2.1. Radio data

2.2. Mid-infrared data: AllWISE catalogue and images

The Wide-field Infrared Survey Explorer (WISE; Wright et al. Reference Wright2010) has imaged the entire sky in the mid-infrared, at 3.4, 4.6, 12, and 22 $\,\mu$ m. These observing bands are referred to as W1, W2, W3, and W4 and correspond to resolutions of 6.1, 6.4, 6.5, and 12.0 arcsec, respectively. We use the AllWISE data release (Cutri et al. Reference Cutri2013), which involved combining data from the cryogenic and post-cryogenic phases of the survey. The result is improved sensitivity (0.054, 0.071, 0.73, and 5.0 mJy, respectively, at 5 $\,\sigma$ ) and astrometric accuracy ( $\ll$ 1 arcsec) with respect to the WISE All-Sky data release (Cutri et al. Reference Cutri2012).

2.3. Optical data: The 6dFGS catalogue

The 6-degree Field Galaxy Survey (6dFGS; Jones et al. Reference Jones2004) used the UK Schmidt Telescope (UKST; Tritton Reference Tritton1978) to obtain optical spectroscopy over the southern hemisphere (Dec. $<0^{\circ}$ , $|b| >10^{\circ}$ ). We use the final data release (DR3; Jones et al. Reference Jones2009), which presents redshifts for all southern sources brighter than $K=12.65$ in the 2MASS (Two Micron All Sky Survey) Extended Source Catalogue (XSC; Jarrett et al. Reference Jarrett, Chester, Cutri, Schneider, Skrutskie and Huchra2000). The resulting median redshift is 0.053.

3.1. Masked sources and the Orion Nebula

For readers unfamiliar with the GLEAM Survey, we clarify that the very brightest sources at Dec. $< 30^{\circ}$ and $|b| >10^{\circ}$ (belonging to a group of radio sources colloquially referred to as the ‘A-team’) are masked for the GLEAM EGC, and so do not appear in the G4Jy Sample. The sources in question are listed in Table 1 and, due to the difficulty in calibrating and imaging them at low frequencies, will be presented in a separate paper (White et al., in preparation). Also masked for the EGC are the Large and Small Magellanic Clouds, for which multi-frequency, integrated flux densities (e.g. $S_{\textrm{150\,MHz}} = 1450\,\text{Jy}$ and $S_{\textrm{150\,MHz}} = 258\,\text{Jy}$ , respectively) are presented by For et al. (Reference For2018). Details of the masked regions are provided in table 3 of Hurley-Walker et al. (Reference Hurley-Walker2017), with $<474\,\text{deg}^2$ of sky coverage being flagged due to the aforementioned sources.

In addition, Table 1 includes the Orion Nebula (or ‘Orion A’). Although its 151-MHz flux density is well above the 4-Jy threshold (Appendix A), it was excluded by Aegean source fitting during the creation of the GLEAM catalogue. This happens when an object’s integrated flux density is more than 10 times its peak flux density, in which case the object is considered to be highly resolved, and so is removed from the catalogue. This criterion is specified because Aegean is optimised for fitting point sources and so would not provide reliable measurements for diffuse radio emission.

Table 1. A list of the brightest sources in the southern sky (Dec. $< 30^{\circ}$ , $|b| >10^{\circ}$ ) that currently do not appear in the G4Jy Sample. Below, we use ‘Cen A’ as shorthand for ‘Centaurus A’. The flux densities ( $S_{\textrm{151\,MHz}}$ ) and spectral indices ( $\alpha$ ) shown are approximate values (Hurley-Walker et al. Reference Hurley-Walker2017), based on measurements (spanning 60–1400 MHz) from the NASA/IPAC Extragalactic Database (NED)Footnote e. The exception is for ^*Orion A (the Orion Nebula), where these values are determined via the method described in Appendix A. Note that its spectral index is valid only very locally at 151 MHz, due to the high degree of spectral curvature.

Figure 1. An overlay, centred at R.A. = 13:36:39, $\text{Dec.} = -33:57:57$ (J2000), for an extended radio galaxy in the G4Jy Sample (G4Jy 1080, also known as IC 4296, at $z=0.012$ ). Radio contours from TGSS (150 MHz; yellow), GLEAM (170–231 MHz; red), and NVSS (1.4 GHz; blue) are overlaid on a mid-infrared image from AllWISE ( $3.4\,\mu$ m; inverted greyscale). For each set of contours, the lowest contour is at the 3 $\,\sigma$ level (where $\sigma$ is the local rms), with the number of $\,\sigma$ doubling with each subsequent contour (i.e. 3, 6, 12 $\,\sigma$ , etc.). Also plotted, in the bottom left-hand corner, are ellipses to indicate the beam sizes for TGSS (yellow with ‘+’ hatching), GLEAM (red with ‘/’ hatching), and NVSS (blue with ‘\’ hatching). This source is an unusual example, in that its GLEAM-component positions (red squares) needed to be refitted using Aegean (Hancock et al. Reference Hancock, Murphy, Gaensler, Hopkins and Curran2012; Reference Hancock, Trott and Hurley-Walker2018)—see Appendix D.1. Also plotted are catalogue positions from TGSS (yellow diamonds) and NVSS (blue crosses). The brightness-weighted centroid position, calculated using the NVSS components, is indicated by a purple hexagon. The cyan square represents an AT20G detection, marking the core of the radio galaxy. Magenta diamonds represent optical positions for sources in 6dFGS, and so we see above that G4Jy 1080 is not in this survey.

5.1. Creating the overlays

We use the APLpy Python module (Robitaille & Bressert Reference Robitaille and Bressert2012) to overlay radio contours from GLEAM, TGSS, and NVSS (or SUMSS, for Dec. $<-39.5^{\circ}$ ) onto mid-infrared (W1) images from WISE (e.g. Figure 1). GLEAM images are obtained via the online GLEAM Postage Stamp Service,Footnote f whilst TGSS, NVSS, SUMSS, and WISE images are downloaded from the SkyView Virtual Observatory.Footnote g For all images, orthographic (i.e. sine) projection is used, with GLEAM images having a pixel scale of $28\,\text{arcsec\,pixel}^{-1}$ . WISE images are at $1.375\,\text{arcsec\,pixel}^{-1}$ , TGSS images are downloaded at $5\,\text{arcsec\,pixel}^{-1}$ , and a scale of $10\,\text{arcsec\,pixel}^{-1}$ is set for the NVSS and SUMSS images. For each set of radio contours, the lowest contour level that we plot is 3 $\,\sigma$ (where $\sigma$ is the local rms).

The reason behind using mid-infrared images as the greyscale ‘base’ for our overlays is that this allows us to identify even the most dust-obscured host galaxies. This would not be possible if optical images were used instead. Furthermore, mid-infrared emission includes contributions from evolved stellar populations and avoids the bias of optical surveys towards actively star-forming galaxies. Of the four possible WISE bands, W1 is chosen for the imaging as this offers the best sensitivity and resolution.

Originally, our overlays were chosen to be 20 arcmin across, but first inspection of the sample revealed that a number of sources extended far beyond this size. Following a few iterations, we decided to create two sets of overlays: one set consisting of images $1^{\circ}\ \text{across}$ (in order to encompass all of the relevant emission for the largest sources, and so more accurately classify the morphology—Section 5.2) and another set using images 10 arcmin across (acting as ‘close-ups’ for identifying the likely host galaxy—Section 5.5). For the $1^{\circ}$ overlays, the GLEAM component’s R.A. and Dec. specifies the centre of the image. As for the 10 arcmin overlays, these are centred on the brightness-weighted centroid positions described in Section 4.

A problem faced when downloading images that are $1^{\circ}$ across is that this size increases the likelihood of running into artefacts associated with poor image processing, or the source being too close to the edge of a mosaic/tile (resulting in a truncated image). Such was the case for the NVSS images of three components: GLEAM J045610 $-$ 215922, GLEAM J122039 $-$ 374017, and GLEAM J154030 $-$ 051436. This was remedied by obtaining multiple images from the NVSS Postage Stamp Server,Footnote h offset in R.A. and Dec., and stitching them together using SWarp (Bertin et al. Reference Bertin, Mellier, Radovich, Missonnier, Didelon, Morin, Bohlender, Durand and Handley2002).

In addition to overlaying radio contours on the mid-infrared images, we plot positions from the GLEAM, TGSS, NVSS/SUMSS, AT20G, and 6dFGS catalogues. Although AT20G is incomplete, detections from this survey indicate the presence of AGN cores, or hotspots in the radio lobes (Massardi et al. Reference Massardi2011). Meanwhile, 6dFGS positions help to identify host galaxies that are nearby/bright enough to have a spectrum from this all-sky—albeit shallow—optical survey. We also mark the centroid positions, described in the previous section, and use the errors in this position ( $\sigma_{\alpha}$ and $\sigma_{\delta}$ ) to draw an error ellipse. However, in most overlays, this ellipse is so small that it appears as a dot. Each of these datasets features in the overlay presented in Figure 1.

Both sets of overlays ( $1^{\circ}$ and 10 arcmin across), and the images from which they are made, are available online.Footnote i As the overlays are created per GLEAM component, radio sources that are multi-component will appear multiple times.

5.2. Morphological classification

As part of visually inspecting the GLEAM components, we provide a classification based on the morphology of the source in NVSS/SUMSS (and/or TGSS, where available). This classification is one of the following four categories:

• ‘single’—the source has a simple (typically compact) morphology in TGSS and NVSS/SUMSS;

• ‘double’—the source has two lobes evident in TGSS or NVSS/SUMSS, but there is no distinct detection of a core; or it has an elongated structure that is suggestive of lobes, but is accompanied by a single, catalogued detection;

• ‘triple’—the source has two lobes evident in TGSS or NVSS/SUMSS, and there is a distinct detection of a core in the same survey;

• ‘complex’—the source has a complicated morphology that does not clearly belong to any of the above categories.

When determining the morphology, we take into account extra information provided by the underlying distribution of mid-infrared sources (i.e. potential host galaxies) and the positions of AT20G detections. This helps to resolve ambiguities, particularly in cases where (for example) two nearby NVSS detections may be interpreted as either a ‘double’ radio source or two unrelated sources. For a ‘double’, we expect the host galaxy to lie about half-way between the two NVSS components, as indicated by a mid-infrared source at the centroid position. If instead there is mid-infrared emission coincident with one (or both) of the radio components, then they are likely to be unrelated. However, it can still be difficult to distinguish between a source with two radio lobes and two unrelated radio sources that are close to one another. In these situations, we consult notes by Jones & McAdam (Reference Jones and McAdam1992) on the observed structure of southern, extragalactic sources and also consider the criterion defined by Magliocchetti et al. (Reference Magliocchetti, Maddox, Lahav and Wall1998). This is where two radio components are likely to be associated if their flux densities are within a factor 4 of each other.

In addition to the morphology, for each G4Jy source, we record the following:

1. i. The number of NVSS/SUMSS detections associated with the radio source. The integrated flux densities for these detections are summed together to determine the total radio emission at $\sim1\,\text{GHz}$ .

2. ii. The number of GLEAM components associated with the radio source. The integrated flux densities for these components are then summed together to determine the total radio emission, in each of GLEAM’s 20 sub-bands.

3. iii. Whether multiple sources (as judged visuallyFootnote j) contribute to the GLEAM component(s) under inspection. This acts as a ‘confusion flag’, indicating cases where the MWA beam has blended unrelated sources together.

Regarding (i), we check whether these detections match those used for the calculation of the centroid position (Section 4). In cases where there is disagreement, the centroid positions are recalculated following manual intervention. We refer to this as ‘recentroiding’ and direct the reader to Section 5.4 for further details. As for the confusion flag (iii), our criteria are that (1) unrelated sources are detected above 6 $\,\sigma$ in NVSS/SUMSS and (2) the positions of the unrelated sources’ peak emission (at $\sim1\text{GHz}$ ) are within the 3- $\sigma$ GLEAM contour for the G4Jy source.

We emphasise that steps (i) and (ii) above are especially important for extended sources (typically larger than 3 arcmin across), as otherwise their total radio emission may be severely underestimated. Meanwhile, step (iii) highlights cases where multiple sources contribute towards a particular detection in GLEAM. Since we are typically interested in only one of these contributing sources, the measured GLEAM flux densities will overestimate the low-frequency radio emission, and therefore must be treated with caution. In light of this, we exploit the better resolution of TGSS to judge whether the GLEAM detection crosses the $S_{\textrm{151\,MHz}}>4\,\text{Jy}$ threshold as a consequence of confusion. However, we do not rely solely on the TGSS flux densities for this assessment, as Hurley-Walker (Reference Hurley-Walker2017) found there to be significant variation in the flux density scale over the TGSS survey area. Hence, we consider what fraction that each blended source contributes to the total emission (corresponding to the GLEAM component) at 150 MHz. If none of the blended sources has a TGSS (150 MHz) integrated flux density that corresponds to $S_{\textrm{151\,MHz}}>4\,\text{Jy}$ , we remove the $S_{\textrm{151\,MHz}}>4\,\text{Jy}$ detection from the GLEAM-component list. Hence, the removal of the following components: GLEAM J093918+015948, GLEAM J101051 $-$ 020137, GLEAM J201707 $-$ 310305, GLEAM J202336 $-$ 191144, and GLEAM J222751 $-$ 303344 (Appendix B).

Meanwhile, the identification of extended low-frequency emission results in 84 components being added to the GLEAM component list by association. These are GLEAM components that individually have $S_{\textrm{151\,MHz}}<4\,\text{Jy}$ but where visual inspection indicates that the emission should be combined with one or more other components for a particular radio source (resulting in a summed $S_{\textrm{151\,MHz}}$ that is $>4\,\text{Jy}$ ; see also Section 7). We create individual overlays for these new components and inspect them in the same way to ensure consistency. For a list of all the sources that are multi-component in GLEAM, see Table C1 in Appendix C. The overlays for these sources are shown in Figures 1, 3–9, Appendices C and D.3, and Paper II (Figures 3–4, 6, 8, 12, 16–17, 19, 21, 23).

Figure 2. Examples of sources that have TGSS artefacts (Section 5.2.1), with contours, symbols, and beams as described for Figure 1. In addition, AllWISE positions (green plus signs) within 3 arcmin of the centroid position (purple hexagon) are plotted, with the host galaxy highlighted in white. (a) G4Jy 679. (b) G4Jy 938. (c) G4Jy 1005. (d) G4Jy 1085. (e) G4Jy 1209. (f) G4Jy 1239.

Table 2. 63 G4Jy sources identified as most likely having artefacts in the TGSS catalogue (Section 5.2.1).

5.3. Refitting with Aegean

Also connected to our visual inspection, we identify radio sources that require refitting using Aegean. This may be due to source fitting not taking into account all of the relevant emission, or the original GLEAM components appearing to have inappropriate positions (given the morphology of the radio emission). Full details regarding such sources are provided in Appendix D, where we also explain how we correct for the refitting process either under- or overestimating the integrated flux densities.

We describe the refitting as ‘unconstrained’ when it corresponds to Aegean being rerun, in its usual mode for source fitting and characterisation, over a larger region of the sky than previously. A ‘refitted flag’ of ‘1’ is used in the G4Jy catalogue to denote GLEAM components that have been refitted this way. For one source, the refitting is unconstrained but requires additional work. We use a refitting flag of ‘2’ for this scenario. In the case of ‘priorised refitting’, we constrain Aegean to use pre-determined positions for the GLEAM components. The components resulting from this type of refitting are assigned a refitting flag of ‘3’. The total number of G4Jy sources that required refitting is eight, corresponding to 15 GLEAM components. The remaining 1,945 GLEAM components, that are not refitted, retain the default flag of ‘0’.

However, we caution that Aegean may still struggle to characterise the flux density for particularly extended radio sources. This is because—like the source-fitting program, vsad (Condon et al. Reference Condon, Cotton, Greisen, Yin, Perley, Taylor and Broderick1998), used for both the NVSS and SUMSS catalogues—it fits radio components using elliptical Gaussians, and so is optimised for point sources.

Figure 3. (a) An overlay for the source G4Jy 1173 that is centred on the component GLEAM J142955+072134. (b) An overlay for the source G4Jy 1282, centred on the component GLEAM J155147+200424. Radio contours from TGSS (150 MHz; yellow), GLEAM (170–231 MHz; red), and NVSS (1.4 GHz; blue) are overlaid on a mid-infrared image from WISE (3.4 $\mu$ m; inverted greyscale). For each set of contours, the lowest contour is at the 3 $\,\sigma$ level (where $\sigma$ is the local rms), with the number of $\sigma$ doubling with each subsequent contour (i.e. 3, 6, 12 $\,\sigma$ , etc.). As discussed in Section 5.4, manual recentroiding was required for both sources shown here, due to their complex morphology. Updated centroid positions (Section 5.4) are indicated by purple hexagons and also plotted are catalogue positions from TGSS (yellow diamonds), GLEAM (red squares), and NVSS (blue crosses).

5.4. Recentroiding after manual intervention

Following visual inspection, we find that a total of 54 sources require their brightness-weighted centroid position (Section 4) to be corrected. In the majority of cases, the error was due to incorrect association of unrelated sources, and so we specify exactly which NVSS/SUMSS components should be used when recalculating the centroid position (and integrated flux density at $\sim1\,\text{GHz}$ ). Such manual intervention is also needed for extended sources with well-separated NVSS/SUMSS components, as illustrated by G4Jy 1080 in Figure 1. (Recentroiding would usually be unnecessary for sources that are multi-component in GLEAM but have their NVSS/SUMSS components enveloped by a single 3- $\sigma$ NVSS/SUMSS contour.) The G4Jy sources, with centroids updated for these two reasons, are assigned a ‘centroid flag’ of ‘1’.

In addition, we note G4Jy Sources with non-axisymmetric, or very-extended, emission. Regarding the former, their morphology may be indicative of radio jets interacting with an inhomogeneous environment. Alternatively, the morphology could be the result of the galaxy’s radio jets being ‘bent backwards’ as it falls into a cluster (see Paper II). In these cases (e.g. Figure 3a), we use only the NVSS/SUMSS components that are closest to the core of the radio galaxy, as the centroid would otherwise be influenced by the geometry of the outermost regions. For extended ‘doubles’ showing evidence of multiple knots of radio emission, we also use only the innermost NVSS/SUMSS components when recalculating the centroid position. To reflect these two cases, we specify ‘2’ as the centroid flag. This is applicable for seven sources, with the updated centroid position acting as a better guide for identifying the host galaxy, as described in the next section.

Another example of association, leading to recentroiding, involves the intriguing morphology of GLEAM J155147+200424 and GLEAM J155226+200556. Both of these components have $S_{\textrm{151\,MHz}}>4\,\text{Jy}$ , and the larger overlays created for them suggest that they are part of a single object (G4Jy 1282; Figure 3b). Indeed, this source appears as 3C 326 in the 3CRR sample (Laing et al. Reference Laing, Riley and Longair1983) and has been classified as an ‘FR II’ radio galaxy. (Such a classification is used for ‘edge-brightened’ radio galaxies, where the brightest radio emission is located in the lobes, far from the AGN (Fanaroff & Riley Reference Fanaroff and Riley1974). Other sources, where the radio luminosity decreases with distance from the AGN, are labelled ‘FR I’.) Based on this morphological interpretation, the component GLEAM J155120+200312 is added to the G4Jy Sample by association. Consequently, the NVSS components for G4Jy 1282 are redetermined manually and used for the updated centroid position.

Although Mauch et al. (Reference Mauch, Murphy, Buttery, Curran, Hunstead, Piestrzynski, Robertson and Sadler2003) invested effort into removing image artefacts from the SUMSS catalogue, we note that some still remain amongst the cutouts for the G4Jy Sample. As a result, erroneous components were being used in the centroid calculation for some sources. We rectify this by updating the centroid position, using only reliable SUMSS components (as identified via visual inspection). The affected sources are also given a centroid flag of ‘1’. The remaining 1 802 sources, which did not have their centroid position updated for any reason, retain the default centroid flag of ‘0’.

5.5. Identifying the likely host galaxy

Through topcat software (Taylor Reference Taylor, Systems, Shopbell, Britton and Ebert2005), we obtain a subset of the AllWISE catalogue, where all objects are within 3 arcmin of a centroid position belonging to the G4Jy Sample (this radius being the maximum value allowed by the ‘CDS Upload X-Match’ facility of topcat). We add these AllWISE positions (green plus signs, ‘+’) to the overlays that are 10 arcmin across and initially use a white ‘+’ to highlight the AllWISE source that is closest to the centroid position (at the centre of the overlay). We then inspect these overlays to determine whether the highlighted mid-infrared source is the likely host galaxy for the G4Jy source in question. In doing so, we also consider the errors in the centroid position (represented by an ellipse), having noted that the errors in the AllWISE positions are negligible by comparison. For 1 388 (i.e. 75%) of the 1 863 G4Jy sources, we find that the appropriate mid-infrared source has been highlighted (e.g. see Figures 2a–d, f, and 4a).

Conversely, 475 G4Jy sources require additional attention. For these radio sources, the nearest AllWISE source does not appear to be the host galaxy for the radio emission (or there is ambiguity), and so they are set aside for reinspection. This is done via interactive Multi-Catalogue Visual Cross-Matching (MCVCM) softwareFootnote l (Swan et al., in preparation), which allows us to manually select the most likely host galaxy. The corresponding 10 arcmin overlay is then updated, so that the white ‘+’ highlights this selected source (e.g. see Figures 2e and 4b–f). The result, across the 10 arcmin overlays for the full sample, is that this symbol indicates the AllWISE host galaxy identification for the G4Jy source.

Having inspected each G4Jy source, we assign a ‘host flag’ that corresponds to one of the following four categories:

• ‘i’—a host galaxy has been identified in the AllWISE catalogue, with the position and mid-infrared magnitudes (W1, W2, W3, W4) recorded as part of the G4Jy catalogue (Section 6),

• ‘u’—it is unclear which AllWISE source is the most likely host galaxy, due to the complexity of the radio morphology and/or the spatial distribution of mid-infrared sources (leading to ambiguity),

• ‘m’—identification of the host galaxy is limited by the mid-infrared data, with the relevant source either being too faint to be detected in AllWISE or affected by bright mid-infrared emission nearby,

• ‘n’—no AllWISE source should be specified, given the type of radio emission involved.

Manual identification of the host galaxy was usually required for the multi-component radio sources, where the geometry of the NVSS/SUMSS radio emission meant that the centroid position was more subject to error. In 37% of such cases, the G4Jy source had a ‘core’ indicated by a detection in 6dFGS and/or AT20G. G4Jy sources with a host galaxy in 6dFGS are noted for later analysis (Franzen et al., in preparation; White et al., in preparation), whilst those with AT20G information are explored further in a separate paper on broadband radio spectra (White et al., in preparation).

As mentioned previously, differing spatial scales of radio emission, and the fact that a single source may have multiple radio components, makes it particularly difficult to cross-match radio catalogues with data at other wavelengths (where sources typically have a singular morphology). This is complicated further by the greater density of sources seen at shorter wavelengths, leading to ambiguity when trying to identify the corresponding galaxy. Therefore, even after careful reinspection and investigation, we cannot always determine which mid-infrared source is the ‘correct’ host—hence our use of the ‘u’ flag for 129 G4Jy sources.

In some cases, we find that the radio position is robust—as suggested by the coincidence of detections from multiple radio surveys—but the likely host galaxy is too faint in the mid-infrared to appear in the AllWISE catalogue. This could be due to the radio source being at very high redshift, with confirmation of this requiring follow-up observations, such as optical/near-infrared spectroscopy (as discussed further in Section 4.10 of Paper II). For these situations (i.e. 126 G4Jy sources), we use the ‘m’ flag. However, the reader should note that this label is also used for G4Jy sources that have a bright mid-infrared host that is absent from the AllWISE catalogue, due to its photometry being affected by (for example) source confusion or a diffraction spike from a nearby star.

Our final host galaxy flag, ‘n’, is used for 2 G4Jy sources for which it is inappropriate to select a single AllWISE source, as there is no ‘host galaxy’ to identify. Such is the case for extended radio emission associated with a nebula and a cluster relic (both of which are presented in Paper II).

6.1. Naming of the G4Jy sources

Having identified which GLEAM components are associated with each other (Section 5) and which additional GLEAM components are to be included in the G4Jy Sample (Section 7), we sort the catalogue in order of increasing R.A. The ‘ncmp_GLEAM’ column is added to indicate the number of GLEAM components that correspond to each source. We then use simple numbering as our naming scheme: ‘G4Jy 1’, ‘G4Jy 2’, ‘G4Jy 3’, etc. This both allows a short-hand way of referring to sources and avoids ‘hard-coding’ a coordinate position that may later be refined. Similarly, we use ‘A’, ‘B’, ‘C’, etc. to label individual GLEAM components belonging to multi-component sources. For example, GLEAM J000456+124810 is the eastern radio lobe of G4Jy 7 and can be referred to as ‘G4Jy 7B’.

6.2. Morphology

The morphology of the source (Section 5.2) is determined through visual inspection and is based on NVSS/SUMSS contours, or TGSS contours where coverage allows. Although literature checks uncover radio images of higher resolution for some sources (see Paper II for details), we do not change the morphology label as we wish these to be consistent across the entire sample. Furthermore, we note that some ‘doubles’ may actually be ‘core-jet’ sources (e.g. Kellermann & Pauliny-Toth Reference Kellermann and Pauliny-Toth1981; Pearson & Readhead Reference Pearson and Readhead1988), where the radio jet emission is one-sided. However, we do not have sufficient resolution to confirm these, and so we apply Occam’s razor and leave the morphology label as ‘double’. We expect many of these morphology labels—the ‘singles’ especially—to be updated as better-resolution ( $<25$ –45 arcsec) radio images come to light.

6.3. Information at $\sim\textit{1}\,\text{GHz}$

The ‘Freq’ column indicates whether NVSS (1400 MHz) or SUMSS (843 MHz) has been considered for the source in question. Alongside this, we provide the number of associated NVSS/ SUMSS components (‘ncmp_NVSSorSUMSS’), the summed flux density across these components (‘S_NVSSorSUMSS’), and the brightness-weighted centroid position (‘centroid_RAJ2000’, ‘centroid_DEJ2000’) based on these components. The ‘centroid flag’ column indicates whether the centroid position is from the original, automated calculation (centroid_flag = ‘0’; see Section 4), or has been updated following manual intervention (centroid_flag = ‘1’ or ‘2’; see Section 5.4). The ‘confusion flag’ is based upon visual inspection (Section 5.2), with G4Jy sources potentially having their GLEAM flux densities affected by unrelated radio sources (confusion_flag = ‘1’; e.g. G4Jy 935 in Figure 4d) or not (confusion_flag = ‘0’; e.g. G4Jy 1628 in Figure 4f).

6.4. Mid-infrared data for the host galaxies

Alongside our visual inspection (Section 5) and extensive checks against the literature (Sections 4 and 5 of Paper II), we use the ‘host_flag’ to indicate whether or not we are able to identify the host galaxy of the radio emission in the mid-infrared (Section 5.5). For G4Jy sources that are identified (host_flag = ‘i’), we provide the AllWISE name, position, and mid-infrared magnitudes (and errors) from the AllWISE catalogue. This information is being used for collating additional multi-wavelength data for the G4Jy sample and subsequent analysis (White et al., in preparation).

6.5. Total integrated GLEAM flux densities

For each of the 20 sub-band measurements provided by the GLEAM Survey, we calculate the total, integrated flux density, summed over all of the GLEAM components associated with a particular G4Jy source. The errors in these total flux densities are determined by adding in quadrature (per sub-band) the integrated flux density errors for the individual GLEAM components. If the G4Jy source is single component in GLEAM, these ‘total’ columns are simply a repeat of the integrated flux densities (and errors) for that single GLEAM component. Note that it is the total, integrated flux density at 151 MHz (‘total_int_flux_151’) that must exceed 4 Jy for a radio source to be listed in the G4Jy Sample.

Furthermore, we remind the reader that some of the individual, integrated flux densities provided in the G4Jy catalogue do not appear in the EGC. They are instead the result of refitting (and rescaling, in some cases), as described in Section 5.3 and Appendix D. We use the ‘refitted_flag’ to indicate for which GLEAM components this applies.

6.6. Four sets of spectral indices

For the majority of GLEAM components in the G4Jy Sample, the spectral index fitted over the GLEAM band (‘GLEAM_alpha’) is inherited from the EGC. In the time since the publication of Hurley-Walker et al. (Reference Hurley-Walker2017), we noticed that the spectral index errors quoted in the parent catalogue were overestimated by a factor of 5. This has been corrected in a new version of the EGC (v2), available online through VizieRFootnote o. We also include the updated error and reduced- $\chi^2$ columns in the G4Jy catalogue, renaming them ‘err_GLEAM_alpha’ and ‘reduced_chi2_GLEAM_alpha’, respectively.

GLEAM components that were refitted for the G4Jy catalogue (refitted_flag $>0$ ) have a newly calculated GLEAM_alpha value. For this, we fit a power-law spectrum to the integrated flux densities for multiple sub-bands, in the same way as done for GLEAM components in the EGC. Hence, we also determine consistent errors and reduced- $\chi^2$ values.

Table 3. The mean and median spectral index, $\alpha$ , for each of the four sets of spectral indices provided in the G4Jy catalogue (Section 6.6). ‘Number’ refers to the number of G4Jy sources for which the statistics apply, except in the case of GLEAM_alpha, where it is the number of GLEAM components.

Since we are interested in the total GLEAM emission associated with each G4Jy source, we also fit a GLEAM-only spectral index using the total (i.e. summed) integrated flux densities (Section 6.5). This we refer to as ‘G4Jy_alpha’, and it will differ from GLEAM_alpha if the G4Jy source is multi-component in GLEAM. Then, in line with the parent catalogue (Hurley-Walker et al. Reference Hurley-Walker2017), we mask the GLEAM_alpha and/or G4Jy_alpha values in the G4Jy catalogue wherever the corresponding reduced- $\chi^2$ value is $>1.93$ .

In addition, we provide the spectral index calculated using (total) $S_{\textrm{151\,MHz}}$ and $S_{\textrm{1400\,MHz}}$ (‘G4Jy_NVSS_alpha’), for sources at Dec. $\geq-39.5^{\circ}$ , and using $S_{\textrm{151\,MHz}}$ and $S_{\textrm{843\,MHz}}$ (‘G4Jy_ SUMSS_alpha’), for sources at Dec. $<-39.5^{\circ}$ . These indices (and their errors) are provided in separate columns, as extrapolating to a common frequency (e.g. 1 GHz) may obscure the different systematics of the two surveys, and/or conflate potentially different distributions of spectral curvature.

We present the mean and median values for each of these four sets of spectral indices in Table 3. Due to the masking involved for GLEAM_alpha and G4Jy_alpha, we also note the number of GLEAM components or G4Jy sources (respectively) for which the spectral index is provided in the catalogue. We direct the reader to Section 8.2 for an initial discussion of these spectral indices, with further analysis to appear in Papers III and IV (White et al., in preparation).

Table 4. Selection criteria for previous radio source samples, which we use to check the completeness of the G4Jy Sample (Section 7.1). ‘MRC’ is the abbreviation for the Molonglo Reference Catalogue of Radio Sources (Large et al. Reference Large, Mills, Little, Crawford and Sutton1981). The giant radio galaxies (GRGs) making up the sample assembled by Malarecki et al. (Reference Malarecki, Jones, Saripalli, Staveley-Smith and Subrahmanyan2015) were originally identified in the MRC ( $>\,0.7\,\text{Jy}$ at 408 MHz) and SUMSS (see Section 2.1.3).

Table 5. Radio sources that were missing from the G4Jy Sample, based on the initial selection (Section 3), but are now included as a result of cross-checks against the samples listed in Table 4 (Section 7.1). Including these radio galaxies gives a total of 1 863 G4Jy sources in the sample.

¹2MASX J06181305-4844580 and ²ESO 509-G003 in van Velzen et al. (Reference van Velzen, Falcke, Schellart, NierstenhÖfer and Kampert2012).

7.1. Literature searches for extended sources

We search for missing, multi-component sources by checking the overlap of the GLEAM catalogue with five existing samples: ‘Southern extragalactic radio sources’ (Jones & McAdam Reference Jones and McAdam1992), ‘Radio galaxies of the local Universe’ (van Velzen et al. Reference van Velzen, Falcke, Schellart, NierstenhÖfer and Kampert2012), the original 2-Jy sample (Wall & Peacock Reference Wall and Peacock1985), ‘Giant radio galaxies’ (Malarecki et al. Reference Malarecki, Jones, Saripalli, Staveley-Smith and Subrahmanyan2015), and the 3CRR sample (Laing et al. Reference Laing, Riley and Longair1983). An overview of these samples is shown in Table 4. The key part of this work is creating and inspecting several hundreds of extra overlays, to avoid any assumptions as to what we may expect the radio sources to look like in GLEAM.

As a result of these cross-checks, we add a total of 15 sources to the G4Jy Sample that otherwise would not have been included. However, extended sources—such as B1302 $-$ 492 and B1610 $-$ 608 in Jones & McAdam (Reference Jones and McAdam1992)—are still absent because they lie in one of the GLEAM catalogue’s masked regions (notably, the Galactic Plane or the region surrounding Centaurus A). Therefore, we define in Section 7.4 the region over which the sample is complete.

7.1.2. Cross-check using van Velzen et al. (2012)

Next we cross-check our sample against radio galaxies of the local Universe, as compiled by van Velzen et al. (Reference van Velzen, Falcke, Schellart, NierstenhÖfer and Kampert2012). Doing so reveals that we need to add seven sources to our sample: GIN 049, NGC 1044, GIN 190, PKS B0616 $-$ 48,Footnote p B1323 $-$ 271, PKS B1834+19, and IC 1347 (Table 5). Six of these sources are presented in Figure 6, and we refer the reader to Figure 17 of Paper II for the seventh source. The latter is NGC 1044 (G4Jy 285), which has unusual, diffuse, low-frequency emission nearby. GIN 190 (G4Jy 475) is a head-tail galaxy (Section 4.7.2 of Paper II), and B1323 $-$ 271 (G4Jy 1067) and PKS B1834+19 (G4Jy 1496) are both WAT radio galaxies (Section 4.7.1 of Paper II).

As part of our comparison with the catalogue produced by van Velzen et al. (Reference van Velzen, Falcke, Schellart, NierstenhÖfer and Kampert2012), we pay closer attention to sources where we significantly disagree as to the flux density measured using NVSS or SUMSS components. In Section 4.7.2 of Paper II, we detail discrepancy with respect to G4Jy 325, and we also note that for IC 4296 (G4Jy 1080 in Figure 1) they measure $S_{\textrm{1.4\,GHz}}=2.42\,\text{Jy}$ . This is the total flux density when summing over the NVSS components for the inner jets, but not including the NVSS components associated with the well-separated lobes. We do include the latter and calculate $S_{\textrm{1.4\,GHz}}=4.91\,\text{Jy}$ over 23 NVSS components.

Comparing our NVSS/SUMSS flux densities also highlighted that we had used the wrong number of components for NGC 253 (G4Jy 86 in Figure 3a of Paper II) and NGC 612 (G4Jy 171 in Figure 7). We recalculate their flux density and brightness-weighted centroid position and duly update the centroid flags to ‘1’ (Section 5.4).

Figure 4. Overlays for six G4Jy sources that were added to the G4Jy Sample following a cross-check against Jones & McAdam (Reference Jones and McAdam1992) (Section 7.1.1). The datasets, contours, symbols, and beams are the same as those used for Figure 1, but where blue contours, crosses, and ellipses correspond to NVSS or SUMSS. In addition, positions from AllWISE are indicated by green plus signs, with host galaxies highlighted in white. (a) G4Jy 234 (B0211−479). (b) G4Jy 543 (B0523−327). (c) G4Jy 579 (B0546−329). (d) G4Jy 935 (B1137−463). (e) G4Jy 1525 (B1910−800). (f) G4Jy 1628 (B2026−414).

Table 6. A list of 3CRR sources (Laing et al. Reference Laing, Riley and Longair1983) that are not in the G4Jy Sample, despite being at Dec. $< 30^{\circ}$ . Their absence is due to each of them having poor-quality data in the GLEAM Survey, and so—with the exception of 3C 433—the region in which they lie is masked (Hurley-Walker et al. Reference Hurley-Walker2017). An explanation of why 3C 433 is present in the GLEAM catalogue, yet absent from the G4Jy Sample, can be found in Section 7.1.5. Below, we use ‘Cen A’ as shorthand for ‘Centaurus A’.

Figure 5. Overlays for two more G4Jy sources that were added to the G4Jy Sample following cross-checks against Jones & McAdam (Reference Jones and McAdam1992) (Section 7.1.1). The datasets, contours, symbols, and beams are the same as those used for Figure 4. (a) G4Jy 1732 (B2147−555). (b) G4Jy 1741 (B2151−461).

Figure 6. Overlays for six G4Jy sources that were added to the G4Jy Sample following a cross-check against van Velzen et al. (Reference van Velzen, Falcke, Schellart, NierstenhÖfer and Kampert2012) (Section 7.1.2). The datasets, contours, symbols, and beams are the same as those used for Figure 4. (a) G4Jy 131 (GIN 049). (b) G4Jy 475 (GIN 190). (c) G4Jy 604 (PKS B0616−48). (d) G4Jy 1067 (B1323−271). (e) G4Jy 1496 (PKS B1834+19). (f) G4Jy 1670 (IC 1347).

Figure 7. An overlay for G4Jy 171 (Section 7.1.2), where the datasets, contours, symbols, and beams are the same as those used for Figure 1. In addition, positions from AllWISE are indicated by green plus signs, with the host galaxy highlighted in white.

7.2. Internal matching of the EGC

We also search for missing sources by cross-matching the GLEAM components into pairs/groups and then selecting potential, extended G4Jy sources for visual inspection. The two methods we use for selecting these candidate sources are described below. Following inspection of internal matches, we add a total of nine sources to the G4Jy Sample that would otherwise be absent.

7.2.2. Applying empirically derived criteria

For our second method, we use two criteria: a flux density ratio of $0.5<S_{1}/S_{2}< 2$ and a normalised separation (in degrees/ $\sqrt{\textrm{Jy}}$ ) of $\theta/\sqrt(S_{1}+S_{2})<0.13$ , where $S_{1}$ and $S_{2}$ are the 151 MHz flux densities in Jy. This parameter space was chosen from examination of flux density ratio plotted against normalised separation, for sources from the FIRST survey (White et al. Reference White, Becker, Helfand and Gregg1997). That analysis has been done as part of the follow-up to an automated cross-identification paper based on the likelihood ratio (lrpy; Weston et al. Reference Weston, Seymour, Gulyaev, Norris, Banfield, Vaccari, Hopkins and Franzen2018). The goal was to select pairs of radio components that could potentially be true ‘doubles’ and then see whether the lrpy code would be more likely to select a counterpart to the radio source if it was a ‘double’, compared to if it were two ‘single’ sources. The normalised separation comes from the assumption that the luminosity is constant and therefore distance is proportional to $1/\sqrt S$ , and that the linear size is also constant. Neither of these assumptions is true, but we note that when plotting these parameters against each other using FIRST, there is a cloud of sources within the region bound by the two criteria, as well as a larger (partially overlapping) distribution. The cloud of sources most likely corresponds to true pairs (i.e. the two lobes of one radio source), and the more widespread distribution (going to higher flux density ratios and normalised separations) is due to random matches. This separation of ‘true pairs’ and ‘random pairs’ is confirmed by visual inspection of a randomly selected sub-sample. We note that this parameter space happens to be equivalent to that from Magliocchetti et al. (Reference Magliocchetti, Maddox, Lahav and Wall1998), albeit derived differently.

Through this analysis we find 47 potential ‘doubles’ where both GLEAM components are brighter than 4 Jy. Of these, 18 are confirmed through visual inspection to be true ‘doubles’, and one is a ‘triple’. (All 19 had already been identified as multi-GLEAM-component sources.) The remaining 28 candidate ‘doubles’ are found to be pairs of GLEAM components that are not associated with one another. Furthermore, there are 14 other previously confirmed ‘doubles’/‘triples’ (Section 5.2) that are not selected via the criteria above. Therefore, for this subset ( $S_{1}$ , $S_{2}>4\,\text{Jy}$ ), we estimate the reliability of the algorithm as $19/47=0.40$ , and its completeness as $19/33=0.58$ .

Table 7. Radio sources that are now included in the G4Jy Sample, having been identified through a friends-of-friends match using the GLEAM EGC (Section 7.2.1). Including these radio galaxies gives a total of 1 863 G4Jy sources in the sample.

Meanwhile, out of eight potential ‘doubles’ where both GLEAM components are fainter than 4 Jy, we find that one of them is a true ‘double’ with total flux density $>4\,$ Jy. This is G4Jy 729 (Figure 8e), which was found via our previous method (Section 7.2.1). That method led to us identifying eight other radio galaxies, but none of these are selected via the criteria based on flux density ratio and normalised separation. Hence, for this subset ( $S_{1}$ , $S_{2}<4\,\text{Jy}$ ; $S_{1}+S_{2}>4\,\text{Jy}$ ), we estimate the reliability of the algorithm as $1/8=0.13$ and its completeness as $1/9=0.11$ .

The main reason why applying this method to GLEAM data did not work very well (considering the reliability and completeness) is likely that the selection criteria were derived for radio sources in FIRST. Radio galaxy populations from this survey are incomplete and biased towards sources with their radio axis close to our line of sight. Furthermore, FIRST is sensitive to bright, compact emission, and so would pick up a greater proportion of radio galaxies that have distinct hotspots (typical of ‘double’, FR-II morphology). In GLEAM, we see radio sources with more diffuse emission and a wider range of morphology, for which the selection criteria are less appropriate. However, this method was able to select very extended radio sources with GLEAM-component separations, $\theta'$ , of up to 8 arcmin. Those with separations of $\theta' < 4'$ (11 sources) would have been selected for visual inspection via the approach taken in Section 7.2.1, while the remaining nine sources (with $4' < \theta' < 8'$ ) would not have been. Nonetheless, the latter subset each have at least one GLEAM component with $S_{\textrm{151\,MHz}}>4\,\text{Jy}$ , and so were already visually inspected following the initial selection (Section 3).

Figure 8. Overlays for six G4Jy sources that were added to the G4Jy Sample following internal matching (Section 7.2.1). The datasets, contours, symbols, and beams are the same as those used for Figure 4. (a) G4Jy 189. (b) G4Jy 270. (c) G4Jy 318. (d) G4Jy 447. (e) G4Jy 729. (f) G4Jy 1021.

Figure 9. Overlays for three more G4Jy sources that were added to the G4Jy Sample following internal matching (Section 7.2.1). Datasets, contours, symbols, and beams are the same as for Figure 4. (a) G4Jy 1428. (b) G4Jy 1480. (c) G4Jy 1718.

Table 8. The 67 G4Jy sources that are also in the 3CRR sample. ‘No. comp.’ refers to the number of GLEAM components associated with the G4Jy source, and ‘3CRR ref.’ indicates the origin of the 3CRR 178-MHz flux density: 1—4CT (Williams et al. Reference Williams, Collins, Caswell and Holden1968; Caswell & Crowther Reference Caswell and Crowther1969; Kellermann et al. Reference Kellermann, Pauliny-Toth and Williams1969); 2—4C (Clarke Reference Clarke1965; Wills & Parker Reference Wills and Parker1966); 3—4C (Pilkington & Scott Reference Pilkington and Scott1965; Gower, Scott, & Wills Reference Gower, Scott and Wills1967); 4—3CR (Bennett Reference Bennett1962); 5—corrected 3CR (Véron Reference VÉron1977); 6—interpolation or extrapolation. The references provide expressions for the corresponding beamsize, which we evaluate at the relevant declination, and present in the next column. These ‘3CRR beams’ are applied to GLEAM images (Section 7.3), from which we derive the $S_{\textrm{178\,MHz}}$ shown in column 7. $S_{\textrm{178\,MHz}}$ values in column 8 are calculated by extrapolating from 181 MHz to 178 MHz using the G4Jy_alpha value (Section 6.6), or the spectral index from the 3CRR catalogue (as indicated by ‘ $\alpha$ flag’ = 1). Due to space considerations, we note here that columns 4, 7, and 8 are in units of Jy. The ‘original ratio’ is the extrapolated, GLEAM $S_{\textrm{178\,MHz}}$ (column 8) divided by the 3CRR $S_{\textrm{178\,MHz}}$ . For the ‘rescaled ratio’ we instead divide by a rescaled version of the 3CRR $S_{\textrm{178\,MHz}}$ , as described in Section 7.3.

Table 8. Continued – The 67 G4Jy sources that are also in the 3CRR sample. Note that beam dimensions cannot be provided for 3CRR sources that have an interpolated/extrapolated $S_{\textrm{178\,MHz}}$ (3CRR ref. = 6). Hence, the remaining columns for these sources are also left unfilled. Due to space considerations, we note here that columns 4, 7, and 8 are in units of Jy.

7.3. Flux density comparison with 3CRR

The G4Jy Sample will enable further investigation of relativistic jets and their interaction with the environment, as already explored using the well-studied 3CRR sample. Given the prominence of the latter, we conduct a flux density analysis for 67 G4Jy sources that overlap with 3CRR (following on from Section 7.1.5). These are listed in Table 8.

First, the closest GLEAM flux density measurement we have to $S_{\textrm{178\,MHz}}$ is that for the 181-MHz sub-band. We extrapolate this to 178 MHz by assuming a power-law description of the radio emission and using the spectral index (G4Jy_alpha) fitted to the G4Jy total flux densities (Sections 6.5 and 6.6). Where the associated reduced- $\chi^2$ value is $>1.93$ , we instead use the spectral index provided in the 3CRR catalogue (obtained through VizieR) for this extrapolation. The ratio of GLEAM $S_{\textrm{178\,MHz}}$ to 3CRR $S_{\textrm{178\,MHz}}$ is presented in Table 8 as the ‘original’ ratio. Looking at the distribution of this ratio (Figure 10), we see that the GLEAM flux density appears to be systematically lower than that measured for 3CRR. Note that the 3CRR catalogue does not provide errors for $S_{\textrm{178\,MHz}}$ (nor for the spectral index), but it uses the RBC scale of Roger et al. (Reference Roger, Bridle and Costain1973),^a which is known to differ by $\sim$ 9% from the KPW scale (Kellermann et al. Reference Kellermann, Pauliny-Toth and Williams1969) at 178 MHz (Laing & Peacock Reference Laing and Peacock1980; Laing et al. Reference Laing, Riley and Longair1983). Meanwhile, the EGC has an uncertainty in the flux density scale of $8.0\pm0.5$ % for sources at $-72.0^{\circ}<$ Dec. $<18.5^{\circ}$ and $11\pm2$ % for sources at Dec. $>18.5^{\circ}$ (Hurley-Walker et al. Reference Hurley-Walker2017). However, a combination of the two flux density scale errors (where we consider the extreme fractional errors of 0.09 and 0.13)

is not enough to explain the discrepancy for the 23 G4Jy–3CRR sources with ratio $<0.78$ .

Figure 10. The ratio of $S_{\textrm{178\,MHz}}$ measured using GLEAM data, to $S_{\textrm{178\,MHz}}$ using the 3CRR catalogue (Laing et al. Reference Laing, Riley and Longair1983). These are for 60 of the 67 3CRR sources that overlap with the G4Jy Sample, where ‘original ratios’ refers to the 3CRR $S_{\textrm{178\,MHz}}$ being the value provided in the 3CRR catalogue. The median original ratio is 0.82 and is indicated by a thick, vertical, red, solid line. ‘Rescaled ratios’ are those where the 3CRR $S_{\textrm{178\,MHz}}$ value has had its corresponding beam size (Table 8) taken into account, leading to rescaling of this flux density (see Section 7.3 for details). The median rescaled ratio is 0.87 and is indicated by a thick, vertical, blue, solid line. For both sets of ratios, the GLEAM $S_{\textrm{178\,MHz}}$ value is extrapolated from the $S_{\textrm{181\,MHz}}$ measurement in the EGC (Hurley-Walker et al. Reference Hurley-Walker2017). Meanwhile, ‘subset’ (see legend) refers to the G4Jy sources for which we are able to use the G4Jy spectral index for extrapolating flux densities from one frequency to another (as indicated by $\alpha$ flag = ‘0’ in Table 8). The thick, vertical, dashed lines indicate the median values for this subset, with respect to the original ratios (median = 0.83; red) and rescaled ratios (median = 0.84; blue).

Next, we note that the 178-MHz flux densities in the 3CRR catalogue are a compilation from numerous surveys: 4CT, 4C, and 3CR (see references in caption of Table 8). Each of these surveys was conducted using a beam ranging from 19 to 235 times larger (by area) than that of the MWA, prompting us to investigate whether confusion/unrelated emission could account for the 3CRR flux densities being systematically higher than those from GLEAM.

As Aegean may underestimate the flux density for extended sources, we only consider for the analysis G4Jy–3CRR sources that are characterised by a single GLEAM component. For each of these sources, we apply an ellipse, of the relevant beam dimensions (column 6 of Table 8), to the 181-MHz sub-band image from GLEAM.Footnote q We then use the solid angle of the MWA beam to calculate the integrated flux density over this ellipse (which involves summing over all pixel values within the ellipse and normalising with respect to the beam). In addition, we wish to characterise how well this method is able to reproduce the 181-MHz, integrated flux density measurement that is provided in the EGC. For this, we apply an ellipse of dimensions fitted by Aegean (i.e. the semi-major and semi-major axes, a_181 and b_181, respectively), along with the fitted position angle (pa_181), and again calculate the integrated flux density over the ellipse. The mean ratio of this ellipse-derived $S_{\textrm{181\,MHz}}$ to the original EGC $S_{\textrm{181\,MHz}}$ then allows us to ‘correct’ other flux densities determined in a similar way. Similarly, we use the standard deviation in the ratio to estimate the error in the integrated flux density calculated over an ellipse. The result is a corrected GLEAM $S_{\textrm{181\,MHz}}$ measured within the ‘3CRR’ beam, which we then extrapolate to 178 MHz (again using either G4Jy_alpha or the 3CRR spectral index, as previously). The extrapolated value is what appears in column 7 of Table 8.

How much extra emission is detected through the large beam associated with 3CRR, compared to the fitted GLEAM measurement, is apparent from comparing columns 7 and 8 of Table 8. Dividing the latter by the former then gives a ‘corrective factor’, which we use to rescale the 3CRR $S_{\textrm{178\,MHz}}$ . The ‘re-scaled’ ratio (column 11) is the ratio of the GLEAM $S_{\textrm{178\,MHz}}$ (column 8) to this rescaled 3CRR $S_{\textrm{178\,MHz}}$ . As shown in Figure 10, these rescaled ratios (mean $= 0.87 \pm 0.16$ ) are closer to 1.0 than the original ratios (mean $= 0.81 \pm 0.11$ ), but more-widely distributed, and now as large as 1.25. Therefore, whilst unrelated emission may still play a part, we cannot conclude that it is the main reason for the offset between GLEAM and 3CRR flux densities. Furthermore, a two-sample Kolmogorov–Smirnov test gives D = 0.27 (where 0.30 is the D statistic to exceed) and p-value = 0.02, indicating that the two distributions are not significantly distinct.

We now return to an explanation that has already been touched upon in this sub-section: that the flux density calibration of GLEAM components is worse at the highest declinations. Whilst this is true for the GLEAM catalogue as a whole, we see no trend in the GLEAM $S_{\textrm{178\,MHz}}$ /3CRR $S_{\textrm{178\,MHz}}$ ratio with declination, as shown in Figure 11a. We also see no trend in the ratio with the integrated flux density of the source (Figure 11b), but cannot use this to rule out non-linearity in the flux scale calibration. This is because the overlap of the G4Jy Sample with 3CRR restricts our investigation to $S_{\textrm{178\,MHz}}\,{\gtrsim}\,10.9\,\text{Jy}$ sources, whereas one of the criteria used to select sources for setting the GLEAM flux density scale ( $S_{\textrm{74\,MHz}}>2\,\text{Jy}$ ; Hurley-Walker et al. Reference Hurley-Walker2017) corresponds to $S_{\textrm{178\,MHz}}\,{\gtrsim}\,1\,\text{Jy}$ (assuming $S_{\nu} \propto \nu^{-0.7}$ ). It is possible that the flux density scale starts to show non-linearity (Scott & Shakeshaft Reference Scott and Shakeshaft1971; Laing & Peacock Reference Laing and Peacock1980) as the 10.9-Jy threshold is approached, but further investigation is beyond the scope of this work. In addition, Eddington bias may be affecting 3CRR sources detected at lower signal to noise (as weakly suggested by Figure 11b), leading to the 3CRR $S_{\textrm{178\,MHz}}$ being overestimated. However, this is difficult to explore further due to the absence of $S_{\textrm{178\,MHz}}$ uncertainties in the 3CRR catalogue.

Next, we plot the total, integrated flux densities across the GLEAM band (72–231 MHz) alongside previous multi-frequency measurements for the 3CRR sample. For this, we include the G4Jy–3CRR sources that have multiple GLEAM components associated with them. The resulting SEDs (spanning 10 MHz to 15 GHz) are available as online supplementary material (Appendix F) and confirm that the G4Jy flux densities are consistently lower for this subset of very bright sources at high declination. Although we are unable to conclusively state the reason(s) for this offset, we point out that the G4Jy catalogue inherits from the EGC the internal-calibration consistency of $\leq$ 3%, as determined over 245,457 GLEAM components (Hurley-Walker et al. Reference Hurley-Walker2017). Furthermore, recent P-band (230–470 MHz) VLA observations of $\sim$ 40 unresolved sources suggest that the GLEAM flux density scale is $\sim$ 3% too low (Callingham et al., in preparation). This is based on a comparison of the $S_{\textrm{230\,MHz}}$ measurement from GLEAM and the expected flux density at 230 MHz, following spectral fitting of the GLEAM and P-band data. The latter are tied to the flux-density scale of Perley & Butler (Reference Perley and Butler2017), over 50 MHz to 50 GHz.

Table 10. Characteristics of the G4Jy Sample (Section 7.4), in terms of the number of GLEAM components associated with an individual source, and the morphology of the NVSS/SUMSS emission (Section 5.2).

Figure 11. The GLEAM $S_{\textrm{178\,MHz}}$ /3CRR $S_{\textrm{178\,MHz}}$ ratio plotted against (a) declination and (b) 3CRR $S_{\textrm{178\,MHz}}$ . These are for 60 of the 67 3CRR sources that overlap with the G4Jy Sample, where ‘original ratios’ refers to the 3CRR $S_{\textrm{178\,MHz}}$ value being that provided in the 3CRR catalogue. ‘Rescaled ratios’ are those where the 3CRR $S_{\textrm{178\,MHz}}$ value has had its corresponding beam size (Table 8) taken into account, leading to rescaling of this flux density (see Section 7.3 for details). As in Figure 10, ‘subset’ (see legends) refers to the G4Jy sources for which we are able to use the G4Jy spectral index for extrapolating flux densities from one frequency to another (as indicated by $\alpha$ flag = ‘0’ in Table 8). For both panels, the vertical, black, dashed line is where the ratio is equal to 1.0, to guide the eye.

Figure 12. The distribution in $S_{\textrm{151\,MHz}}$ for the full sample, and when split by morphology (‘single’, ‘double’, ‘triple’, and ‘complex’) in NVSS/SUMSS/TGSS (Section 5.2 and 7.4). The vertical line is where $S_{\textrm{151\,MHz}} = 12.2\,\text{Jy}$ , which corresponds to $S_{\textrm{178\,MHz}} = 10.9\,\text{Jy}$ (assuming a power-law radio spectrum with spectral index, $\alpha = -0.7$ ). Therefore, the G4Jy sources to the right of the vertical line are akin to those in the 3CRR sample (Laing et al. Reference Laing, Riley and Longair1983).

7.4. Summary of the results from visual inspection and checks for completeness

As a result of our visual inspection and further checks, the original list of 1879 GLEAM components becomes a list of 1 960 components. In conjunction, this is reduced to a list of 1 863 GLEAM sources, and it is this source list that we refer to as the G4Jy Sample. 67% of the G4Jy sources are ‘singles’, 26% are ‘doubles’, 4% are ‘triples’, and 3% have ‘complex’ morphology (Table 10). In Figure 12, we show the distributions in $S_{\textrm{151\,MHz}}$ for these subsets, in addition to that for the full sample. We note that there are 233 G4Jy sources brighter than 12.2 Jy at 151 MHz, which corresponds to the flux density limit for the 3CRR sample (173 sources). Of these sources, the fraction that are a ‘double’ or a ‘triple’ is 41%, whilst for the 1630 G4Jy sources below this threshold, the fraction falls to 28%. Without redshifts to consider the radio luminosities, we hypothesise that the brighter sources are likely to be closer and more extended, and therefore resolved in NVSS/SUMSS/TGSS (which are the surveys we use to determine the morphology). Meanwhile, it is important to note that 21% (383) of the G4Jy sources are affected by confusion (Section 5.2), and so the GLEAM flux densities will need to be updated in the future.

Following our best efforts, the G4Jy Sample of $S_{\textrm{151\,MHz}}>4\,\text{Jy}$ radio sources is effectively complete over the footprint of the EGC (Hurley-Walker et al. Reference Hurley-Walker2017) minus the region defined as $-18.3^{\circ} < b < -10.0^{\circ}$ , $65.4^{\circ} < l < 81.1^{\circ}$ , Dec. $<30.0^{\circ}$ (Section 7.1.5). This covers $24\,731 \text{deg}^2$ (i.e. 60% of the entire sky), all of which is accessible to the SKA and its precursor telescopes. The sky density of the G4Jy Sample is therefore one source per $\sim13\,\text{deg}^2$ . Within this total sky area, we know that at least one $>4\,\text{Jy}$ source is absent (Orion A; see Section 3.1) and acknowledge that we may still be missing a few extended radio sources. Hence, we estimate that the G4Jy Sample is 99.50–99.95% complete. In addition, the brightest G4Jy source (G4Jy 1402; 3C 353) is at $S_{\textrm{151\,MHz}}=232\,\text{Jy}$ , with our sample being biased against sources that are brighter than this (namely, ‘A-team’ sources, which are masked for the EGC; see Table 1).

Finally, in light of a $\sim$ 3% offset (Callingham et al., in preparation; Section 7.3) between the flux-density scale of GLEAM and that of Perley & Butler (Reference Perley and Butler2017), we consider the effect that this would have on the completeness of the G4Jy Sample. We find that there are 88 GLEAM components in the EGC at $3.89 < S_{\textrm{151\,MHz}}\textrm{/Jy}< 4.00$ that would then need to be considered for inclusion. One of these is GLEAM J151635+001603, which is already in the sample as being associated with GLEAM J151643+001410 (together composing G4Jy 1238). Similarly, some of the remaining 87 components may be associated with each other, but equally, some components $<$  3.89 Jy may sum together to $>\,3.89\,\text{Jy}$ (cf. Sections 7.1 and 7.2, regarding the 4-Jy threshold). Therefore, for simplicity (and remembering that Orion A is absent from the considered footprint), we estimate the completeness to be $1863 / (1863 + 87 +1) = 95.5$ % on the flux-density scale of Perley & Butler (Reference Perley and Butler2017).

8.1. Angular size information

An overview of linear, physical sizes for G4Jy sources will be provided in Paper III, as calculating these sizes is reliant on redshifts being compiled for the sample. These may reveal that additional sources are GRGs, further to those listed in Table 3 of Paper II.

In the meantime, we can obtain sample-wide information by considering the distribution in the angular sizes of the 1 863 sources, since we know how the angular size scale (kpc/arcsec) varies with redshift. This distribution is presented in Figure 13, where the median angular size of 43.8 arcsec is marked by a vertical, dashed line. (Note that for this analysis, we fix all angular sizes to their upper limits. This is applicable for 855 sources, with the largest upper limit being 129.8 arcsec.) As shown in the left-hand panels of Figure 13, at least half of the G4Jy Sample is smaller than 370 kpc, regardless of redshift. Furthermore, if a source is $\,{\gtrsim}\,$ 500 arcsec in angular size, its physical size must be at least 100 kpc, even at the very low redshift of 0.01 (Figure 13b). However, we remind the reader that the angular sizes are derived using NVSS or SUMSS (Section 6.3.1), and so are limited by the 45 arcsec resolution of these surveys. If we consider only the 657 sources that are multi-component in NVSS or SUMSS, we find that the median angular size is 74.5 arcsec.

Table 11. 22 G4Jy sources previously identified by Chhetri et al. (Reference Chhetri, Morgan, Ekers, Macquart, Sadler, Giroletti, Callingham and Tingay2018) as showing moderate ( $0.4\,{\leq}\,$ NSI $\,{<}\,0.9$ ) or strong (NSI $\,{\geq}\,0.9$ ) interplanetary scintillation (Section 8.1). NSI = normalised scintillation index.

Figure 13. The solid lines in the upper panels of this figure show how the observed angular size varies with redshift for a source of fixed physical size (100 kpc, 370 kpc, 1 Mpc). These functions are calculated in accordance with the cosmology described at the end of Section 1. The lower panels show the angular size distribution for sources in the G4Jy Sample, with the median angular size marked by a dashed, vertical line (Section 8.1).

Figure 14. (a) The distributions for the four sets of spectral index provided in the G4Jy catalogue: G4Jy $\alpha$ , GLEAM $\alpha$ , G4Jy–NVSS $\alpha$ , and G4Jy–SUMSS $\alpha$ (see Section 6.6). The median values for each spectral index are indicated by vertical lines (using the same colour and linestyle as for the corresponding histogram; see legend). (b) The distribution in G4Jy $\alpha$ for the full sample, and for sources with ‘single’, ‘double’, ‘triple’, and ‘complex’ morphology in NVSS/SUMSS/TGSS (Sections 5.2 and 8.2). The black, dashed, vertical line is where $\alpha = -0.7$ , which is the canonical spectral index that we use for extrapolation of flux densities (assuming $S_{\nu} \propto \nu^{\alpha}$ ). For comparison, we also plot the median G4Jy $\alpha$ value for the full sample (orange, solid, vertical line).

Next, particularly with unresolved G4Jy sources in mind, we explore the compactness of the radio emission by considering whether the source exhibits interplanetary scintillation (Little & Hewish Reference Little and Hewish1966; Morgan et al. Reference Morgan2018). This is where radio sources appear to ‘twinkle’ due to the turbulence of the intervening solar wind, allowing sub-arcsecond scales to be probed. Chhetri et al. (Reference Chhetri, Morgan, Ekers, Macquart, Sadler, Giroletti, Callingham and Tingay2018) demonstrated the power of this method over $30\times30\,\text{deg}^2$ (i.e. the field of view for a single MWA pointing) by characterising the scintillation properties of 2 550 sources. In total, 131 of these sources are in the G4Jy Sample, with two being described as ‘strong’ scintillators (normalised scintillation index, NSI $\geq0.9$ ). This means that a single sub-arcsecond component is dominating the flux density at 162 MHz (their observing frequency). Another 20 sources are ‘moderate’ scintillators ( $0.4\leq$ NSI $<0.9$ ), which may include sources with multiple sub-arcsecond components, and sources where there is a single sub-arcsecond component but it is surrounded by more-extended low-frequency emission. The 22 moderate/strong scintillators cross-matched with the G4Jy Sample are listed in Table 11. However, another 43 of the 131 cross-matched sources may also have compact emission on sub-arcsecond scales, but for them Chhetri et al. (Reference Chhetri, Morgan, Ekers, Macquart, Sadler, Giroletti, Callingham and Tingay2018) could only provide upper limits in NSI, due to the scintillation not reaching the detection threshold.

8.2. Spectral information

In Figure 14a, we present the distributions for each of the four spectral indices that we provide in the G4Jy catalogue (see Section 6.6). Although these refer to the ‘full sample’, we remind the reader that a different number of G4Jy sources (or GLEAM components, as the case may be) is used for each distribution, as indicated in Table 3. In the following analysis, $\alpha^{\textrm{231\,MHz}}_{\textrm{72\,MHz}} = \text{G4Jy}\ \alpha$ , $\alpha^{\textrm{1400\,MHz}}_{\textrm{151\,MHz}} = \text{G4Jy--NVSS} \alpha$ , and $\alpha^{\textrm{843\,MHz}}_{\textrm{151\,MHz}} = \text{G4Jy--SUMSS} \alpha$ (with each assuming radio emission of the spectral form, $S_{\nu} \propto \nu^{\alpha}$ ).

Table 12. 67 G4Jy sources previously identified by Callingham et al. (Reference Callingham2017) as having a spectral peak at a frequency ( $\nu_{\textrm{peak}}$ ) between 72 and 1400 MHz (Section 8.2). G4Jy 136 and G4Jy 178 are the strong scintillators mentioned in Section 8.1.

Note that for the majority of the sample (i.e. 1603/1863 = 86% of the sources), a power-law spectrum is an accurate description of the total radio emission between 72 and 231 MHz. If this were not the case, the reduced- $\chi^2$ value corresponding to $\alpha^{\textrm{231\,MHz}}_{\textrm{72\,MHz}}$ (the ‘G4Jy_alpha’ column in the G4Jy catalogue) would be $>1.93,$ and we would mask the spectral index for the catalogue. Therefore, for the remaining 14% of sources, the radio emission shows evidence of spectral curvature within the GLEAM band. Further evidence of curvature is apparent from the median value for the low-frequency spectral index ( $\alpha^{\textrm{231\,MHz}}_{\textrm{72\,MHz}}$ ) being steeper than the median value for the spectral index calculated between 151 MHz and 843 MHz/1400 MHz ( $\alpha^{\textrm{843\,MHz}}_{\textrm{151\,MHz}}$ / $\alpha^{\textrm{1400\,MHz}}_{\textrm{151\,MHz}}$ , respectively)—see Table 3 and the vertical lines in Figure 14a. The reasons for this will be discussed further in Papers III and IV, following additional analysis (White et al., in preparation).

Conversely, a source with a flatter spectrum within the GLEAM band than towards higher frequencies (i.e. $\alpha^{\textrm{231\,MHz}}_{\textrm{72\,MHz}} > \alpha^{\textrm{843\,MHz}}_{\textrm{151\,MHz}}$ or $\alpha^{\textrm{1400\,MHz}}_{\textrm{151\,MHz}}$ ) is likely to be turning over due to free-free absorption or synchrotron self-absorption (Lacki Reference Lacki2013). Such sources have previously been identified in the EGC by Callingham et al. (Reference Callingham2017), and in cross-matching the G4Jy Sample with their catalogues, we find an overlap of one  GHz-peaked spectrum (GPS) source (G4Jy 1533; GLEAM J192451 $-$ 291426), 67 sources with a spectral peak between 72 and 1400 MHz (listed in Table 12), and 19 sources with a spectral peak below 72 MHz (listed in Table 13). Each of these sources is ‘single’ in morphology, with the exception of G4Jy 1233 (GLEAM J151340+260718), which we label as ‘complex’. This is due to its X-shaped morphology, which is shown in Figure 4d of Paper II. Furthermore, G4Jy 352, G4Jy 420, G4Jy 819, G4Jy 965, G4Jy 1597, G4Jy 1772, and G4Jy 1801 are 7 of 15 sources found to have low-frequency variability by Bell et al. (Reference Bell2019), who use a preliminary version of the G4Jy Sample for their study.

Returning to the distribution in $\alpha^{\textrm{231\,MHz}}_{\textrm{72\,MHz}}$ for the full sample, we also present this spectral index for each of the categories in morphology (Figure 14b). The ‘doubles’ and ‘triples’ have (mostly) steep spectral indices that span a range of $-1.6$ to $-0.4$ , which is as expected if the lobes are dominating the radio emission. Meanwhile, for ‘single’ sources, the range in $\alpha^{\textrm{231\,MHz}}_{\textrm{72\,MHz}}$ is considerably wider from $-2.3$ to $0.4$ . This subset encompasses ultra-steep sources at high redshift and flat-spectrum sources (where the core is believed to be dominating the radio emission).Footnote r However, this is complicated by the size of the MWA beam, which leads to G4Jy/GLEAM flux densities being affected by confusion. As a result, the fitted spectral index of the G4Jy source differs from its true value.