend to deviate from RACS-low1.

4.5. Efficacy of the primary beam models

As RACS-low2 is the first RACS epoch to make use of holography-derived models of the square6x6 PAF footprint at 887.5 MHz, we explored the resulting brightness scale in our images, as a function of position on the images. Paper IV and Paper VI explored how the mid- and high-band closepack36 PAF footprint beam models affect the resultant brightness scale, finding that the image edges suffered from discrepancies of up to $\approx20$ % that was suggested to be a residual telescope pointing error, though the definite cause is not yet known.

Figure 8.

The binned flux density ratios between RACS-low2 and NVSS (a and d), SUMSS (b and e), and the original RACS-low (c and f) as a function of position on the individual images (top row) and full-sensitivity mosaics (bottom row). The ratios are normalised to the median of each comparison. The bin sizes are $15.8 \times 15.8$ arcmin $^{2}$ . The solid contour is drawn at 1, and dashed contours are drawn at $[\pm5\%, \pm10\%, \pm 15\%, \pm 20\%]$ .

Figure 8. Long description

Panel A: A heat map showing the binned flux density ratios between RACS-low2 and NVSS as a function of position on the individual images. The axes are labeled in degrees, with the x-axis representing longitude and the y-axis representing latitude. The color scale ranges from 0.83 to 1.2, indicating the ratio values. The solid contour is drawn at 1, and dashed contours are drawn at 0.9 and 1.1. Panel B: A heat map showing the binned flux density ratios between RACS-low2 and SUMSS as a function of position on the individual images. The axes are labeled in degrees, with the x-axis representing longitude and the y-axis representing latitude. The color scale ranges from 0.83 to 1.2, indicating the ratio values. The solid contour is drawn at 1, and dashed contours are drawn at 0.9 and 1.1. Panel C: A heat map showing the binned flux density ratios between RACS-low2 and RACS-low1 as a function of position on the individual images. The axes are labeled in degrees, with the x-axis representing longitude and the y-axis representing latitude. The color scale ranges from 0.83 to 1.2, indicating the ratio values. The solid contour is drawn at 1, and dashed contours are drawn at 0.9 and 1.1. Panel D: A heat map showing the binned flux density ratios between RACS-low2 and NVSS as a function of position on the full-sensitivity mosaics. The axes are labeled in degrees, with the x-axis representing longitude and the y-axis representing latitude. The color scale ranges from 0.83 to 1.2, indicating the ratio values. The solid contour is drawn at 1, and dashed contours are drawn at 0.9 and 1.1. Panel E: A heat map showing the binned flux density ratios between RACS-low2 and SUMSS as a function of position on the full-sensitivity mosaics. The axes are labeled in degrees, with the x-axis representing longitude and the y-axis representing latitude. The color scale ranges from 0.83 to 1.2, indicating the ratio values. The solid contour is drawn at 1, and dashed contours are drawn at 0.9 and 1.1. Panel F: A heat map showing the binned flux density ratios between RACS-low2 and RACS-low1 as a function of position on the full-sensitivity mosaics. The axes are labeled in degrees, with the x-axis representing longitude and the y-axis representing latitude. The color scale ranges from 0.83 to 1.2, indicating the ratio values. The solid contour is drawn at 1, and dashed contours are drawn at 0.9 and 1.1.

Figure 9.

Top row. The binned flux density ratios between RACS-low2 and NVSS for three of the four common beam-former weights periods during RACS-low2 (each with their own primary beam models) as a function of position on the individual images. The number of individual observations that go into each comparison are reported at the top of each panel, and the specific holography observation is also reported. Bottom row. The binned flux density ratios between RACS-low1 and NVSS for three of the five common beam-former weights periods during RACS-low1, as a function of position on the individual images. The number of individual observations that go into each comparison are reported at the top of each panel. Note because RACS-low1 SBIDs contained multiple pointings we have referred to the individual pointings as ‘fields’. Other details are as in Figure 8.

We initially look at only the individual SBID images (i.e. prior to mosaicking neighbouring observations) to assess how effective the primary beam correction is for the individual observations. As part of the ASKAP pipeline run, we generate a source list of each individual SBID image with Selavy (Whiting & Humphreys Reference Whiting and Humphreys2012)Footnote ^o which is cross-matched to the Sydney University Molonglo Sky Survey (SUMSS; Bock et al. Reference Bock, Large and Sadler1999; Mauch et al. Reference Mauch, Murphy, Buttery, Curran, Hunstead, Piestrzynski, Robertson and Sadler2003), the NRAOFootnote ^p VLA Sky Survey (NVSS; Condon et al. Reference Condon, Cotton, Greisen, Yin, Perley, Taylor and Broderick1998), and the original RACS-low1 catalogue (Paper II, specifically after making the equivalent full-sensitivity images). We only consider sources that are isolated (no neighbours within $90^{\prime\prime}$ ) and unresolved ( $0.8 \leq S_{\text{total}} / S_{\text{peak}} \leq 1.2$ )Footnote ^q , resulting in an average of $\approx2\,500$ sources per image available for cross-matching. We scale the flux densities of each external survey to 887.5 MHz assuming a fixed spectral index $\alpha = -0.83$ (the median spectral index between SUMSS and NVSS reported by Mauch et al. Reference Mauch, Murphy, Buttery, Curran, Hunstead, Piestrzynski, Robertson and Sadler2003), though note for the purpose of assessing the brightness scale across the image we normalise the ratios to the overall median.

With the cross-matched source lists, we remove sources with RACS-low2 SNR $\lt 10$ , and assign direction cosine, l and m, to the source positions corresponding to the directions from the image centres. We then bin the ratios in l and m, taking a median for each bin. Figure 8 shows the binned medians as a function of l and m for the NVSS, SUMSS, and RACS-low1 comparisons. We see a residual brightness scale error across the images in all three comparisons. There is a ring of $\approx4$ –5% elevated brightness at $\approx2$ – $3^{\circ}$ from the image centre, ending in up to $\lesssim20$ % reduced brightness at the image corners.

As noted, similar effects were seen with RACS-mid and RACS-high for the closepack36 PAF footprint, though the change in footprint has altered the pattern of the residual error. The comparison with NVSS (for images $\delta_{\text{J2000}} \gtrsim -40^{\circ}$ ) in particular highlights the same north to south bias in the error that was observed in Paper IV, though the magnitude is smaller here at $\approx5$ % difference in the median between $m \gt +2.5^{\circ}$ and $m\lt-2.5^{\circ}$ parts of the image. The SUMSS comparison (for images $\delta_{\text{J2000}} \lesssim -30^{\circ}$ ) shows a more symmetric error ( $\approx3$ % difference) The comparison with RACS-low1 also features the N-S effect with a reduced magnitude ( $\approx4$ % difference) compared to the comparison with NVSS, highlighting a potential declination-/elevation-dependent residual primary beam error.

We split the RACS-low2 Selavy source list and NVSS cross-matches and grouped by which holography-based model was used for primary beam correction. Figure 9 shows the equivalent of Figure 8(a) for three of the four holography models, with the fourth not shown due to having only a small number of SBIDs and therefore few sources for cross-matching. We see the same ring-shaped pattern occur in all cases, though with a slight lateral shift which is to be expected as beam-former weight updates may shift the beam positions.

In the bottom row of Figure 9 we also show the equivalent common beam-former weights periods for RACS-low1, using the same cross-matching outlined in Section 4.5 with the Selavy source lists available on CASDA. For RACS-low1, a post-mosaic primary beam correction was applied using a primary beam model based on holographic observations of Virgo A (see Section 3.3.2 and Appendix A in Paper I). A single correction is applied for all observations, rather than individual models for each common weights period. We see marginal decrease in the residual errors, and the pronounced ring feature from RACS-low2 is not present. The Virgo A holography observation was recorded with different beamformer weights to the entirety of RACS-low1, and beam models derived from Virgo A for RACS-low1 extend out to the first sidelobe at 887.5 MHz. Conversely, RACS-low2 primary beam models are only evaluated out to some fraction of the primary beam main lobe, where the extent of the modelled main lobe for each beam varies based on coma distortion and the general beam shape variation for a given set of beamformer weights. This can be up to $\approx21$ % for some corner beams (e.g. beam 31 from holography SBID 38709), whereas our mosaicking procedure clips images when attenuation is $\lt12$ %, so the actual coverage of the primary beam models is less than ideal.

We also cross-matched the PyBDSF-derived source lists for each of the full-sensitivity mosaic to explore how the edge effects change through the mosaicking process. We repeat the same cross-matching (from an average of $\approx$ $3\,300$ unresolved and isolated sources per image) and subsequent binning and show the result with comparison to NVSS, SUMSS, and RACS-low1 in Figure 8(d)–(f). We see a reduction in edge effects as individual images overlap with the same spacing as the PAF beam images, so the edge contribution is significantly down-weighted in the full-sensitivity mosaics. As the tile centres are largely unchanged, we still see some residual errors, with maximum difference of up to $\approx$ 5%.

4.6. Time-dependence of the brightness scale

In all released RACS epochs so far, we have observed a time-dependent fluctuation of the brightness scale (Paper I; Paper IV; Paper VI). This fluctuation has been investigated down to only the 15-min interval as an SBID-dependent fluctuation. Figure 10 shows the median flux density ratios for the NVSS and RACS-low1 $\text{SNR}\gt10$ cross-matches for each SBID described in the previous section. In general, we see the familiar scatter in the brightness scale as a function of time with an overall standard deviation of $\approx$ 4% for both surveys. While there is some periodicity to the fluctuations, the magnitude of this periodic signal is reduced compared to RACS-high and RACS-mid and is similar to RACS-low1. We do not rescale the RACS-low2 data due to the lack of significant periodic signature, and attempts at rescaling with the same method as RACS-high with a sinusoidal model provides no significant reduction in the variance of the residual flux density ratios (as with RACS-low1; Paper I, see their Section 3.3.3).

Figure 10.

Median flux density ratios against NVSS (red circles) and RACS-low1 (blue squares) for each SBID as a function of time, highlighting the time-dependent variation of the brightness scale common to all RACS epochs. The solid horizontal line is drawn at a ratio of 1, and the dashed and dotted horizontal lines are drawn at $\pm 5$ % and $\pm 10$ %, respectively. Vertical black lines mark the end of the labelled month.

We suspect the magnitude of these fluctuations is driven by temperature variations of the PAFs, which is more significant in the Australian Summer months. RACS-mid, RACS-high, and RACS-low3 (Galvin et al. in preparation) had the bulk of their observations conducted during Summer months, whereas RACS-low2 was observed predominantly over the comparatively cooler Autumn. In addition, RACS-low1 data was observed over Winter, and while the time-dependent brightness scale fluctuation is still present the magnitude is also smaller in that case. Despite these fluctuations, the source lists (and images) from individual RACS-low1 and RACS-low2 observations are still suitable for studying time-variability if taking into account the appropriate brightness scale uncertainty for each epoch.

4.7. Absolute brightness scale

As a last assessment of the brightness scale for Stokes I, we also compare 887.5-MHz flux density measurements of bright calibrator sources from Perley & Butler (Reference Perley and Butler2017) and PKS B1934 $-$ 638 (Reynolds Reference Reynolds1994). For sources in the survey region, we compare the catalogued flux density against the model flux density evaluated at 887.5 MHz if they are cross-matched within their source size. Fornax A and PKS J0133 $-$ 3629 are detected as multiple sources. In the case of Fornax A, we simply consider its full extent beyond the detectability of the RACS snapshot observations, but for PKS J0133 $-$ 3629 we combine the two sources it resolves into for the purpose of this comparison as each lobe is well-detected. The measured flux densities are shown on Figure 11 against their model values at 887.5 MHz, coloured by source size. We see good general agreement, with a standard deviation of 4% for the full sample. As expected due the (u, v) cut, larger sources tend to have their total flux density underestimated (e.g. PKS J0133 $-$ 3629 and Virgo A, highlighted on the plot) or not catalogued as a single source as in the case of Fornax A (not present on the plot). We note that the median flux density ratio between the measured and model values is $1.03$ . We suggest our overall brightness scale is similar to RACS-low1, with a similar bulk uncertainty of 7% in the full sensitivity images, though note this will increase if measuring sources at the edges of the pre-mosaic single-SBID images.

Figure 11.

RACS-low2 measured flux densities for bright calibrator sources as a function of their model values from (Reynolds Reference Reynolds1994, for PKS B1934 $-$ 638, highlighted with a box) and (Perley & Butler Reference Perley and Butler2017, for all others). The sources are coloured by their angular size, with orange colouring indicating a source is unresolved in the RACS-low2 image. The diagonal dashed line indicates measured and model flux densities are equal. Note that measurement uncertainties are drawn but are smaller than the circular markers. A brightness scale uncertainty is not included.

As noted in Section 3.2.2, some of these sources will have their flux densities slightly underestimated in the images (but not in the catalogue). A full list of sources and the patched flux densities versus their pre-patched values are reported in Appendix A, and care should be taken if measuring them from the images directly.

4.8. Astrometry

RACS data products tend to have astrometric precision of order $1-2^{\prime\prime}$ for most of the sky, though this becomes worse for low-elevation pointings, reducing to $\gtrsim$ $2^{\prime\prime}$ (typically high declination, $\delta_{\text{J2000}} \gtrsim +20^{\circ}$ ; see e.g. Paper V, Paper VI, and Jaini et al. Reference Jaini, Deller, Wang, Lenc and Glowacki2025). For RACS-mid and RACS-high, a declination-dependent correction to the offsets in declination was applied to the catalogues (but not the images). While there is ongoing work to improve the astrometric precision of RACS (and ASKAP data in general) through post-imaging corrections on single image catalogues or individual images (Jaini et al. Reference Jaini, Deller, Wang, Lenc and Glowacki2025, Galvin et al. in preparation), RACS-low2 made use of the standard observing and processing so does not benefit from these efforts.

We initially look at the declination-dependent declination offsets with respect to the Radio Fundamental Catalogue (RFC; Petrov & Kovalev Reference Petrov and Kovalev2025).Footnote ^r We cross-match the 2 121 918 unresolved (Section 4.2) and isolated sources, and show the declination offsets in Figure 12 after removing sources with SNR $\lt 10$ . We see an overall increase in scatter at high declination ( $\gtrsim$ $+20^{\circ}$ ) as well as an additional bulk offset, similar to what was seen in RACS-mid and RACS-high. As with RACS-mid and RACS-high, we fit polynomial model to the offsets following previous work, largely to provide a correction for high declinations. The model is obtained by trialling polynomial orders up to five, with the fitted model chosen from the Akaike Information Criterion (AIC; Akaike Reference Akaike1974). This results in a 4-th order polynomial model (as with Paper VI) with fitted parameters

(1) \begin{align} \Delta\delta & = +(0.15 \pm 0.04) - (29 \pm 21)\times 10^{-3} \delta \nonumber\\[3pt]&\quad - (3.1 \pm 0.4) \times 10^{-4} \delta^2 - (8.3 \pm 1.2) \times 10^{-6} \delta^3 \nonumber\\[3pt] &\quad -(6.5\pm 1.4)\times 10^{-8} \delta^4 \, \text{arcsec} , \\[-10pt] \nonumber \end{align}

The resulting model, and residuals after application, are shown on Figure 12. This does not reduce overall scatter inherent to RACS, but can be used to aid in cross-matching to high-declination data.

Figure 12.

Declination offsets with respect to the RFC, as a function of declination. The blue markers are medians within 5-deg bins, and the solid red line in the top panel is the polynomial fit. The horizontal solid grey line is drawn at an offset of 0, with the dashed grey lines indicating the pixel size. The bottom panel shows the residuals after applying the polynomial model.

Figure 12. Long description

The image contains two scatter plots with polynomial fits and histograms. Panel A: A scatter plot with declination offsets on the vertical axis and declination on the horizontal axis. The vertical axis is labeled with declination offsets in arcseconds, and the horizontal axis is labeled with declination in degrees. Blue markers represent medians within 5-degree bins, and a solid red line represents the polynomial fit. A solid grey line is drawn at an offset of 0, with dashed grey lines indicating the pixel size. Panel B: A scatter plot showing the residuals after applying the polynomial model. The vertical axis is labeled with residuals in arcseconds, and the horizontal axis is labeled with declination in degrees. Blue markers represent medians within 5-degree bins. Both panels include histograms on the right side showing the distribution of the data points.

Figure 13.

Astrometric offsets between the RACS-low2 catalogue and the VLASS-QL catalogue (a), the RFC (b), and RACS-low1 (c), after applying the declination offset correction. The solid grey vertical and horizontal lines are drawn at an offset of zero, and the red box indicates the pixel size of $2.5^{\prime\prime} \times 2.5^{\prime\prime}$ . The dashed red vertical and horizontal lines are drawn at the sample means.

To further check RACS-low2 astrometric accuracy, we cross-match to the VLA Sky Survey (VLASS; Lacy et al. Reference Lacy2020) quick-look catalogue version 2 (VLASS-QL; Gordon et al. Reference Gordon2020, after correction of a known astrometry issue), as well as RACS-low1. Figure 13 shows the cross-match results for isolated and unresolved sources $\gt$ $100\sigma_{\text{rms}}$ for VLASS-QL, the RFC, and RACS-low1. We use the ‘corrected’ declination for the purpose of cross-matching sources within $10^{\prime\prime}$ and show the corrected declination offsets in Figure 13. In general, we see the typical scatter we expect from RACS, with larger scatter in declination due to the increased PSF size in the N-S direction. Table 3 summarises the weighted mean offsets for each survey, both before and after applying declination offset corrections. Overall, we suggest that RACS-low2 retains the $1-2^{\prime\prime}$ astrometric uncertainty of previous RACS epochs, with larger offsets still expected at high declination.

Table 3.

Astrometric offsets of sources cross-matched between the RACS-low2 catalogue and external catalogues, with offsets defined as $\Delta\delta = \delta_{\text{RACS-low2}}-\delta_{\text{survey}}$ and $\Delta\alpha\cos\delta = (\alpha_{\text{RACS-low2}} - \alpha_{\text{survey}})\cos\delta$ for declination and R. A. offsets, respectively.

Table 3. Long description

The table presents weighted mean offsets for different surveys, including the RFC, VLASS-QL, and RACS-low, both before and after applying declination offset corrections. It has 7 rows and 4 columns. The columns are labeled Survey, N sources, Delta alpha cos delta, Delta delta, and Delta delta corr. The rows are grouped into two sections: Full sky and delta J2000 > +0 degrees. Each row lists the survey name, number of sources, and the respective offsets in arcseconds. For the Full sky section: Row 1: RFC, 2749, -0.42 to 0.80, -0.25 to 1.17, -0.05 to 1.12. Row 2: VLASS-QL, 78257, -0.36 to 0.80, -0.31 to 1.10, -0.12 to 1.05. Row 3: RACS-low, 104046, +0.23 to 0.82, -0.42 to 1.00, -0.44 to 1.00. For the delta J2000 > +0 degrees section: Row 1: RFC, 1428, -0.37 to 0.89, -0.42 to 1.40, 0.01 to 1.34. Row 2: VLASS-QL, 43543, -0.21 to 0.88, -0.46 to 1.28, -0.06 to 1.22. Row 3: RACS-low, 36161, +0.40 to 0.97, -0.60 to 1.07, -0.56 to 1.07.

5.1. Leakage

Before counting Stokes V sources, we investigate the residual widefield leakage of Stokes I into Stokes V. We can expect some residual widefield leakage as we have seen this in previous RACS epochs Paper IV and data from the VAST survey using the same PAF footprint and frequency (Pritchard et al. Reference Pritchard, Murphy, Heald, Wheatland, Kaplan, Lenc, O’Brien and Wang2024). Due to the third roll axis of the ASKAP dishes, the parallactic angle is fixed in time during each observation, and sources within the field maintain fixed positions with respect to the primary beam. We therefore do not expect the recovered widefield leakage patterns shown in Figure 15 to vary over a single observation (see Thomson et al. Reference Thomson2023, for further detail on RACS and ASKAP polarimetry). As we only use an unpolarised source for calibration and removal of leakage (PKS B1934 $-$ 638) we are not able to remove on-axis leakage of Stokes Q or U into V with the same process used for Stokes I into V. A maximum of $\approx$ 10% of the Stokes Q/U brightness has been observed to leak into V, though has only been observed for very sbright ( $\gt$ Jy) highly linearl polarised sources (e.g. the Vela pulsar). For modelling the overall leakage, we have only considered Stokes I leakage into V, as we do not produce Stokes U or Q images as part of the standard RACS processing.

Figure 15.

Binned median residual $V/I$ as a function of position across the PAF footprint for Stokes I sources above $500\sigma_{\text{rms}}$ , highlighting the residual widefield leakage pattern. Each panel shows a separate holography grouping (see Table 2). We do not show holography SBID 41055 due to the low number of observations associated with it.

To assess the leakage of Stokes I into V, we initially consider Stokes I sources above $500\sigma_{\text{rms}}$ and look at the fractional circular polarisation reported for these sources in the concatenated catalogue. We also only consider unresolved sources, based on the definition in Section 4.2. First, we show the residual leakage $V/I$ as a function of position on the tile (as in Section 4.5 for the brightness scale), split by the first three holography groups in Figure 15. Each grouping shows the same general widefield leakage pattern, similar to the fairly consistent residual brightness scale error.

We then consider only Stokes I sources above $1\,000\sigma_{\text{rms}}$ and in Figure 16 show the absolute fractional circular polarisation $|V/I|$ as a function of declination and as a function of angular separation from the centre of PAF footprint. As a function of declination, we see regular spikes in the leakage which correspond to the higher leakage seen at the edge of each image (i.e. far from the PAF footprint centre). Despite this and the lack of widefield leakage correction, the image centres feature low residual leakage $\lt$ 1%. While the residual leakage does vary in sign (see Figure 15), in the absence of knowing where exactly the sign changes occur we opt to consider only an absolute leakage threshold for determining real circularly polarised sources. To obtain the residual leakage, we bin $|V/I|$ as a function of angular separation from the footprint centre and take the median $|V/I|$ for each bin. The medians for each bin are shown as red markers in Figure 16. We then set $7 \times \text{median}\left|V/I\right|$ as a threshold above which to consider real emission, linearly interpolating between the binned points. The resultant threshold is shown on the bottom panel of Figure 16. We note that leakage is only considered in the absolute sense, and to properly consider a signed leakage would require position dependence in both l and m (e.g. Pritchard et al. Reference Pritchard, Murphy, Heald, Wheatland, Kaplan, Lenc, O’Brien and Wang2024). The final threshold ranges from $\approx$ $0.4$ –12%

Figure 16.

Residual absolute fractional circular polarisation ( $|V/I$ ) for unresolved Stokes I sources above $1\,000\sigma_{\text{rms}}$ as an estimate of residual Stokes I leakage. Top panel. The fractional circular polarisation as a function of declination. Bottom panel. The same as a function of angular separation from the centre of the PAF footprint. The red circles are the median absolute $|V/I|$ in coordinate bins. The blue line in the bottom panel shows the leakage threshold we use to define search for real circularly polarised sources.

Figure 16. Long description

Two scatter plots depict the residual absolute fractional circular polarisation for unresolved Stokes I sources. Panel A: The scatter plot shows the fractional circular polarisation as a function of declination. The x-axis is labeled with declination in degrees, and the y-axis is labeled with the percentage of fractional circular polarisation. Red circles represent the median absolute values in coordinate bins. Panel B: The scatter plot shows the fractional circular polarisation as a function of angular separation from the centre of the PAF footprint. The x-axis is labeled with angular separation in degrees, and the y-axis is labeled with the percentage of fractional circular polarisation. Red circles represent the median absolute values in coordinate bins. A blue line indicates the leakage threshold used to define the search for real circularly polarised sources.

This residual leakage is overall lower than what was reported for RACS-high (cf. $\approx$ 2% for the image centre, and $\approx$ 6% towards the image edges), despite RACS-high also lacking widefield leakage corrections, though probing brighter Stokes I sources allows for a lower estimate. The results we see here are more in line with RACS-mid, which after widefield leakage correction results in a residual leakage of $\approx$ $0.9$ % for most of the survey. We note, however, that the residual leakage at the image edges for RACS-low2 is more significant than for RACS-mid, which is where the widefield leakage correction becomes important.

5.2. Circularly polarised sources

As most radio sources in the sky do not have significant circularly polarised emission at MHz–GHz frequencies (e.g. Lenc et al. Reference Lenc, Murphy, Lynch, Kaplan and Zhang2018; Callingham et al. Reference Callingham2023) we do not expect many real circularly polarised sources in the RACS-low2 Stokes V images. Most sources with significant Stokes V flux density are likely to be leakage from Stokes I, with the remaining likely to be either stellar systems, pulsars, or (less likely) AGN. We do not expect to see large-scale circularly polarised emission due to the lack of sensitivity on very large angular scales and the low fractional polarisation expected from such emission (Enßlin et al. Reference Enßlin, Hutschenreuter, Vacca and Oppermann2017).

Stellar emission generated by incoherent processes at radio wavelengths is generally too faint to detect in stars more than a few parsec away (e.g. Gary Reference Gary1985; Güdel Reference Güdel2002). Coherent mechanisms, like the electron cyclotron maser or plasma emission, can generate emission with much higher brightness temperatures (e.g. Dulk Reference Dulk1985). The emission from these coherent processes can be highly circularly polarised (up to 100%, e.g. Hallinan et al. Reference Hallinan2007) and provide insights into the stellar magnetosphere, as well as constraints on the magnetoionic properties of the local plasma environment. Pulsars have also been observed with both linear and circularly polarised emission, with reasonably high ( $\gtrsim$ 10%) fractional polarisation (e.g. Sobey et al. Reference Sobey2021; Anumarlapudi et al. Reference Anumarlapudi2023), though pulsar emission mechanisms remain uncertain (e.g. Melrose et al. Reference Melrose, Rafat and Mastrano2021).

In comparison, circular polarisation from AGN is either related to synchrotron processes directly or through conversion of linear polarisation to circular polarisation through Faraday rotation. AGN are expected to show far less than $\approx$ 1% fractional circular polarisation (e.g. Rayner et al. Reference Rayner, Norris and Sault2000; Macquart Reference Macquart2002; Taylor & Legodi Reference Taylor and Legodi2024; Kramer et al. Reference Kramer, Müller, Röder and Ros2025), which has historically fallen below the leakage threshold in previous untargeted circular polarisation surveys (e.g. Pritchard et al. Reference Pritchard2021).

5.2.1. Selection criteria

We refine the catalogue of Stokes V measurements described in Section 3.3 to remove measurements that are likely to be noise, artefacts, or sources of leakage. We begin by selecting sources with significant Stokes V signal, i.e.

(2) \begin{align}|S_{\text{peak},V}|/\sigma_{\text{rms},V}\gt5 \, ,\end{align}

where $S_{\text{peak},V}$ is the peak Stokes V flux density, and sources that have Stokes V emission significantly above the relevant leakage threshold satisfying

(3) \begin{align}\left| \frac{S_{\text{peak,}V}}{S_{\text{peak,}I}} \right| - \sigma_{\text{lower}} \gt 7 \times \text{median}\left(|V/I|\right) \, ,\end{align}

where $\sigma_{\text{lower}}$ is the lower bound of the measurement uncertainty in $|S_{\text{peak,}V} / S_{\text{peak,}I}|$ . Finally, as much circularly polarised emission is expected to be from spatial regions smaller than the RACS-low2 angular resolution, and to lower the likelihood of cataloguing artefacts near bright extended sources, we only consider unresolved Stokes I sources (using the definition from Section 4.2). This yields 221 Stokes V measurements, and we show the distribution of these across the sky on Figure 14, and in Figure 17 as a function of angular separation from the centre of the PAF footprint with the leakage threshold. On Figure 17, we also show the distribution of bright Stokes I sources and those with significant ( $\gt$ $5\sigma_{\text{rms},V}$ ) Stokes V emission to illustrate how the sample of circularly polarised sources is constructed. This sample includes duplicate measurements of the same source, but is unlikely to be a complete list of circularly polarised sources detected in RACS-low2 data as we only consider unresolved Stokes I sources and sources that are detected in the Stokes I images above $5\sigma_{\text{rms},I}$ .

Figure 17.

Fractional circular polarisation of sources as a function of angular separation from the PAF footprint centre, coloured by source type. Open markers indicate probable associations. We also show the distribution of presumably unpolarised bright sources (black circles, as in Figure 16) and sources with Stokes V flux density above $5\sigma_{\text{rms},V}$ (red circles). The leakage threshold is shown as a blue line, as in Figure 16.

For the purpose of assessing the individual circularly polarised sources selected above, we produce small cutouts from the Stokes I and V images, alongside a cutout from the Digitised Sky Survey 2 (DSS2) infrared band, and query the SIMBAD astronomical databaseFootnote ^s (Wenger et al. Reference Wenger2000) for all sources within $8^{\prime}$ .Footnote ^t We then correct the positions of sources with proper motion (PM) measurements to the epoch of our observations, and plot all sources within $5 \times \theta_{\text{M}}$ , where $\theta_{\text{M}}$ is the FWHM of the major axis of the PSF for the given radio image. We consider the RACS-low2 source associated with the astronomical source if it lies within $0.5\times\sqrt{\theta_{\text{M}}\theta_{\text{m}}}$ of the source positions after PM correction. While this varies by source, the average radius is $\approx 7^{\prime\prime}$ (note the astrometric error is of order $1^{\prime\prime}$ – $2^{\prime\prime}$ and the image pixel size is $2.5^{\prime\prime} \times 2.5^{\prime\prime}$ ).

These cutouts with nearby sources overlaid are used for visual inspection to assess (1) the general quality of our selection criteria noted above to avoid leakage sources and to check for residual imaging artefacts, and (2) to assess the automated cross-matching to sources in the SIMBAD database. We manually inspect all cross-matches for validity, and with extra considerations for each source type discussed in the following sections. We show examples of these sources in Figure 19 (specifically radio stars) and Figure 20. In total, we identify 67 Stokes V measurements to be associated with stars, 105 to (likely) be associated with pulsars, and 48 to (likely) be associated with AGN. One final source is not associated with any known object and not likely to be an AGN. This unassociated source was recently found with VASTER, the short-timescale imaging and transient detection pipeline using ASKAP data (Wang et al., submitted), and a detailed follow-up will be presented in future work (Wang et al. in preparation).

Figure 18.

Fractional circular polarisation of sources as a function of Stokes I flux density, coloured by source type. Open markers reflect probable associations (mostly AGN – see Section 5.2.5). The solid and dotted horizontal lines indicate the minimum and maximum leakage thresholds, respectively. Only unresolved sources with $S_V \gt 5\sigma_{\text{rms},V}$ are shown. The dashed line drawn at $5\sigma_{\text{rms},V}/S_I$ assumes a median Stokes V rms noise from the catalogue of $\sigma_{\text{rms},V} = 163$ $\unicode{x03BC}$ Jy PSF $^{-1}$ .

Figure 18. Long description

A scatter plot representing the relationship between Stokes I flux density and fractional circular polarisation of sources, categorized by source type. The horizontal axis represents the Stokes I flux density in millijanskys, and the vertical axis represents the fractional circular polarisation in percent. The plot includes several data points, each marked with different symbols representing stars, pulsars, active galactic nuclei (AGN), unclassified sources, and leakage or artefacts. The solid and dotted horizontal lines indicate the minimum and maximum leakage thresholds, respectively. The dashed line represents a median Stokes V rms noise level. The data points show a trend where the fractional circular polarisation generally decreases as the Stokes I flux density increases. The plot also includes a legend explaining the symbols used for different source types.

Figure 19.

Example cutouts used for visual inspection of the circularly polarised sources, showcasing three example radio stars: BD $+$ 44 2051 (a), ^* bet Aql (b), and UV Ceti (c). Left panels: Stokes V image; centre panels: Stokes I image; right panels: DSS2 infrared image. On each panel, the dashed circle is drawn at $5\times\theta_{\text{M}}$ , and the crosshairs point to the RACS-low2 Stokes I source position. Markers shown on the centre and right panels are sources within the dashed circle from SIMBAD (after proper motion correction, where relevant) with the sources ordered in the legend by angular separation from the source – the source names in the legend also include the object type as reported in SIMBAD, and the yellow star symbol is generally the closest source. Source names in bold font are within $0.5\times\sqrt{\theta_{\text{M}}\theta_{\text{m}}}$ of the radio position. The ellipses in the bottom left corner of the Stokes V and Stokes I images show the PSF size.

The details of the columns included in the reduced Stokes V catalogue of 221 are shown in Table B3 in Appendix B, including host identification and Stokes V measurement information.

Figure 20.

Example cutouts used for visual inspection of the circularly polarised sources, showing the pulsars PSR B1929 $+$ 10 (a) and PSR B1929 $+$ 10 (b), and the AGN ATPMN J075651.9 $-$ 634918 (c). The other details are the same as in Figure 19.

Figure 20. Long description

Panel A: Three heatmap-style images show the pulsar PSR B192910. Each panel includes a color scale indicating Stokes V in millijansky per beam squared, with specific values and leakage percentages noted. The axes are labeled with right ascension and declination coordinates. Panel B: Three similar heatmap-style images display the pulsar PSR B192910, with the same color scale and axis labels as Panel A. Panel C: Three heatmap-style images present the AGN ATPMN J075651.9634918, following the same format as the previous panels.

5.2.5. AGN and galaxies

In addition to the original SIMBAD database search, we also query the NASA/IPAC Extragalactic DatabaseFootnote ^x using the same search radius, and consider any source with a match to an AGN, galaxy, absorptions line system, or quasar classification or if it has an extragalactic redshift to be an AGN.

We also cross-matched the Stokes V sources to the All WISE Footnote ^y catalogue (Cutri et al. Reference Cutri2021) using the same cross-matching radius used for other catalogues/databases. After cross-matching, we take WISE magnitudes in the 3.4, 4.6, and 12 $\unicode{x03BC}$ m bands above signal-to-noise ratios of 2 and plot them on the standard three-band WISE colour-colour plot (e.g. Jarrett et al. Reference Jarrett2011; Jarrett et al. Reference Jarrett2017) in Figure 21. We also show the empirically-derived AGN region from Jarrett et al. (Reference Jarrett2011), highlighting the approximate expected location of AGN on the colour-colour plot. We do not show the pulsar cross-matches as the WISE source is unlikely to be associated with the pulsar. We note that some of the stars may not be correctly cross-matched to WISE sources resulting in some spurious WISE colours in Figure 21. The sources not specifically classified as AGN or stars have similar WISE colours to the AGN sample, and lie within or near the empirical AGN region, making them likely to be AGN. We consider any sources that are coincident with a previously-detected radio source (but not confirmed as an AGN or similar source in NED or the SIMBAD database) to likely be AGN as well.

Figure 21.

WISE colour-colour plot showing the star and AGN associations in the RACS-low2 circular polarisation catalogue. The open markers for some AGN associations are for ‘probable’ AGN. The dashed region is the empirically-derived location of AGN (Jarrett et al. Reference Jarrett2011).

Finally, some AGN are recorded with spuriously-high fractional polarisation (i.e. much greater than the leakage threshold). In these cases, the Stokes I and V measurements are close to the detection thresholds and the Stokes V measurement is likely to be artificially increased due to noise. As the Stokes V measurement is an absolute peak within a box surrounding the Stokes I position, it is sensitive to noise peaks if there is no actual source present. These cases are classified as ‘AGN’/‘AGN?’ since the sources are still associated with AGN even if the Stokes V measurement is likely to be incorrect. These sources can be seen clearly in Figures 17 and 18 occupying the same regions as stars and pulsars.

In total, we find 43 unique AGN, with 48 total measurements, with 27 of the measurements having a positive fractional polarisation. It is likely most of the AGN detections that are not spurious noise detections are the result of leakage. We show an example BL Lac, ATPMN J075651.9-634918 (RACS-LOW2 J075651.8 $-$ 634917), in Figure 20(c). We note that AGN with detected circular polarisation typically have flat spectra (e.g. Rayner et al. Reference Rayner, Norris and Sault2000; Taylor & Legodi Reference Taylor and Legodi2024; Callingham et al. Reference Callingham2023), so to further investigate our sample we cross-matched the AGN to the RACS-mid catalogue, obtaining spectral indices between 887.5 and 1 367.5 MHz. The median spectral index for our sample is $\alpha_{887}^{1\,367} = -0.11 \pm 0.67$ , showing a sample of flat-spectrum sources are present. While the large range is inconclusive, it is consistent with there being real circularly polarised AGN in our sample. The leakage threshold derived from bright Stokes I sources as a function of angular separation from the image centres may not adequately capture all aspects of the actual leakage in our data. While we have not taken signed leakage into account (see e.g. Figure 15), the absolute leakage model should capture an upper limit to the leakage of Stokes I into V. As previously noted, we have not assessed leakage of Stokes Q/U into V. While a specific set of SBIDs from RACS-mid were found to have higher leakage than other SBIDs (see Section 2.4.3 in Paper V), we cannot identify other observation-, time-, or position-dependence to the measured $|V/I|$ for bright sources that allows us to further refine the leakage model for the full field images.