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EMU/GAMA: A new approach to characterising radio luminosity functions

T0 review · 4 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A statistical redshift-assignment scheme using only radio flux and r-band magnitude reconstructs the 888 MHz radio luminosity functions of star-forming galaxies and AGN, matching published surveys from z≈0 to z≈5.5.

desk verdict Low-z validation is genuine; high-z agreement is largely built into the input redshift distribution, so treat this as a promising proof-of-concept rather than a measured constraint above z≈0.5. read the letter →

arxiv 2505.11453 v1 pith:MXC7ZGSC submitted 2025-05-16 astro-ph.GA

J. Prathap , A. M. Hopkins , J. Afonso , M. Bilicki , M. Cowley , S. M. Croom , Y. Gordon , S. Phillipps
show 11 more authors
E. M. Sadler S. S. Shabala U. T. Ahmed S. Amarantidis M. J. I. Brown R. Carvajal D. Leahy J. R. Marvil T. Mukherjee J. Willingham T. Zafar
This is my paper · ORCID
classification astro-ph.GA
keywords radioluminosityfunctionsstatisticalredshiftestimationAGNstar-forminggalaxiesEMUearlyscienceGAMA1/Vmaxmethodcontinuumsurveys
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the radio luminosity function of a large radio-selected sample can be measured without individual redshifts for most sources. It takes a radio catalogue of 39,812 sources, of which only 6,425 have spectroscopic redshifts, and assigns the missing redshifts statistically from the redshift distributions of spectroscopically identified sources in the same bins of radio flux density and r-band magnitude; sources with no optical counterpart are assigned redshifts from a high-redshift distribution. Repeating the assignment one hundred times and building 1/Vmax luminosity functions, the paper finds that the total, star-forming, and AGN luminosity functions follow published 1.4 GHz luminosity functions from z≈0 to z≈0.5 for sources with optical counterparts, and out to z≈5.5 once the optically blank sources are redistributed. The point of the exercise is that population-level statistics, not individual redshifts, may be enough to characterise how the radio source population evolves.

What carries the argument

The load-bearing device is distributional redshift assignment. Radio sources are divided into small bins of observed radio flux density and, when available, r-band magnitude; for each bin the redshift distribution of the spectroscopically complete subsample is approximated by a single Gaussian, and sources missing redshifts are assigned redshifts drawn at random from that fitted Gaussian. Two refinements carry the high-redshift side: optically blank sources are redistributed using a redshift distribution inferred from a published 1.4 GHz luminosity function extending to $z\approx 6$, and the statistical AGN/SFG classification from BPT-diagram fractions is supplemented by a radio-luminosity cut. One hundred Monte Carlo realisations of the assignments yield the reported luminosity functions and their scatter.

What would settle it

A reader could test the method by taking a complete radio survey with full spectroscopic redshifts, hiding a random subset of those redshifts, running the same bin-and-draw procedure, and comparing the reconstructed luminosity functions with the true ones; a significant mismatch in any redshift bin, particularly above z≈0.5, would show the statistical assignments are not representative. The same test can be run on the optically blank sample once follow-up spectroscopy reaches those sources.

Watch

Extended reading notes

Core claim

The central discovery is that statistical redshifts drawn from coarsely binned empirical distributions reproduce the measured radio luminosity functions. For the 6,425 radio sources with both an r-band magnitude and a spectrum, the authors bin them in ($\log S_{888\,\mathrm{MHz}}$, $m_r$) space, fit a single Gaussian to each bin's redshift distribution, and draw random redshifts for the 4,566 sources with only $m_r$; the 28,821 sources with no optical counterpart are treated separately, first with the same flux-only bins and then with a higher-redshift prior. AGN versus star-forming classification is likewise assigned from the spectroscopic subsample through flux-binned probability mass functions, with a radio-luminosity threshold of $L_{888\,\mathrm{MHz}} > 10^{23.5}\,\mathrm{W\,Hz^{-1}}$ used to label strong radio sources as AGN. The resulting 888 MHz luminosity functions for the full 39,812-source sample follow the reference low-redshift functions to $z=0.5$ and the high-redshift function to $z \approx 5.5$; a faint-end upturn in the lowest redshift bin suggests a population of low-luminosity, low-mass sources not captured by the reference fit.

Load-bearing premise

The argument stands on the assumption that radio sources without spectroscopy in a given radio flux density and r-band magnitude bin, and radio sources with no optical counterpart in a given radio flux bin, have the same redshift distribution as the spectroscopically measured sources in that bin; nothing else tests this representativeness except the low-redshift agreement with a published luminosity function.

Editorial extensions

If this is right

  • The full 39,812-source radio sample can be assigned redshifts statistically and its 888 MHz luminosity functions match published measurements, so the radio luminosity function does not require complete spectroscopy.
  • Separate star-forming and AGN luminosity functions are recovered once radio-loud sources are classified as AGN by luminosity rather than by optical line ratios alone.
  • Random assignments from flux and magnitude bins smooth over large-scale-structure features in the redshift distribution, so the recovered luminosity functions trace the broad population rather than individual structures.
  • The faint-end upturn implies a previously unpredicted population of low-luminosity radio sources at low redshift, corresponding to star formation rates near $0.07\,M_\odot\,\mathrm{yr^{-1}}$.
  • The approach scales to future wide radio surveys where most sources will lack deep multiwavelength photometry and spectroscopy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • [editorial inference] Because the high-redshift prior for optically blank sources is drawn from the same published luminosity function later used as the high-redshift comparison, the agreement in that regime is a weaker test than it would be with an independent redshift prior; clustering-based or SED-based redshifts could supply that independent check.
  • [editorial inference] The same bin-and-draw machinery could be applied to other wavebands where spectroscopic completeness is low, such as far-infrared or X-ray surveys, with the same caveat that the training sample's redshift distribution must match the target population.
  • [editorial inference] The faint-end upturn at $L_{888\,\mathrm{MHz}}\approx10^{20}\,\mathrm{W\,Hz^{-1}}$ predicts an abundant population of low-mass, star-forming dwarf galaxies; deeper radio surveys with complete optical identifications could confirm or rule out this excess.
  • [editorial inference] The method's success is tied to the optical magnitude limit selecting a nearly complete low-redshift population; in surveys with a different depth or flux limit the bin-and-draw approach would need retesting before it can be trusted.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. This paper uses EMU early-science 887.5 MHz data in the GAMA G23 field to construct three samples: GEM I (6,425 radio sources with spectroscopy and r-band magnitudes), GEM II (4,566 with r-band magnitudes but no spectroscopy), and GEM III (28,821 with no optical counterpart). The authors assign statistical redshifts to GEM II by fitting Gaussians to GEM I redshift distributions in (log S888, mr) bins, and to GEM III first from GEM I flux-only templates and then, in §6.1, from a 'realistic' high-redshift distribution taken from Smolčić et al. (2017) or from a uniform distribution in 0.5<z<6. AGN/SFG classifications are transferred from GEM I via flux-bin probability mass functions and subsequently modified with a radio-luminosity threshold. RLFs are computed with the 1/Vmax method including completeness and area corrections, and are compared with Mauch & Sadler (2007) at low redshift and Smolčić et al. (2017) at high redshift. The central claim is that the statistical redshift assignment reproduces measured RLFs, including separate SFG and AGN LFs.

Significance. If the method is valid, it would offer a practical route to RLF measurements for future wide-area radio surveys where spectroscopic completeness is low and multiwavelength photometry is sparse. The low-redshift comparison against Mauch & Sadler (2007) is a genuine external test and works, and the multiple realisations provide a sensible treatment of statistical uncertainties. The uniform-redshift experiment in §7.1 is also a useful robustness check. However, the high-redshift validation is largely circular because the input redshift distribution and the benchmark LF come from the same Smolčić et al. (2017) work, and the separate SFG/AGN comparison is partly adjusted post hoc with a luminosity threshold. These issues need to be addressed before the central claim can be accepted.

major comments (4)
  1. [§6.1 and §7, Fig. 15] The high-redshift comparison is not independent: the GEM III sources (28,821 of 39,812) are assigned redshifts by sampling the Smolčić et al. (2017) redshift distribution (§6.1, Fig. 13), and the resulting LFs are then compared with Smolčić et al. (2017) LFs (§7, Fig. 15). Because L888 is computed from exactly those assigned redshifts, the agreement largely verifies that the 1/Vmax machinery and binning are self-consistent, rather than validating that the statistical redshift assignment is representative. Please add an external high-redshift test, for example using sources with secure spectroscopic or reliable photometric redshifts from a deep survey such as VLA-COSMOS, or explicitly present the high-redshift comparison as a consistency check rather than as validation.
  2. [§6.1, Fig. 14] The AGN/SFG separation is adjusted post hoc: after the BPT-based PMF transfer, all sources with L888 > 1e23.5 W Hz–1 are relabelled as AGN in §6.1. The subsequent agreement of the separate SFG and AGN LFs with Mauch & Sadler (2007) in Fig. 14 is therefore partly built in by this criterion rather than being a prediction of the method. Please show the SFG and AGN LFs both before and after this relabelling and quantify the fraction of sources moved, so the reader can assess how much of the improvement comes from the redshift modelling and how much from the luminosity threshold.
  3. [§7.1] The uniform-distribution experiment, while useful, actually weakens the high-redshift validation. Even with a flat input distribution in 0.5<z<6, the derived LFs agree with Smolčić et al. (2017) to within about 0.6 dex at the highest redshift bin. This indicates that the high-redshift RLF bins are insensitive to the input redshift distribution, so the agreement in Fig. 15 does not establish that the Smolčić-based assignment is physically realistic. The text should state this limitation explicitly when claiming that the LFs match well with measured LFs.
  4. [§3.1] The representativeness of the GEM I templates is only indirectly tested. The paper assumes that radio sources in the same (log S888, mr) bin share the GEM I redshift distribution, but GEM I is defined by the GAMA spectroscopic limit (mr<19.8), and no direct comparison is made between modelled GEM II redshifts and independent spectroscopic redshifts outside GEM I. The low-redshift agreement with Mauch & Sadler (2007) is promising, but a dedicated test, for example using withheld spectroscopic redshifts or an external overlapping survey, would substantially strengthen the method.
minor comments (3)
  1. [§7.1] There is a typo in the sentence 'in the absence of redshfits' near the end of §7.1; it should read 'redshifts'.
  2. [§2.2] The citation 'Hopkins et al., submitted' appears in the text but is not included in the reference list; please add it or replace it with a published reference.
  3. [Figures 3 and 4] The description in §3.1 of how mr and S888 vary across the panels of Figures 3 and 4 is confusing; please label the axes of the individual histograms or add a schematic so the bin layout is immediately clear to the reader.

Circularity Check

1 steps flagged · score 5.0 of 10

High-z validation is semi-circular: GEM III redshifts are drawn from Smolčić et al. (2017), the same work used as the LF benchmark.

  1. fitted input called prediction [§6.1 and §7.1 (Figure 15)]
    "To account for this, we choose a more realistic high redshift distribution for these radio galaxies. Smolčić et al. (2017) derived the 1.4 GHz RLF for AGN out to z ≈ 5.5 using the VLA-COSMOS observations and the COSMOS mutliwavelength data. We use this distribution and rederive the redshifts for the GEM III sources (as described in § 3.2)."

    The GEM III sources (~72% of the radio sample) are assigned redshifts by sampling the Smolčić et al. (2017) redshift distribution, and luminosities are then computed from those assigned redshifts. The paper's validation compares the resulting LF against the Smolčić et al. (2017) LF and reports that they 'follow each other well'. Because the input redshift distribution is taken from the same work that supplies the benchmark LF, the agreement partly verifies internal consistency of the 1/Vmax machinery rather than independently testing whether the statistical redshift assignment is representative.

full rationale

The low-redshift part of the paper is genuinely self-contained: GEM I redshifts are spectroscopic, GEM II redshifts are drawn from GEM I templates in (S888, mr) bins, and the comparison to Mauch & Sadler (2007) up to z=0.5 uses an external, independent local LF. That validation does not reduce to the input. The circularity concerns the high-redshift GEM III component: in §6.1 the authors adopt the Smolčić et al. (2017) redshift distribution as the input for the 28,821 sources without optical counterparts, and in §7.1 they compare the resulting LFs against Smolčić et al. (2017). The match is therefore partly by construction, since the redshift prior and the benchmark come from the same measurement. The paper's own §7.1 uniform-redshift test shows that a completely different input distribution also reproduces the Smolčić LF to within ~0.6 dex, indicating that the high-z bins are not strongly sensitive to the prior; this lowers the severity of the circularity but does not convert the Smolčić-versus-Smolčić comparison into an independent validation. The AGN relabelling at L888 MHz > 10^23.5 W Hz^-1 is a post hoc adjustment informed by the literature, adding flexibility when comparing the SFG/AGN split, but it is not the core circular step. There is no load-bearing self-citation chain or imported uniqueness theorem. Overall, the central low-z claim is independent, while the high-z match is partially circular, giving a score of 5.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central derivation rests on a small number of domain assumptions. The main free parameters are the fitted Gaussian redshift templates for each bin, the hand-chosen AGN radio luminosity threshold, and the assumed spectral index. There are no invented entities.

free parameters (4)
  • Gaussian mean and sigma for each (log S888, mr) bin = not tabulated; fitted per bin
    Fitted to GEM I redshift distributions in §3.1 to create the redshift templates for GEM II.
  • Gaussian mean and sigma for each log S888 bin (GEM III template) = not tabulated; fitted per bin
    Fitted to GEM I redshift distributions in §3.2 for GEM III before redistribution.
  • AGN radio luminosity threshold = 10^23.5 W Hz^-1
    Introduced in §6.1 to reclassify high-luminosity sources as AGN after the BPT-based classification underestimated high-z AGN LFs.
  • Spectral index α = -0.7
    Assumed for K-correction and the conversion of 1.4 GHz RLFs to 888 MHz (§5.2).
assumptions (6)
  • domain assumption Radio sources with similar (log S888, mr) or similar log S888 share redshift distributions with the GEM I reference sample.
    Stated in §3; the entire statistical redshift assignment depends on this.
  • domain assumption GAMA spectroscopy (mr<19.8) is complete enough to represent the low-redshift (z≤0.5) radio source population.
    Used to justify using GEM I as the redshift prior for GEM II and initially GEM III.
  • domain assumption GEM III sources (no optical counterpart) predominantly lie at z>0.5 and follow the Smolčić et al. (2017) COSMOS redshift distribution.
    Adopted in §6.1 to redistribute GEM III redshifts; not independently verified.
  • domain assumption Radio sources with L888 MHz > 10^23.5 W Hz^-1 are AGN.
    Imposed in §6.1 based on literature; directly changes the AGN/SFG classification.
  • domain assumption Completeness corrections from Gürkan et al. (2022) apply for the full EMU sample down to the 200 μJy flux limit.
    Used in Eq. 7; assumes the completeness function is accurately known and transferable.
  • standard math Standard 1/Vmax estimator (Schmidt 1968) and the Planck 2016 cosmology are valid.
    Background methodology.

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Pith. "Pith review of EMU/GAMA: A new approach to characterising radio luminosity functions." pith.science (2026). https://pith.science/paper/MXC7ZGSC

@misc{pith2026250511453,
  author       = {Pith},
  title        = {Pith review of: EMU/GAMA: A new approach to characterising radio luminosity functions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MXC7ZGSC}},
  note         = {Machine review of arXiv:2505.11453}
}
read the original abstract

This study characterises the radio luminosity functions (RLFs) for SFGs and AGN using statistical redshift estimation in the absence of comprehensive spectroscopic data. Sensitive radio surveys over large areas detect many sources with faint optical and infrared counterparts, for which redshifts and spectra are unavailable. This challenges our attempt to understand the population of radio sources. Statistical tools are often used to model parameters (such as redshift) as an alternative to observational data. Using the data from GAMA G23 and EMU early science observations, we explore simple statistical techniques to estimate the redshifts in order to measure the RLFs of the G23 radio sources as a whole and for SFGs and AGN separately. Redshifts and AGN/SFG classifications are assigned statistically for those radio sources without spectroscopic data. The calculated RLFs are compared with existing studies, and the results suggest that the RLFs match remarkably well for low redshift galaxies with an optical counterpart. We use a more realistic high redshift distribution to model the redshifts of (most likely) high redshift radio sources and find that the LFs from our approach match well with measured LFs. We also look at strategies to compare the RLFs of radio sources without an optical counterpart to existing studies.

Figures

Figures reproduced from arXiv: 2505.11453 by the authors.

Figure 1
Figure 1. The 888 MHz radio flux density distributions of EMU (black), GEM III (blue), GEM I (orange), and GEM II (green) samples. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Redshift 10 1 10 2 10 3 Count GEM I [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. 2D histograms of radio flux densities and r-band magnitudes, (a): GEM I, (b): GEM II. Each bin is colour-coded based on the number counts. In both panels, radio sources are preferentially distributed towards lower radio flux densities (below log S888 MHz = –2.5 Jy) and fainter r-band magnitudes (above mr = 16). One white-coloured bin in (b) corresponds to zero sources in that bin. 10 0 10 1 10 2 10 3 (a) 179 mr = 12… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: The redshift distribution of the GEM I sources corresponding to figure 3a. The x-axis shows the redshift, and the counts are shown in the y-axis. The number of sources in each bin is shown in the upper right corner. The mr and S888 values shown outside the panel corres…
Figure 5
Figure 5. Figure 5: The modelled redshift distribution of the GEM II sample (solid line). The redshift distribution of the GEM I sample used for modelling is also shown (dashed line). The blue dot-dashed line shows the GEM I redshift distribution modelled using GEM I spectroscopic redshif…
Figure 6
Figure 6. Figure 6: shows the radio flux density distributions of GEM I (dashed histogram) and GEM III (solid histogram) samples. GEM III is significantly larger in size than GEM I, reflect￾ing the fact that the full sample of radio sources far outstrips those with spectroscopic counterpa…
Figure 7
Figure 7. Figure 7: The redshift distribution of GEM I sources, used as the template for assigning redshifts to GEM III sources, arranged according to the bins in figure 6. The x-axis in each panel corresponds to redshift, and the y-axis shows the counts. The radio flux density increases …
Figure 8
Figure 8. Figure 8: The modelled redshift distribution of GEM III sources (solid line). The redshift distribution of GEM I sources used for modelling is also shown (dashed line). GEM II+GEM III sample is also divided into the same bins of radio flux densities. Probability mass functions (…
Figure 10
Figure 10. Figure 10: The redshift distributions of (a) the EMU sample (solid line) and the GEM I sample (dashed line), (b) EMU SFGs (solid line) and GEM I SFGs (dashed line), and (c) EMU AGN (solid line) and GEM I AGN (dashed line), before reassigning redshifts (see § 6.1) and AGN classif…
Figure 11
Figure 11. Figure 11: The figure shows the variation of the 888 MHz luminosities with redshift of (a) the entire EMU sample (blue circles) and GEM I sample (orange circles), (b) EMU star formers (blue circles) and GEM I star formers (orange circles), and (c) EMU AGN (blue circles) and GEM …
Figure 12
Figure 12. Figure 12: The 888 MHz RLFs of the EMU sample (blue circles) compared with GEM I+II SFGs (the stars) and GEM I+II AGN (the triangles). The error bars assume that the numbers are Poisson distributed. The solid and dashed lines correspond to the parametric fits of Mauch & Sadler (…
Figure 13
Figure 13. Figure 13: Solid line: the redshift distribution of the high redshift universe probed by Smolčić et al.(2017). This scaled up version in the range 0.5 < z < 6 is a more realistic representation that can be used to model the GEM III source redshifts. Dashed line: the uniform reds…
Figure 14
Figure 14. Figure 14: The 888 MHz RLFs derived from the one hundred realisations. The symbols and lines follow the previous figures. The LFs plotted here are the median of the one hundred estimated LFs, and the error bars correspond to the Poisson errors. It is remarkable to see that the S…
Figure 15
Figure 15. Figure 15: The 888 MHz RLFs derived using Smolčić et al. (2017) distribution (blue triangles), uniform distribution (red triangles), and 1.4 GHz RLFs derived by Smolčić et al. (2017) (magenta dots). The magenta dashed line shows the analytical fit to Smolčić et al. (2017) data w…

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