The GLEAM 4-Jy (G4Jy) Sample: V. Broadband spectral analysis

Introduction

Active galactic nuclei (AGN) are known to have an important role in galaxy evolution, with the supermassive black-hole at the centre appearing to be correlated with growth of the host galaxy (e.g. Gültekin et al. 2009). For this work we focus on those that are deemed to be ‘radio loud’ AGN, where the radio jets can have both a positive impact on star-formation (e.g. Croton et al. 2006) and a negative impact (e.g. Croton et al. 2006). The overall impact of AGN feedback is thus open to debate.

We aim to investigate further by studying the brightest radio galaxies in the southern sky, known as the G4Jy Sample (White et al. 2020a,b). Being selected at low frequencies ($S_{151\ \mathrm{MHz}} > 4$ Jy), via the GaLactic and Extragalactic All-sky Murchison Widefield Array catalogue (GLEAM; Wayth et al. 2015; Hurley-Walker et al. 2017), these sources are unbiased with respect to the orientation of the radio-jet axis (Barthel 1989) and therefore give us the most complete picture of how AGN interact with their surroundings. For such a study we need to construct broadband radio spectral energy distributions (SEDs) in order to place constraints on the electron energies associated with extended radio emission (e.g. Mack et al. 1998). GLEAM provides excellent constraints at the low-frequency end, and we employ radio data from the Australian Square Kilometre Array Pathfinder (ASKAP) and the Australia Telescope Compact Array (ATCA) to constrain emission at mid-to-high radio frequencies.

As shown by previous work (e.g. Turner et al. 2018b), broadband SEDs allow us to understand intrinsic properties such as the jet power of the sources. This differs from the radio luminosity as it incorporates information on the ‘work done’ by the radio source on its surroundings (Turner et al. 2026), rather than tracing synchrotron radiation (and inverse-Compton losses). Broadband SEDs are also fundamental for estimating the age of the radio source (e.g. Harwood et al. 2017; Quici et al. 2022), with lower frequencies enabling longer AGN lifecycles to be probed. This is particularly interesting as some AGN may have more-recently ‘switched off’, meaning that the radio offers the only window into past black-hole accretion activity (Shulevski et al. 2017).

The difference with the current work is that past spectral analyses tend to have each revolved around a handful of sources, whereas we complete our analysis en masse for nearly $\sim$2,000 radio galaxies. Doing so allows us to draw out general trends that allow us to put extreme examples (e.g. giant radio galaxies) into context. Furthermore, we emphasise that a significant fraction of sources have spectral curvature that is indicative of restarted AGN activity (White et al. 2026b), which further highlights that we cannot assume that a power-law function ($S_{\nu} \propto\nu^{\alpha}$) accurately describes the SED.

Paper outline

In the next section we outline the radio data that is used for our work, followed by how the Rapid ASKAP Continuum Survey (RACS) allows us to determine mid-frequency flux-densities, extending the work by Gawenda et al. (2026) for the G4Jy-3CRE subset ($S_{178\,\mathrm{MHz}} > 9\,\mathrm{Jy}$). Then, in § 4, we present the results of fitting the broadband radio SEDs of G4Jy sources, from low to mid-frequencies. For a subset of the sample, we can extend this fitting to higher frequencies, as described in § 5. Based on this multi-frequency analysis, we then use theoretical models in § 6 to determine intrinsic properties, namely the source age and jet power. Finally, in § 7 we present our conclusions.

Data

We supplement the multiwavelength G4Jy catalogue (White et al. 2026a,b) with radio data from the Rapid ASKAP Continuum Survey (RACS) and the Australia Telescope Compact Array (ATCA). Doing so allows us to study broadband radio spectra from low frequencies via GLEAM (72–231 MHz) up to frequencies as high as 20 GHz, with the spectral shape providing insights into the physical processes of these radio-bright sources.

RACS-low images and catalogue

RACS is a survey carried out at three frequencies using ASKAP, with the first data release being the Stokes-$I$ images and catalogue at 887.5 MHz (McConnell et al. 2020; Hale et al. 2021). Given its similar observing frequency at 843 MHz, Hale et al. (2021) use the Sydney University Molonglo Sky Survey (SUMSS; Mauch et al. 2003; Murphy et al. 2007) to assess the flux-density scale of RACS-low and determine that the latter has an error of $\pm16$ per cent. Furthermore, RACS-low has a point-source completeness of $\sim95$ per cent for sources with an integrated flux-density of $\sim3$ mJy. The images are convolved to a common resolution of 25 arcsec, which is applied for the Declination range of $-80$ to $+30$ deg. (We here note that 15 G4Jy sources are at more-southerly Declinations.) Like for each of the RACS catalogues, source-finding is completed with PyBDSF (Mohan & Rafferty 2015), and we make use of the Gaussian-component catalogue over the extragalactic sky (i.e. with a $\lvert b\rvert< 5$ deg removal of the Galactic Plane).

RACS-mid images and catalogue

The second observing frequency of RACS is at 1367.5 MHz, with images released by Duchesne et al. (2023) and the corresponding catalogue generated by Duchesne et al. (2024). The former retain their native, Declination-dependent spatial resolution of 8.1–47.5 arcsec in order to preserve surface-brightness sensitivity, where the median noise is 198 $\mu$Jy PSF$^{-1}$. Covering the sky below Dec. $= +49$ deg, the median angular resolution is 11.2 arcsec $\times$ 9.3 arcsec. Again, we use the original Gaussian-component catalogue (rather than the source catalogue subsequently produced by PyBDSF) in order to better-determine the spatial extent of the fitted radio emission. Finally, we note that Duchesne et al. (2023, 2024) estimated a 6-per-cent uncertainty in the brightness scale based upon comparison with the NRAO (National Radio Astronomy Observatory) VLA (Very Large Array) Sky Survey (NVSS; Condon et al. 1998) at 1400 MHz.

RACS-high images and catalogue

The third and final observing frequency of RACS, corresponding to ‘RACS-high’, is 1655.5 MHz (Duchesne et al. 2025). The catalogue is constructed from images that have a median spatial resolution of 11.8 arcsec $\times$ 8.1 arcsec and a median noise level of $\sim195\,\mu$Jy PSF$^{-1}$. These cover the southern sky up to Dec. $\simeq+48$ deg, with the brightness scale estimated to have an uncertainty of 10 per cent. We acknowledge that a Declination-dependent offset has been discovered in the astrometry (Duchesne et al. 2025), of maximum magnitude 2.5 arcsec, but we continue with the original Declination determinations in order to maintain consistency between the catalogued components and the imaging from which they are derived.

ATCA data

As part of the original visual inspection completed for the G4Jy Sample (White et al. 2020a,b), it was noted which sources coincided with detections from the Australia Telescope 20-GHz (AT20G) Survey (Murphy et al. 2010). Tracing the highest frequencies of the radio emission from G4Jy sources, these detections either pin-pointed the position of the radio core or revealed the location of a hotspot amongst otherwise poor-spatial-resolution imaging ($\sim45$ arcsec from SUMSS and NVSS). The AT20G detections have a positional accuracy of $\sim1$ arcsec and the survey reaches an $8$-$\sigma$ flux-density limit of 40 mJy. However, this blind-scan survey has varying completeness (e.g. 92 per cent at 50 mJy beam$^{-1}$; Hancock et al. 2011) on account of weather conditions strongly affecting 20-GHz observations. AT20G covers the southern hemisphere (at $\lvert b\rvert> 1.5$ deg) and includes near-simultaneous follow-up observations at 4.8 GHz and 8.6 GHz for detections below Dec. $= -15$ deg (Figure 1).

To supplement the AT20G data, ATCA follow-up was conducted (specifically for G4Jy sources) at 5, 8, and 18 GHz (PI: C. Jackson). We note that the highest frequency was centred on 18 GHz rather than 20 GHz in order to take advantage of the better continuum sensitivity available there. These new data are made available in the G4Jy catalogue accompanying this paper, with flags to indicate unreliable flux-density measurements due to poor coverage in the $u-v$ visibility plane. Whilst the AT20G catalogue provides peak flux-density measurements, we provide integrated flux-density measurements based on images generated using MIRIAD (Sault et al. 1995). The result is that 177 G4Jy sources have coverage at 18/20 GHz for high-frequency spectral-index calculations (§ 5). Furthermore, we treat 18/20-GHz flux-densities as lower limits owing to extended radio emission being resolved out in the ATCA images.

Determining associated RACS emission

The excellent spectral coverage provided by GLEAM (Hurley-Walker et al. 2017) at low radio frequencies means that broadband radio spectra for the G4Jy Sample (White et al. 2020a,b) are very well-constrained below $\sim230$ MHz. Meanwhile, we take advantage of the multiple RACS data releases (§ 2.1–§ 2.3) to better-constrain the ‘mid-frequency’ range of the spectrum, $\sim1$ GHz. This is not as straightforward as it sounds due to the varying sensitivity of the data towards extended radio emission, and irregular morphologies being approximated by multiple Gaussian components. Consequently, we conduct thorough visual inspection of G4Jy sources, accompanied by hundreds of manual adjustments, as summarised in this section.

Downloading RACS cutouts

For downloading RACS-low, RACS-mid and RACS-high data, we used a modified version of the Jupyter notebook provided on the CASDA website (https://research.csiro.au/casda/services/). This uses the astroquery Python package (Ginsburg et al. 2019) to generate image cutouts via the TAP (Table Access Protocol) URL https://casda.csiro.au/casda_vo_tools/tap. These cutouts are centred on the radio centroid position determined by White et al. (2020a,b) using SUMSS/NVSS, and are large enough to encompass all of the radio emission associated with G4Jy sources.

A flood-fill algorithm as the basis

For each of the RACS datasets, we begin by considering all RACS components (light-grey squares in Figure 2) that are within 5 arcmin of the radio centroid position (blue hexagon) for the G4Jy source. We then apply a flood-filling algorithm that aims to fill to the $6\text{-}\sigma$ contour (where $\sigma$ is the local root-mean-square of the pixel values) and starts from the host-galaxy position (cyan diamond). The latter is available for 93 per cent of the sample (White et al. 2026a) and RACS components that lie within the $6\text{-}\sigma$ contour are deemed to be associated with the source (black squares in Figure 2).

Naturally, not all of the components will be properly associated if the source has radio-core emission that is well-separated from the lobes, so (as is the case for G4Jy 189 in Figure 3) manual adjustment is needed. This involves editing a RACS-component list (that is created per G4Jy source) and using TOPCAT (Taylor 2005) to visually identify which components need to be included (or disassociated). Meanwhile, the criterion that the flood-filled region must encompass the host-galaxy position means that unrelated radio-sources are not included in the association.

However, in the case of G4Jy 579 (Figure 4) and hundreds of G4Jy sources, the flood-filling does not work completely owing to discontinuities in the radio emission. To identify and correct for this scenario, we visually inspect intermediate contour plots (Figure 4a) and again use TOPCAT to adjust the corresponding RACS-component list. The result is an updated contour plot (Figure 4b) that is then assessed for accuracy. The flags that we assign to the RACS-low (red), RACS-mid (purple), and RACS-high (blue) contours are:

• 0 – The correct number of RACS components are associated with the G4Jy source.

• −1 – The total RACS flux-density will be slightly underestimated due to a RACS component being missed.

• 1 – The total RACS flux-density will be slightly overestimated due to a RACS component being associated when it should not be. For example, this flag is assigned when the associated components include artefacts (Figure 5).

We provide these flags, integrated RACS flux-densities, and number-of-RACS-components in the G4Jy catalogue associated with this paper. In addition, we make the RACS contour-plots available via the G4Jy Zenodo repository: https://zenodo.org/communities/g4jy/records.

More on visual inspection and manual adjustments

In this sub-section we highlight additional limitations of the flood-filling algorithm, which we correct for via manual adjustment. Firstly, Figure 5 illustrates a case where the 6-$\sigma$ contour of the G4Jy source intersects with the 6-$\sigma$ contour of a neighbouring source, leading to both being considered for the summed flux-density in RACS-low.

Secondly, a search radius of 5 arcmin is used by default, but some G4Jy sources are more extended than 10 arcmin across. In these cases we extend the search radius based upon the angular size listed in the G4Jy catalogue (courtesy of NVSS/SUMSS imaging) and re-run the flood-fill algorithm and subsequent inspection. (For interest, each of these larger G4Jy sources are presented in Appendix A.)

Thirdly, we caution that the RACS flux-densities that we determine via contouring and visual-inspection may still be underestimates due to PyBDSF not fitting diffuse emission very well. This is because small box-sizes are used by the source-finder to calculate the local rms, and so relatively-uniform emission may be misinterpreted as noise. A couple of such examples are shown in Figure 6 and should be borne in mind when interpreting the broadband radio SEDs. Specifically, this affects 28 sources (1.6 per cent of the sample), which are listed in Table 1.

Source name
G4Jy 74	G4Jy 133	G4Jy 151	G4Jy 171	G4Jy 204
G4Jy 224	G4Jy 347	G4Jy 381	G4Jy 386	G4Jy 462
G4Jy 614	G4Jy 619	G4Jy 641	G4Jy 680	G4Jy 886
G4Jy 949	G4Jy 990	G4Jy 1034	G4Jy 1048	G4Jy 1135
G4Jy 1172	G4Jy 1173	G4Jy 1216	G4Jy 1402	G4Jy 1496
G4Jy 1499	G4Jy 1670	G4Jy 1671

Broadband radio SEDs (72 – 1700 MHz)

Having determined integrated flux-densities at RACS frequencies (§ 3), we revisit the spectral-index calculation of G4Jy Paper IV ((White et al. 2026b)) before further analysing the broadband radio spectra.

Spectral indices between 151MHz and 1.4GHz

In previous work for the G4Jy Sample we studied the degree of spectral curvature in the radio by combining G4Jy flux-densities ((White et al. 2020a,b)) with those from NVSS ((Condon et al. 1998)). The NVSS coverage (at 1.4 GHz) accounts for 77 per cent of the G4Jy Sample, whereas RACS-mid (at 1.3675 GHz) provides us with (1,728/1,733) $\sim$100 per cent coverage (Table 2). As such, we recalculate the two-point spectral index, $\alpha_{\mathrm{mid}} = \alpha_{151\ \mathrm{MHz}}^{1368\ \mathrm{MHz}}$, assuming a power-law description of the radio emission ($S_{\nu} \propto\nu^{\alpha}$) and using 1.3675 GHz rather than 1.4 GHz for the calculation. Another difference is that we define the low-frequency spectral-index, $\alpha_{\mathrm{low}}$, to also be between two frequencies (76 and 227 MHz), rather than a power-law fitted to 20 low-frequency flux-density measurements. Such a relaxation of the spectral-index calculation means that we can also consider G4Jy sources that show significant spectral curvature within the GLEAM band (spanning 72 to 231 MHz).

Characteristic	No. sources
The full G4Jy Sample ((White et al. 2020a,b))	1,863
Sources that suffer from confusion at 151 MHz	386
Sources with host-galaxy identifications	1,733
Coverage provided by NVSS (Dec. > −39.5 deg)	1,437
Coverage provided by RACS-low (at 887.5 MHz)	1,705
Sources with underestimated RACS-low flux-density	15
Sources with overestimated RACS-low flux-density	22
Coverage provided by RACS-mid (at 1367.5 MHz)	1,728
Sources with underestimated RACS-mid flux-density	15
Sources with overestimated RACS-mid flux-density	65
Coverage provided by RACS-high (at 1655.5 MHz)	1,727
Sources with underestimated RACS-high flux-density	30
Sources with overestimated RACS-high flux-density	114

Following White et al. (2026b), we define the spectral-curvature index as SCI $=\alpha_{\mathrm{low}}-\alpha_{\mathrm{mid}}$ and present the two spectral indices against one another in Figure 7a. As previously, sources with SCI < −0.05 have concave radio spectra (indicative of restarted AGN activity) whilst sources with SCI > 0.05 have convex radio spectra (which could be due to spectral ageing or absorption processes). However,

within each SCI interval there are a number of sources where the radio emission is best-fit by a third-order polynomial (Figure 7b–Figure 7f).

Low- to mid-radio-frequency SEDs

We fit the low-to-mid radio-frequency flux-densities in log-log space, with the highest polynomial considered being of third order:

where $a$, $b$, $c$ and $d$ are the polynomial coefficients. We use (reduced) $\chi^2$-minimisation to identify which sources are better-fit by a given polynomial, prioritising the fits where the $\chi^2_{\mathrm{reduced}} < 2.0$ (Table 3), and provide the fitted coefficients in the accompanying G4Jy catalogue. As part of the fitting, we consider the brightness-scale systematic errors added in quadrature to the flux-density errors. The former are Declination-dependent (8–13 per cent) for the GLEAM/G4Jy flux-densities ((Hurley-Walker et al. 2017)), 16 per cent for the RACS-low flux-densities ((Hale et al. 2021)), 6 per cent for the RACS-mid flux-densities ((Duchesne et al. 2024)), and 10 per cent for the RACS-high flux-densities ((Duchesne et al. 2025)). Overall, we find that 89 per cent of the sample is well-fit by a first-order polynomial, i.e. by a power-law description of the radio emission. If the source is not well fit by any-order polynomial, we deem this as non-convergent behaviour and do not assign the source a $\chi^2_{\mathrm{reduced}}$ value.

Characteristic	No. sources
Best-fit by a first-order polynomial	1,645
Best-fit by a second-order polynomial	159
Best-fit by a third-order polynomial	42
Not well-fitted by any polynomial considered	17

For sources that have a spectroscopic redshift in the G4Jy catalogue ((White et al. 2026a,b)), we also present the radio SEDs in the rest frame (Figure 8) for interest. These have been evaluated at the median flux-density at 151 MHz in the observed frame and then ‘deredshifted’. We note that only first-order polynomial fits are present for sources in the highest redshift-bins, which is likely a consequence of small-number statistics.

Next, we investigate whether free-free absorption (FFA; e.g. Figure 9) or synchrotron self-absorption (SSA; e.g. Figure 10) can explain the spectral behaviour of G4Jy sources that are not well-fitted by a power-law spectrum. In the case of FFA, we consider the scenario where the absorbing ionised medium is mixed with the synchrotron-emitting electrons. As such, the radio spectrum has the following functional form:

where $\tau_0$ governs the frequency at which the radio emission pivots. An alternative fitting is considered via the following parameterisation of a spectral turnover in the radio:

where $x = \nu/\nu_m$, $S_m$ is the flux-density at frequency $\nu_m$, and $\alpha_{\mathrm{thin}}$ and $\alpha_{\mathrm{thick}}$ represent the spectral indices in the optically-thin and optically-thick regimes of the radio spectrum, respectively. This parameterisation reduces to the SSA equation in the event that $\alpha_{\mathrm{thick}} = +2.5$. Otherwise, it is assumed that this model will fit a convex radio spectrum (where $\alpha_{\mathrm{thick}} < \alpha_{\mathrm{thin}}$) and we find that this is the case where the fitting is robust (Table 4).

Combination of the polynomial fitting and subsequent FFA/SSA-like/SPL fitting	SCI < −0.15	−0.15 < SCI < −0.05	−0.05 < SCI < 0.05	0.05 < SCI < 0.15	SCI > 0.15
Best-fit by a second-order polynomial and FFA	7	3	0	2	16
Best-fit by a second-order polynomial and SSA-like	0	3	10	25	72
Best-fit by a second-order polynomial and SPL	0	0	2	0	0
Best-fit by a third-order polynomial and FFA	5	6	3	1	9
Best-fit by a third-order polynomial and SSA-like	2	4	14	1	18
Best-fit by a third-order polynomial and SPL	0	0	1	0	2
Total	14	16	30	29	117

Table 4 summarises the number of sources that are classed within either category (‘FFA’ or ‘SSA-like’) for different SCI values. As before, the model with the lowest reduced $\chi^2$ value is interpreted as the best fit. We find that 3 per cent of (all) G4Jy sources exhibit FFA, whilst 8 per cent of G4Jy sources exhibit SSA-like spectra. Notably, the majority of such-fitted sources have SCI > 0.15.

Broadband radio SEDs (72 MHz – 20 GHz)

For a subset of 177 G4Jy sources, we have ATCA flux-density measurements that allow us to study the radio spectrum from 72 MHz to 20 GHz (e.g. see Figure 11 to Figure 13). We therefore re-fit polynomials (Equation (1)) to the data and provide updated coefficients in the accompanying G4Jy catalogue. Noting that the majority of the ATCA flux-densities are via the AT20G catalogue (Murphy et al. 2010), which is a blind-scan survey, we expect this subset to be biased towards sources that have their radio-jet axis close to the line-of-sight. As such, we may also expect the radio spectrum to exhibit a concave spectral shape, but this is not borne out (as illustrated by Figure 14). This is likely because hotspots, which are also traced by 20-GHz emission, do not have ‘directionality’ connected to their detection. (Note that we have also checked the literature to determine whether the source in question is a blazar, with cross-identifications presented in Appendix B.)

As part of visually inspecting the broadband radio SEDs, we identify sources where the contiguous coverage provided by GLEAM reveals a ‘kink’ in the radio spectrum. We show a few examples of these in Figure 15. Whilst multiple epochs of AGN activity could result in these distinctive shapes, we caution that this could also be the result of unrelated radio sources having their radio emission blended by the 2-arcmin MWA beam.

Modelling the radio emission

With broadband radio SEDs in place, we are now in prime position for their physical interpretation. For this we make use of RAiSE (Radio AGN in Semi-analytic Environments) models (Turner & Shabala 2015; Turner et al. 2018a; Turner et al. 2023), which provide estimates of the source age and jet power across the sample (§ 6.3). Firstly, we introduce RAiSE (§ 6.1) and note the considerations that were made for the present work (§ 6.2).

The RAiSE framework

The RAiSE model captures the dynamics of the jet, lobe formation, and active-to-relic expansion phases of the resulting radio lobe (Turner et al. 2023). The conservation equations for a relativistic fluid are used to derive an analytic description for the expansion of the jet, while the lobe evolution is similarly modelled with the inclusion of a non-trivial adiabatic equation of state. The RAiSE framework solves a system of ordinary differential equations to self-consistently transition the dynamics from the analytic solutions describing the jet and lobe expansion. The properties of the host group/cluster environment, into which the jet expands, are described by a density profile informed by X-ray observations of nearby relaxed clusters (Vikhlinin et al. 2006). The core density and virial radius (overdensity of 200) of these profiles are scaled for a given halo mass to provide a range of plausible host environments; we assume the mean density profile and temperature for each halo mass following Turner & Shabala (2015). The semi-analytic approach of the RAiSE model predicts very comparable evolution in the size, volume and pressure of jets/lobes to hydrodynamic simulations (Turner et al. 2023, their fig. 3).

The radio emissivity of the RAiSE lobes at a given frequency, due to synchrotron-emission from shock-accelerated particles, is calculated based on their volume and the time-evolution of their magnetic field; related to the thermal pressure by some factor $q$ of the equipartition value (Turner & Shabala 2015; Kaiser et al. 1997). This analytic calculation includes both adiabatic expansion and radiative loss process (i.e., inverse-Compton and synchrotron). Turner et al. 2018a considered the spatial distribution of the time of last shock-acceleration for ‘packets’ of synchrotron-emitting electrons, with Turner et al. 2023 including local and large-scale inhomogeneities in the magnetic field. This yields surface brightness images consistent with those of hydrodynamic simulations (e.g. Stewart et al. 2025), and consequently, very comparable estimates for the integrated flux density Turner et al. 2023, their fig. 11).

The analytic underpinning of the RAiSE framework, and comparable analytic models (for review, see Turner & Shabala 2023), is critical to perform a Bayesian inversion from observations to intrinsic

parameters. Turner & Shabala (2015) employ a grid-based maximum likelihood algorithm to transform the $P$–$D$ diagram to the jet power–source age parameter space for each host environment and redshift. Turner et al. (2018b) constrain the lobe magnetic field, in addition the jet power and source age, using spectral curvature and propose prior probability density functions for sources with more limited spectral coverage; Quici et al. (2022) introduce further constraints based on the spatial surface brightness distribution to measure the ‘on’ and ‘off’ times of relic radio galaxies. The Turner & Stewart (2026) version of RAiSE is used in this work, taking advantage of its greatly improved computational efficiency when applied to simpler parameter inversions. This permits a fine sampling of the jet power and source age in the hyper-dimensional parameter space.

Considerations for the present work

We perform a Bayesian inversion following the approach of Turner et al. (2018b) based on the RACS-mid flux density, angular size of the source, and the best redshift estimate for the identified host galaxy. The 1367.5 MHz observer-frame frequency of the RACS-mid images largely excludes the low-frequency spectral turnover of compact sources (e.g., Young et al. (2025)), while simultaneously probing the ‘young’ synchrotron population that has experienced minimal radiative losses; although we note that such radiative losses are explicitly

modelled in RAiSE. We include the $\alpha_{\mathrm{mid}}$ spectral-index and SCI as additional constraints in the inversion for a subset of 405 objects with $\alpha_{\mathrm{mid}} < 0.0$ and SCI > 0.0; this subset excludes peaked-spectrum sources not captured by the Turner & Stewart (2026) version of RAiSE. We consider an additional systematic uncertainty in the spectral index due to the unknown value of the freshly shock-accelerated population; we assume $\Delta\alpha_{\mathrm{mid}} = 0.117$ based on the spectral fits by Turner et al. (2018b). The properties of the host group/cluster environments are modelled for three plausible halo masses: $10^{12.5}$, $10^{13.5}$ and $10^{14.5}$ M$_{\odot}$. These values are in agreement with halo masses derived in previous work (e.g. Wake et al. 2008; Mandelbaum et al. 2009). The high central density ($\sim\rho= 10^{21}$ kg m$^{-3}$) of the $10^{14.5}$ M$_{\odot}$ halo provides a rough approximation for the interaction of compact sources with a denser galaxy environment.

We generate a dense grid of synthetic RAiSE sources for the following set of parameters: jet power ($Q = 10^{36}$ to $10^{42}$ W with a 0.1 dex step size; both jets), source age ($t = 0.1$ to 1000 Myr with a 0.1 dex step size), and the redshift dependence of the radiative losses and cosmological scaling of the halo virial radius ($z = 0.1$ to 1 with a 0.1 step size; the exact redshift is used in the modelling). The model parameters adopt the default values of Turner et al. (2023), including an electron–proton plasma in the lobe, an equipartition factor of $q = 10^{-1\pm0.5}$, an injection spectral index of $\alpha= -0.7$, and a lobe axis ratio of A = 2.83. The Bayesian inversion is performed for each source (converting the physical size and luminosity from RAiSE to angular size and flux density based on the host redshift) with the median and 16/84th percentiles of the resulting marginal posterior probability density functions recorded. This yields three estimates for the jet power and source age of each object in our sample; one corresponding to each plausible halo mass.

Results of RAiSE modelling

As discussed in the literature, the $P$–$D$ diagram (Baldwin 1982) allows the evolutionary stage of radio galaxies to be appreciated as a function of radio-power ($P$) and linear size ($D$). Theory dictates that sources traverse this parameter space from left to right, corresponding to a radio galaxy showing (at first) increasing radio luminosity with source size. After time, the radio galaxy then fades due to synchrotron radiation and adiabatic expansion, resulting in these sources appearing in the lower right-hand region of the $P$–$D$ diagram. This is exactly what we see for the $P$–$D$ diagram plotted as a function of source age (Figure 16a) – the first time that this has been presented for such a large sample of AGN.

Accompanying this is the $P$–$D$ diagram as a function of intrinsic jet-power (Figure 16b), noting the formal difference between radio luminosity and radio power¹. The former is an intrinsic property of the radio galaxies calculated directly from the measured flux-density (in this case, at 151 MHz), whilst the latter is inferred via modelling of the radio galaxy’s interaction with the ambient medium. To simplify the analysis, our modelling assumes a single halo mass ($10^{12.5}$, $10^{13.5}$, or $10^{14.5}\,\mathrm{M}_{\odot}$) is applicable for the whole sample (§ 6.2). In addition, we only consider the modelling of sources that have ‘single’ or ‘double’ radio morphologies, for which the RAiSE results are most applicable (as opposed to ‘triple’ and ‘complex’ radio morphologies; White et al. 2020a,b).

Through comparing the $P$–$D$ diagrams for different halo masses (Figure 16–Figure 18), we see a general trend of increasing source age and jet power with increasing halo mass. This can be explained as follows: with higher halo mass, the virial mass of the galaxy is larger (e.g. Croton et al. 2006), resulting in higher densities of gas/material in the core. The impact that this has is to slow the expansion of the radio jets/lobes, necessitating higher jet-powers and longer source-ages in order to reach the same size. However, the relationship is complicated by a competing effect: higher densities also lead to higher pressures and magnetic fields in the lobes, and consequently higher radio luminosities, thus restricting the increase in jet power with halo mass.

To tie this work in with the earlier results regarding spectral curvature across the sample (§ 4.1), we plot the distribution in source age as a function of SCI in Figure 19. As expected, the oldest sources have the highest degree of spectral curvature, likely due to radiative losses through inverse-Compton and synchrotron processes. However, the SCI $> 0.15$ sources do also span a wide range in source ages, indicating that we cannot assume that high spectral curvature corresponds to ageing radio-sources (cf. White et al. 2026b). Nevertheless, this category gives us a firm basis for exploring the remnant radio-galaxy fraction in future work. Related to this, we note that Dutta et al. (2026) find that remnant radio galaxies (SCI $\gtrsim0.5$) have spectral ages of $\sim$8–42 Myr, signalling that the remnant phase may be more short-lived than originally assumed.

In Figure 20 we explore the results of the RAiSE modelling in fur-

ther detail. We start by considering the SCI distribution in radio-power($Q$)–source-age($t$) space, and note that there appear to be two sub-populations with SCI > 0.15 (Figure 20a). Those with longer source ages are coupled with lower jet powers, which suggests that the power is not large enough to replenish the electrons that result in synchrotron radiation (leading to steepening of the spectrum). This is supported by the corresponding spectral index (Figure 20b) being steeper than the general population for this subset. The second population of SCI > 0.15 sources have lower source ages coupled with higher jet powers, but these do not dominate the general population’s higher jet powers. This could be a consequence of assuming a single halo mass (and therefore magnetic-field structure) across the sample, when in fact radio sources inhabit a wide range of environments.

As expected, the largest sizes are achieved through a combination of high radio-jet power and long source age, with Figure 20c also demonstrating the relative rarity of giant radio-galaxies across the G4Jy Sample. We also present the $Q-t$ distribution as a function of radio luminosity (Figure 20d), and note the diagonal trend in the colouration of the datapoints. This can be explained by our earlier comment on the density of the material in the halo core: that is, the more confined the radio galaxy is, the higher the radio-power and/or source age that is needed in order to reach a given luminosity.

Conclusions

To better understand the interplay of radio galaxies and their environments, it is important to use a complete sample that is unbiased with respect to the orientation of the radio-jet axis. Hence our focus on the G4Jy Sample, which is a compilation of the radio-brightest sources in the southern sky, made in preparation for studies with the Square Kilometre Array (SKA). In the meantime, the sample is being used for commissioning of SKA-Low, and a subset of sources have been observed through MeerKAT Open Time (Sejake et al. 2023, Clews et al. 2026; Mitha et al., in prep.).

In this work we have enhanced previous studies of the G4Jy Sample by considering the extended radio emission that is exhibited at each of the RACS observing frequencies (887.5, 1367.5 and 1655.5 MHz). Correctly determining the associated mid-frequency radio-emission involves a significant amount of manual work, and we find that in 1.6 per cent of cases PyBDSF fails to accurately characterise diffuse

radio emission. We update the G4Jy catalogue to include the newly-determined RACS radio flux-densities and use these to construct broadband radio SEDs for the G4Jy Sample. These SEDs are extended to 20 GHz for a subset of 177 G4Jy sources, thanks to further measurements from ATCA, and they demonstrate a wide variety of spectral behaviour. Convex spectra (SCI > 0) are indicative of spectral ageing or low-frequency absorption, whilst concave spectra (SCI < 0) are indicative of restarted AGN activity or blazars. The full set of flux densities and redshifts (where available) are used by the RASIE modelling to determine the source age and jet power for a given, assumed density profile of the surrounding halo. For a halo mass of $10^{13.5}\,M_\odot$, the source age ranges from 0.1 to 891 Myr, whilst the jet power ranges from $10^{36}$ to $10^{41}$ W. The radio-power–size ($P$–$D$) diagram shows the expected distribution when plotted as a function of source age – the first time that this has been presented for such a large sample. Meanwhile, non-linearities in the jet-power distribution suggest that the environment is constricting the expansion of the radio jets/lobes for some sources. Future work will include investigating the impact of the environment on a source-by-source basis.

Acknowledgements

This work is based on the research supported in part by the National Research Foundation of South Africa (Grant Number 151060). We thank Stefan Duchesne for helpful discussion of the RACS data, and Alessandro Peca for advice regarding ingestion of the G4Jy catalogue into the Active Galactic Nuclei DataBase (AGN-DB; Peca et al. 2026).

This scientific work uses data obtained from Inyarrimanha Ilgari Bundara, the CSIRO Murchison Radio-astronomy Observatory. We acknowledge the Wajarri Yamaji People as the Traditional Owners and native title holders of the Observatory site. CSIRO’s ASKAP radio telescope is part of the Australia Telescope National Facility ({https://ror.org/05qajvd42}). Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing Research Centre. Establishment of ASKAP, Inyarrimanha Ilgari Bundara, the CSIRO Murchison Radio-astronomy Observatory and the Pawsey Supercomputing Research Centre are initiatives of the Australian Government, with support from the Government of Western Australia and the Science and Industry Endowment Fund.

The Australia Telescope Compact Array is part of the Australia Telescope National Facility ({https://ror.org/05qajvd42}) which is funded by the Australian Government for operation as a National Facility managed by CSIRO. We acknowledge the Gomeroi people as the Traditional Owners of the Observatory site.

Data availability

RACS contour plots, individual RACS component lists, broadband SEDs, and an updated G4Jy catalogue are all made available via the G4Jy repository on Zenodo: https://zenodo.org/communities/g4jy/records.

References

The most-extended radio galaxies

In this Appendix we present the G4Jy sources that have the largest angular size (Figure A1–Figure A9). As such, the default search radius for identifying RACS components (§ 3.2) is increased accordingly from 5 arcmin to a maximum of 30 arcmin.

Radio spectra for known blazars

We visually identify 27 G4Jy-ATCA radio spectra that are particularly ‘concave’ in their shape (with an ‘upturn’ at higher frequencies; Massaro et al. (2013); d’Antonio et al. (2019)) – see Figure B1. These are listed in Table B1, and we find that 70 per cent of these sources appear in the BLAZE blazar catalogue (Hämmerich et al. (2026)). We note that these radio spectra (Figure B2–Figure B4) need to be treated with caution given the time variability of the radio emission at high frequencies.

G4Jy name	Alternative name	Blazar classification
G4Jy 28	–	–
G4Jy 86	–	–
G4Jy 134	4FGL J0116.0−1136	fsrq
G4Jy 229	4FGL J0210.7−5101	fsrq
G4Jy 260	–	–
G4Jy 292	4FGL J0245.5−4502	fsrq
G4Jy 344	4FGL J0317.8−4414	fsrq
G4Jy 415	5BZU J0407−1211	bcu
G4Jy 466	–	–
G4Jy 483	5BZQ J0437−2954	fsrq
G4Jy 509	4FGL J0455.7−4617	fsrq
G4Jy 518	5BZQ J0506−6109	fsrq
G4Jy 871	4FGL J1048.0−1912	fsrq
G4Jy 891	–	–
G4Jy 1071	–	–
G4Jy 1074	–	–
G4Jy 1080	ABC J1336−3357	bcuc
G4Jy 1168	4FGL J1427.9−4206	fsrq
G4Jy 1202	4FGL J1454.4−3744	fsrq
G4Jy 1360	4FGL J1643.0−7714	bll
G4Jy 1521	WIBRaLS2 J191739.62−453030.7	bllc
G4Jy 1533	4FGL J1924.8−2914	fsrq
G4Jy 1621	4FGL J2025.6−0735	fsrq
G4Jy 1665	4FGL J2056.2−4714	fsrq
G4Jy 1732	–	–
G4Jy 1777	4FGL J2225.7−0457	fsrq
G4Jy 1802	5BZU J2303−1841	bcu

New columns of the G4Jy catalogue

Descriptions of newly-added/newly-named columns in the updated G4Jy catalogue, along with 17th-row entries, can be found in Table C1. This includes the addition of a ‘classification’ column, where the G4Jy source is listed as an AGN if it satisfies at least one of the following criteria: (i) has a ‘double’, ‘triple’ or ‘complex’ radio morphology; (ii) has a $151$-MHz radio luminosity that exceeds $10^{24}\ \mathrm{W\ Hz^{-1}}$ (noting that star-forming galaxies have lower luminosities; Gürkan et al. (2018)); or (iii) has a blazar classification (as indicated via the BLAZE_CLASS column). Exceptions to this logic are G4Jy 77 (a radio phoenix; Raja et al. (2024)), G4Jy 86 (a star-forming galaxy), G4Jy 288 (aka NGC 1068, a known AGN), G4Jy 571 (the Flame Nebula), G4Jy 1081 (a star-forming galaxy), and G4Jy 1605 (a cluster relic).

Column no.	Column name	Units	Description	17th-row entry
3	classification	–	Source-type classification	AGN
24	alpha_mid	–	Spectral index between 151 MHz and 1367.5 MHz	−0.809757
25	err_alpha_mid	–	Error on the spectral index between 151 MHz and 1367.5 MHz	0.041011
26	alpha_low	–	Spectral index between 76 MHz and 227 MHz	−0.670262
27	err_alpha_low	–	Error on the spectral index between 76 MHz and 227 MHz	0.007851
33	syserr_total_int_flux_076	Jy	Systematic error at 72-80 MHz due to flux-density scale	0.970512
36	syserr_total_int_flux_084	Jy	Systematic error at 80-88 MHz due to flux-density scale	0.922980
39	syserr_total_int_flux_092	Jy	Systematic error at 88-95 MHz due to flux-density scale	0.880273
42	syserr_total_int_flux_099	Jy	Systematic error at 95-103 MHz due to flux-density scale	0.817363
45	syserr_total_int_flux_107	Jy	Systematic error at 103-111 MHz due to flux-density scale	0.795469
48	syserr_total_int_flux_115	Jy	Systematic error at 111-118 MHz due to flux-density scale	0.755457
51	syserr_total_int_flux_122	Jy	Systematic error at 118-126 MHz due to flux-density scale	0.726722
54	syserr_total_int_flux_130	Jy	Systematic error at 126-134 MHz due to flux-density scale	0.691611
57	syserr_total_int_flux_143	Jy	Systematic error at 139-147 MHz due to flux-density scale	0.661601
60	syserr_total_int_flux_151	Jy	Systematic error at 147-154 MHz due to flux-density scale	0.636181
63	syserr_total_int_flux_158	Jy	Systematic error at 154-162 MHz due to flux-density scale	0.615912
66	syserr_total_int_flux_166	Jy	Systematic error at 162-170 MHz due to flux-density scale	0.597573
69	syserr_total_int_flux_174	Jy	Systematic error at 170-177 MHz due to flux-density scale	0.584969
72	syserr_total_int_flux_181	Jy	Systematic error at 177-185 MHz due to flux-density scale	0.566740
75	syserr_total_int_flux_189	Jy	Systematic error at 185-193 MHz due to flux-density scale	0.549959
78	syserr_total_int_flux_197	Jy	Systematic error at 193-200 MHz due to flux-density scale	0.529204
81	syserr_total_int_flux_204	Jy	Systematic error at 200-208 MHz due to flux-density scale	0.520924
84	syserr_total_int_flux_212	Jy	Systematic error at 208-216 MHz due to flux-density scale	0.505618
87	syserr_total_int_flux_220	Jy	Systematic error at 216-223 MHz due to flux-density scale	0.491888
90	syserr_total_int_flux_227	Jy	Systematic error at 223-232 MHz due to flux-density scale	0.477011
155	RACS-low_localrms	Jy beam$^{-1}$	Local rms in the RACS-low image	0.466105
156	RACS-low_n_cmp	–	Number of associated RACS-low Gaussian components	1
157	RACS-low_flag	–	Flags: an under-(−1) or over-estimated (+1) RACS-low flux-density	0
158	S_RACS_low_int	Jy	Integrated flux-density in RACS-low at 887.5 MHz	2.086022
159	err_S_RACS_low_int	Jy	Error on the integrated RACS-low flux-density	0.146531
160	RACS_mid_localrms	Jy beam$^{-1}$	Local rms in the RACS-mid image	0.003357
161	RACS-mid_n_cmp	–	Number of associated RACS-mid Gaussian components	4
162	RACS_mid_flag	–	Flags: an under-(−1) or over-estimated (+1) RACS-mid flux-density	0
163	S_RACS_mid_int	Jy	Integrated flux-density in RACS-mid at 1367.5 MHz	1.335346
164	err_S_RACS_mid_int	Jy	Error on the integrated RACS-mid flux-density	0.056138
165	RACS_high_localrms	Jy beam$^{-1}$	Local rms in the RACS-high image	0.000336
166	RACS_high_n_cmp	–	Number of associated RACS-high Gaussian components	1
167	RACS_high_flag	–	Flags: an under-(−1) or over-estimated (+1) RACS-high flux-density	0
168	S_RACS_high_int	Jy	Integrated flux-density in RACS-high at 1655.5 MHz	1.098967
169	err_S_RACS_high_int	Jy	Error on the integrated RACS-high flux-density	0.067028
170	polynomial_constant	Jy	Constant for polynomial fit of 72-MHz to 1.4-GHz data	2.657688
171	first_polynomial_coeff	–	First polynomial coefficient for fitting 72-MHz to 1.4-GHz data	−0.866632
Column no.	Column name	Units	Description	17th-row entry
172	second_polynomial_coeff	–	Second polynomial coefficient for fitting 72-MHz to 1.4-GHz data	–
173	third_polynomial_coeff	–	Third polynomial coefficient for fitting 72-MHz to 1.4-GHz data	–
174	polynomial_reduced_chi2	–	Reduced $\chi^2$ value for polynomial fitting	0.452083
175	restframe_polynomial_constant	–	Constant for rest-frame polynomial fit of 72-MHz to 1.4-GHz data	–
176	restframe_first_polynomial_coeff	–	First polynomial coefficient for fitting 72-MHz to 1.4-GHz data in the rest-frame	–
177	restframe_second_polynomial_coeff	–	Second polynomial coefficient for fitting 72-MHz to 1.4-GHz data in the rest-frame	–
178	restframe_third_polynomial_coeff	–	Third polynomial coefficient for fitting 72-MHz to 1.4-GHz data in the rest-frame	–
179	restframe_polynomial_reduced_chi2	–	Reduced $\chi^2$ value for rest-frame polynomial fitting	–
180	Name_AT20G	–	Name in the AT20G catalogue	AT20GJ000829−055845
181	RA_hms_AT20G	h:m:s	Right Ascension in the AT20G catalogue, in sexagesimal units	00:08:29.33
182	Dec_dms_AT20G	d:m:s	Declination in the AT20G catalogue, in sexagesimal units	−05:58:45.2
183	RA_deg_AT20G	deg	Right Ascension in the AT20G catalogue, in degrees	2.12208
184	Dec_deg_AT20G	deg	Declination in the AT20G catalogue, in degrees	−5.97922
185	S5_AT20G_peak	mJy	Peak flux-density at 5 GHz in the AT20G catalogue	–
186	err_S5_AT20G_peak	mJy	Error in the peak flux-density at 5 GHz in the AT20G catalogue	–
187	S8_AT20G_peak	mJy	Peak flux-density at 8 GHz in the AT20G catalogue	–
188	err_S8_AT20G_peak	mJy	Error in the peak flux-density at 8 GHz in the AT20G catalogue	–
189	S20_AT20G_peak	mJy	Peak flux-density at 20 GHz in the AT20G catalogue	66.0
190	err_S20_AT20G_peak	mJy	Error in the peak flux-density at 20 GHz in the AT20G catalogue	4
191	Epoch_AT20G	–	Epochs of the observations at 20, 8, 5 GHz	6
192	Quality_AT20G	–	Quality flag (g = good or p = poor) in the AT20G catalogue	g
193	Flags_AT20G	–	Other flags in the AT20G catalogue	–
194	P20_mJy_beam_AT20G	mJy	Polarised flux density (or limit) at 20 GHz	< 7
195	e_P20_AT20G	mJy	Error in polarised flux density at 20 GHz	–
196	m20_AT20G	%	Fractional polarisation at 20 GHz	< 10.5
197	PA20_AT20G	deg	Position angle at 20 GHz	–
198	P8_mJy_beam_AT20G	mJy	Polarised flux density (or limit) at 8 GHz	–
199	e_P8_AT20G	mJy	Error in the polarised flux density at 8 GHz	–
200	m8_AT20G	%	Fractional polarisation at 8 GHz	–
201	PA8_AT20G	deg	Position angle at 8 GHz	–
202	P5_mJy_beam_AT20G	mJy	Polarised flux density (or limit) at 5 GHz	–
203	e_P5_AT20G	mJy	Error in polarised flux density at 5 GHz	–
204	m5_AT20G	%	Fractional polarisation at 5 GHz	–
205	PA5_AT20G	deg	Position angle at 5 GHz	–
206	S5_ATCA_followup	mJy	Integrated flux-density at 5 GHz from ATCA follow-up	–
207	err_S5_ATCAfollowup_int	mJy	Error in the integrated flux-density at 5 GHz, from ATCA follow-up	–
208	flags_ATCAfollowup_int	–	Flags to indicate 5 GHz data	–
209	DR5_ATCAfollowup	–	Dynamic range at 5 GHz, from ATCA follow-up	–
210	nmaps_ATCAfollowup	–	Number of 5 GHz components, from ATCA follow-up	–
211	S5_ATCAfollowup	mJy	Integrated flux-density at 5 GHz from ATCA follow-up	–
212	S9_ATCAfollowup_int	mJy	Integrated flux-density at 9 GHz from ATCA follow-up	16.5
Column no.	Column name	Units	Description	17th-row entry
213	err_S9_ATCAfollowup_int	mJy	Error in the integrated flux-density at 9 GHz, from ATCA follow-up	–
214	flag9_ATCAfollowup_int	–	Flag to indicate unreliability of the 9 GHz data	–
215	DR9_ATCAfollowup	–	Dynamic range at 9 GHz, from ATCA follow-up	–
216	ncmp9_ATCAfollowup	–	Number of 9 GHz components, from ATCA follow-up	–
217	S18_ATCAfollowup_int	mJy	Integrated flux-density at 18 GHz from ATCA follow-up	–
218	err_S18_ATCAfollowup_int	mJy	Error in the integrated flux-density at 18 GHz, from ATCA follow-up	–
219	flag18_ATCAfollowup_int	–	Flag to indicate unreliability of the 18 GHz data	–
220	DR18_ATCAfollowup	–	Dynamic range at 18 GHz, from ATCA follow-up	–
221	ncmp18_ATCAfollowup	–	Number of 18 GHz components, from ATCA follow-up	–
222	polynomial_constant_ATCA	–	Constant for polynomial fit of 72-MHz to 20-GHz data	1.611203
223	first_polynomial_coeff_ATCA	–	First polynomial coefficient for fitting 72-MHz to 20-GHz data	0.003040
224	second_polynomial_coeff_ATCA	–	Second polynomial coefficient for fitting 72-MHz to 20-GHz data	−0.151617
225	third_polynomial_coeff_ATCA	–	Third polynomial coefficient for fitting 72-MHz to 20-GHz data	–
226	polynomial_reduced_chi2_ATCA	–	Reduced $\chi^2$ value for polynomial fitting	0.033276
227	alpha_high	–	Spectral index between 1367.5 MHz and 18/20 GHz	−1.120974
228	err_alpha_high	–	Error on the spectral index between 1367.5 MHz and 18/20 GHz	0.015093
229	BLAZE_SEP	arcsec	Angular separation between G4Jy source and BLAZE counterpart	–
230	BLAZE_SRC_NAME	–	Name of the source in the BLAZE catalogue	–
231	BLAZE_CLASS	–	Blazar classification in the BLAZE catalogue	–
232	BLAZER1_SEP	arcsec	Angular separation between G4Jy source and BLAZER1 counterpart	–
233	BLAZER1_SRC_NAME	–	Name of the source in the BLAZER1 catalogue	–
234	BLAZER1_CLASS	–	Blazar classification in the BLAZER1 catalogue	–
235	redshift_for_models	–	Redshift used for modelling sources with RAiSE	0.226
236	log10_jet_power_12d5_low	W	Lower limit of the jet power, assuming a halo mass of $10^{12.5} \mathrm{M}_{\odot}$	38.616359
237	log10_jet_power_12d5_med	W	Median of the jet power, assuming a halo mass of $10^{12.5} \mathrm{M}_{\odot}$	38.652865
238	log10_jet_power_12d5_up	W	Upper limit of the jet power, assuming a halo mass of $10^{12.5} \mathrm{M}_{\odot}$	38.613970
239	log10_jet_power_13d5_low	W	Lower limit of the jet power, assuming a halo mass of $10^{13.5} \mathrm{M}_{\odot}$	38.909064
240	log10_jet_power_13d5_med	W	Median of the jet power, assuming a halo mass of $10^{13.5} \mathrm{M}_{\odot}$	38.946214
241	log10_jet_power_13d5_up	W	Upper limit of the jet power, assuming a halo mass of $10^{13.5} \mathrm{M}_{\odot}$	38.972866
242	log10_jet_power_14d5_low	W	Lower limit of the jet power, assuming a halo mass of $10^{14.5} \mathrm{M}_{\odot}$	39.078540
243	log10_jet_power_14d5_med	W	Median of the jet power, assuming a halo mass of $10^{14.5} \mathrm{M}_{\odot}$	39.137201
244	log10_jet_power_14d5_up	W	Upper limit of the jet power, assuming a halo mass of $10^{14.5} \mathrm{M}_{\odot}$	39.179044
245	log10_source_age_12d5_low	yr	Lower limit of the source age, assuming a halo mass of $10^{12.5} \mathrm{M}_{\odot}$	6.216359
246	log10_source_age_12d5_med	yr	Median of the source age, assuming a halo mass of $10^{12.5} \mathrm{M}_{\odot}$	6.252865
247	log10_source_age_12d5_up	yr	Upper limit of the source age, assuming a halo mass of $10^{12.5} \mathrm{M}_{\odot}$	6.289370
248	log10_source_age_13d5_low	yr	Lower limit of the source age, assuming a halo mass of $10^{13.5} \mathrm{M}_{\odot}$	6.509064
249	log10_source_age_13d5_med	yr	Median of the source age, assuming a halo mass of $10^{13.5} \mathrm{M}_{\odot}$	6.546214
250	log10_source_age_13d5_up	yr	Upper limit of the source age, assuming a halo mass of $10^{13.5} \mathrm{M}_{\odot}$	6.582789
251	log10_source_age_14d5_low	yr	Lower limit of the source age, assuming a halo mass of $10^{14.5} \mathrm{M}_{\odot}$	6.737230
252	log10_source_age_14d5_med	yr	Median of the source age, assuming a halo mass of $10^{14.5} \mathrm{M}_{\odot}$	6.779066
253	log10_source_age_14d5_up	yr	Upper limit of the source age, assuming a halo mass of $10^{14.5} \mathrm{M}_{\odot}$

Table B1. G4Jy-ATCA sources that are visually determined as having particularly concave radio spectra (Figure B2–Figure B4). Their blazar classification and alternative name are as adopted from the BLAZE/BlazEr1 catalogue (Hämmerich et al. (2026)). ‘fsrq’ = flat-spectrum radio quasar, ‘bll’ = BL Lac, ‘bcu’ = blazar of unknown type, and a suffix of ‘c’ indicates that the source is a blazar candidate. The alternative-name prefix of ‘4FGL’ refers to the fourth Fermi-LAT source catalogue (Abdollahi et al. (2022)), ‘5BZQ’ and ‘5BZU’ refer to the 5th Roma BZCAT (Massaro et al. (2015)), ‘ABC’ refers to the ABC catalogue (Paggi et al. (2020)), and the prefix ‘WIBRaLS2’ refers to a blazar catalogue of D’Abrusco et al. (2019).

!Radio spectrum of G4Jy 509, showing $\log_{10}[S_{\nu}/\mathrm{Jy}]$ against $\log_{10}[\nu_{\mathrm{obs}}/\mathrm{MHz}]$, with $R^2=0.67$, $\alpha=-0.21$, $\chi^2=0.69$, and a 2nd-order fit bbox=0.13,0.08,0.46,0.31

!Radio spectrum of G4Jy 518, showing $\log_{10}[S_{\nu}/\mathrm{Jy}]$ against $\log_{10}[\nu_{\mathrm{obs}}/\mathrm{MHz}]$, with $R^2=0.95$, $\alpha=-0.44$, $\chi^2=1.07$, and a 2nd-order fit bbox=0.54,0.08,0.87,0.31

!Radio spectrum of G4Jy 871, showing $\log_{10}[S_{\nu}/\mathrm{Jy}]$ against $\log_{10}[\nu_{\mathrm{obs}}/\mathrm{MHz}]$, with $R^2=0.83$, $\alpha=-0.34$, $\chi^2=100000.00$, and a 3rd-order fit bbox=0.14,0.35,0.46,0.59

!Radio spectrum of G4Jy 1202, showing $\log_{10}[S_{\nu}/\mathrm{Jy}]$ against $\log_{10}[\nu_{\mathrm{obs}}/\mathrm{MHz}]$, with $R^2=0.79$, $\alpha=-0.27$, $\chi^2=100000.00$, and a 3rd-order fit bbox=0.54,0.35,0.87,0.59

!Radio spectrum of G4Jy 1360, showing $\log_{10}[S_{\nu}/\mathrm{Jy}]$ against $\log_{10}[\nu_{\mathrm{obs}}/\mathrm{MHz}]$, with $R^2=0.94$, $\alpha=-1.00$, $\chi^2=1.26$, and a 2nd-order fit bbox=0.13,0.62,0.46,0.85

!Radio spectrum of G4Jy 1521, showing $\log_{10}[S_{\nu}/\mathrm{Jy}]$ against $\log_{10}[\nu_{\mathrm{obs}}/\mathrm{MHz}]$, with $R^2=0.97$, $\alpha=-0.99$, $\chi^2=9.56$, and a 3rd-order fit bbox=0.54,0.62,0.87,0.85

This paper has been typeset from a T_EX/L_AT_EX file prepared by the author.