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Spectroscopic classification of 251k LoTSS radio sources shows LERGs accrete below 1% of Eddington and HERGs above it.

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2026-07-10 17:26 UTC pith:D7TA5NNA

load-bearing objection Largest high-confidence spectroscopic radio catalogue to date; LERG/HERG accretion split reconfirmed cleanly, with the known [OIII] bolometric-correction caveat already flagged by the authors. the 2 major comments →

arxiv 2607.07818 v1 pith:D7TA5NNA submitted 2026-07-08 astro-ph.GA

The DESI View of the Faint Radio Source Population in LoTSS DR2

M. I. Arnaudova , L. R. Holden , D. J. B. Smith , P. N. Best , R. Kondapally , K. J. Duncan , A. Bushi , S. Das
show 5 more authors
S. R. Flury C. L. Hale M. J. Hardcastle H. J. A. Rottgering S. Shenoy
This is my paper
classification astro-ph.GA
keywords radio galaxiesLERGHERGstar-forming galaxiesDESILoTSSEddington ratiospectroscopic classification
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper builds the largest high-confidence spectroscopic classification of the faint radio sky yet, matching 251,413 LoTSS DR2 sources to DESI DR1 spectra and assigning each a probability of being a star-forming galaxy, radio-quiet AGN, LERG or HERG. At the 90% probability cut the sample contains 68,820 SFGs, 32,288 RQ AGN, 35,210 LERGs and 3,085 HERGs. With that sample the authors recover, at higher statistical power than earlier work, the classic accretion dichotomy: LERGs sit below ~1% of the Eddington limit while HERGs sit above it. They also isolate a small high-accreting LERG tail whose stacked spectra show star-forming lines, showing that [OIII]-based accretion rates can be contaminated by host star formation. The catalogue and method are offered as a foundation for SKA-era studies of how star formation and black-hole accretion jointly shape galaxies.

Core claim

When radio-excess, BPT, modified MEx and [OIII] equivalent-width diagnostics are combined with Monte-Carlo error propagation on DESI spectra, LERGs and HERGs remain cleanly separated in Eddington-scaled accretion rate out to z~1, with LERGs peaking below 1% Eddington and HERGs above it; a minority high-accreting LERG subpopulation nevertheless displays star-forming spectral features that complicate the interpretation of their accretion rates.

What carries the argument

A hierarchical probabilistic classifier that first applies radio-excess plus BPT (or modified MEx at higher z), then recovers additional weak-lined LERGs with EW[OIII]<3 Å, all inside 1,000 Monte-Carlo realisations that propagate flux, mass and aperture uncertainties into class probabilities.

Load-bearing premise

The conversion of [OIII] luminosity into bolometric luminosity (and thence Eddington ratio) is assumed to be reliable for both LERGs and HERGs even though the paper notes the correction is less secure for LERGs and can be inflated by star formation.

What would settle it

X-ray or mid-infrared bolometric luminosities independent of [OIII] that place the high-accreting LERG tail firmly below 1% Eddington would falsify the claim that those objects are genuinely high-accretion systems rather than star-formation-contaminated LERGs.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper presents a probabilistic spectroscopic classification of 251,413 LoTSS DR2 radio sources cross-matched with DESI DR1 spectra. Combining a radio-excess diagnostic (re-derived L_Hα–L_144 relation), BPT and modified MEx diagrams, and an EW[OIII] cut, with Monte Carlo propagation of flux and mass uncertainties, the authors produce class probabilities for SFGs, RQ AGN, LERGs and HERGs. At a 90% probability threshold they report 68,820 SFGs, 32,288 RQ AGN, 35,210 LERGs and 3,085 HERGs—the largest high-confidence spectroscopic radio sample to date. They then show that LERGs and HERGs occupy distinct Eddington-scaled accretion-rate distributions (typically below and above ~1% of Eddington, respectively) and identify a minority high-λ_Edd LERG tail whose stacked spectra exhibit star-forming features.

Significance. If the classifications and accretion-rate dichotomy hold, the work supplies the largest spectroscopically classified faint-radio catalogue available and a clear foundation for SKA-era demographic studies. Strengths include transparent Monte Carlo treatment of negative fluxes and warning flags, hierarchical use of multiple diagnostics, explicit quantification of DESI selection (BGS vs LRG), and a direct ~95% agreement check against the Drake et al. SDSS classifications on jointly classified sources. The catalogue and stacked spectra will be of immediate community value.

major comments (2)
  1. Section 6.1 and the strongest claim rest on λ_Edd = log10[(L_bol + L_mech)/L_Edd] with L_bol = 3500 L_[OIII] (Heckman et al. 2004) and the Häring & Rix (2004) M_BH–M_* relation applied uniformly. The manuscript itself notes that the [OIII] bolometric correction is less reliable for LERGs and that high-λ_Edd LERGs show star-forming features that can inflate L_[OIII] (Sections 6.1, 6.3; stacked spectra in Fig. 11 and BPT locations in Fig. 12). The dichotomy remains visible even when L_mech is omitted, and EW-selected LERGs are correctly treated as upper limits, but the paper should quantify how much the high-λ_Edd LERG tail shrinks under plausible alternative bolometric corrections or X-ray priors, or else state more explicitly that the absolute scale of λ_Edd for LERGs is model-dependent while the relative separation is robust.
  2. Section 4.1: dust-corrected Hα luminosities for the high-z sample (and for low-S/N low-z sources) are assigned from UVJ-binned A_V medians measured on the low-z Balmer-decrement sample. The authors validate the trend only qualitatively with stacked Hγ/Hβ and note that ~10% of sources fall outside the bins. Because the radio-excess cut (Eq. 3) and therefore the LERG/HERG split depend on this A_V assignment, a quantitative residual comparison (or a sensitivity test that varies the UVJ A_V by its 16–84 percentile width) is needed to show that the high-z LERG/HERG numbers and the accretion-rate distributions are not driven by the UVJ mapping.
minor comments (5)
  1. Table 2 and Section 4.4: the large unclassified fraction (79,314 at 90%) is expected given the conservative threshold, but a short statement of how many of these become classifiable at 70% (already given in the text) would help readers decide which threshold to adopt for their science.
  2. Figure 1 right panel and Section 5.2: the DESI selection effects (BGS vs LRG) are well quantified; a brief note that WEAVE-LOFAR will remove the optical bias would strengthen the forward-looking claim in the conclusions.
  3. Section 3.4: the Type-1 flag (FWHM_Hβ > FWHM_[OIII] in ≥99% of realisations and FWHM_Hβ > 1000 km s−1) is sensible; a one-sentence comparison of the recovered Type-1 fraction with literature DESI or SDSS Type-1 rates would reassure readers that the cut is not overly aggressive.
  4. Equation (3) and the accompanying text: the radio-excess offset is given as 15.00(±0.02); stating whether this uncertainty is propagated into the Monte Carlo realisations (or only the line fluxes and masses) would clarify the final probability uncertainties.
  5. Minor typographical issues: occasional missing spaces around units and a few long sentences in Sections 4.4 and 6.1 that could be split for readability.

Circularity Check

1 steps flagged

No significant circularity: classification diagnostics and Eddington-ratio scalings are external literature relations applied to new DESI+LoTSS data; self-citations supply methods only.

specific steps
  1. self citation load bearing [Section 4.2 / Eq. (4) and Section 1]
    "the modified version incorporates a redshift-dependent offset … defined as: log10 M = log10 M−[1−exp(−1.2z)]. … by adopting the method introduced by A25, in which a modified Mass–Excitation (MEx) diagram is used"

    The redshift-dependent MEx offset and the hierarchical probabilistic scheme are taken from the authors' own prior paper (A25). This is a methodological self-citation, not a uniqueness claim that forces the LERG/HERG dichotomy or the sample sizes; the offset is an empirical correction for mass–metallicity evolution already discussed in external literature (Henry et al. 2021; Cleri et al. 2023). It does not make the final classifications tautological.

full rationale

The paper's central results (sample sizes at >90% probability and the LERG/HERG λ_Edd dichotomy) are obtained by applying well-known external demarcation lines (Kauffmann et al. 2003b, Cid Fernandes et al. 2010, Juneau et al. 2014, Laing et al. 1994) and scaling relations (Heckman et al. 2004 L_bol=3500 L_[OIII], Häring & Rix 2004 M_BH–M_*, Cavagnolo et al. 2010 L_mech) to a new spectroscopic sample. The radio-excess threshold is re-derived as a 99th-percentile cut on the present data, which is a standard empirical procedure rather than a free parameter tuned to force the final claim. Self-citations to A25 and Dr24 provide the hierarchical Monte-Carlo framework and the modified MEx offset, but those works themselves rest on the same external diagnostics; they do not supply the target numerical results. The high-accreting LERG tail is reported as an observational finding with explicit caveats (upper limits, possible SF contamination of [OIII]), not as a prediction derived from the classification inputs. No equation reduces by construction to its own fitted input, and no uniqueness theorem is imported to forbid alternatives. Score 1 reflects only the minor, non-load-bearing self-citation of method papers by overlapping authors.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central scientific claims rest on standard emission-line diagnostics, literature scaling relations for bolometric luminosity and black-hole mass, and a re-derived but conventional radio-excess threshold. No new physical entities are postulated; free parameters are limited to the percentile cuts and the adopted L_bol conversion factor.

free parameters (4)
  • radio-excess demarcation offset = 15.00 ± 0.02
    log10(L_144) > log10(L_Hα_corr) + 15.00, set to the 99th percentile of the SFG Gaussian; small change (±0.08) when restricted to BPT-SFGs.
  • L_bol / L_[OIII] conversion factor = 3500
    Fixed literature value 3500 from Heckman et al. (2004); known to have large scatter and to be less reliable for LERGs.
  • EW_[OIII] LERG/HERG cut = 3 Å
    Adopted 3 Å from Laing et al. (1994) to recover weak-lined LERGs.
  • probability threshold for high-confidence sample = 0.90
    User-chosen 90% cut that defines the headline sample sizes; results change quantitatively but not qualitatively at 70%.
axioms (4)
  • domain assumption The Kauffmann et al. (2003b) and Cid Fernandes et al. (2010) lines on the BPT diagram cleanly separate SFGs, RQ AGN, LERGs and HERGs.
    Invoked throughout §4.2; standard but known to have composite and LINER ambiguities.
  • domain assumption L_bol = 3500 L_[OIII] and the Häring & Rix M_BH–M_* relation yield usable Eddington ratios for both accretion modes.
    Central to §6.1; paper itself flags reduced reliability for LERGs.
  • ad hoc to paper UVJ colours can be used to assign A_V (and therefore dust-corrected Hα) for the high-z sample where Balmer decrement is unavailable.
    §4.1; validated only qualitatively with stacked Hγ/Hβ.
  • domain assumption Spectral index α = −0.7 for converting 144 MHz to 1.4 GHz luminosities.
    Used for L_mech and L_144 throughout.

pith-pipeline@v1.1.0-grok45 · 37476 in / 2962 out tokens · 28060 ms · 2026-07-10T17:26:20.225829+00:00 · methodology

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read the original abstract

The faint radio-source population includes galaxies dominated by both star formation (SF) and active galactic nuclei (AGN), which are two key processes shaping galaxy evolution. To investigate this population, we probabilistically classified 251,413 radio sources from the second data release of the LOFAR Two-metre Sky Survey (LoTSS DR2) using spectroscopic data from the first release of the Dark Energy Spectroscopic Instrument (DESI DR1). Our classification method includes: (i) the identification of radio excess relative to SF, (ii) the Baldwin, Philips & Terlevich (BPT) diagram, (iii) a modified Mass Excitation (MEx) diagram, and (iv) the [OIII]5007 equivalent width. These are combined with Monte Carlo methods to estimate the probability that each source is a star-forming galaxy (SFG), a radio-quiet AGN (RQ AGN), or a low- or high-excitation radio galaxy (LERG or HERG), allowing various thresholds to be applied depending on science goals. Considering classifications above a 90 per cent probability threshold, we identify 68,820 SFGs, 32,288 RQ AGN, 35,210 LERGs and 3,085 HERGs, representing the largest radio sample to date with high-confidence spectroscopic classifications. Using this sample, we show with higher statistical power than previous studies that LERGs typically accrete below 1 per cent of the Eddington limit and HERGs above it. We also identify a small subset of high-accreting LERGs whose stacked spectra reveal prominent star-forming features, highlighting difficulties in interpreting their accretion properties. Our results demonstrate the power of large spectroscopic samples to characterise the radio-source population, providing a foundation for studies in the SKA era.

Figures

Figures reproduced from arXiv: 2607.07818 by A. Bushi, C. L. Hale, D. J. B. Smith, H. J. A. Rottgering, K. J. Duncan, L. R. Holden, M. I. Arnaudova, M. J. Hardcastle, P. N. Best, R. Kondapally, S. Das, S. R. Flury, S. Shenoy.

Figure 1
Figure 1. Figure 1: Left panel: Sky coverage of DESI DR1 and LoTSS DR2. The grey region indicates all DESI DR1 sources, the black lines show the LoTSS DR2 footprint, while the colour scale represents the number density of sources in our classification sample. Right panel: The redshift-radio rest-frame luminosity plane for all radio sources with a multi-wavelength counterpart (in grey), the sources with spectroscopic informati… view at source ↗
Figure 2
Figure 2. Figure 2: An example fit of a random galaxy spectrum using WL-SLAYER. The observed data are shown in grey, the continuum model in orange, the emission-line model in blue, and the total best-fitting model in black. The top panel displays the fit to the full spectrum, which is used for continuum subtraction, while the bottom panels focus on the H𝛽, [Oiii]𝜆𝜆4959, 5007, and H𝛼+[Nii] complexes to highlight the emission-l… view at source ↗
Figure 3
Figure 3. Figure 3: FWHM values for the total [O III]𝜆5007 and H𝛽 line profiles measured by WL-SLAYER. The probability density function for the objects in our sample that are identified as likely Type 1 AGN by our flag_type1 flag are shown as solid blue contours, while objects not flagged as Type 1 AGN are shown as dashed red contours.. Contours contain 10, 30, 50, 70, and 90 per cent of the total objects for each flag value … view at source ↗
Figure 4
Figure 4. Figure 4: The rest-frame 𝑈 − 𝑉 versus 𝑉 − 𝐽 (the 𝑈𝑉 𝐽 diagram) for all sources in our sample that satisfy the CIGALE SED-fitting goodness-of-fit criteria and have a 5𝜎 detection in H𝛽 and H𝛼, colour-coded based on the 50th percentile of the Balmer-decrement-derived A𝑉 distribution for that bin (left), as well as the spread in those values as estimated by half the difference between the 16th and 84th percentile (righ… view at source ↗
Figure 5
Figure 5. Figure 5: The left panel shows the BPT diagram for sources classified at >90 per cent confidence, where the demarcation line from Kauffmann et al. (2003b) separates sources into SFGs (dashed blue contours) and RQ AGN (solid red contours), while the combination of the Kauffmann et al. (2003b) line and the diagnostic line from Cid Fernandes et al. (2010) distinguishes LERGs (purple dots) from HERGs (orange dots). The … view at source ↗
Figure 6
Figure 6. Figure 6: The distribution of EW[OIII] for sources classified at >90 per cent confidence as LERGs and HERGs using the BPT and MEx classification schemes. The vertical solid, dashed and dotted lines denote the suggested divisions from Laing et al. (1994) at EW[OIII]=3Å, Best & Heckman (2012) at EW[OIII]=5Å, and Tadhunter et al. (1998) at EW[OIII]=10Å, respectively. natural way to incorporate informative priors that m… view at source ↗
Figure 7
Figure 7. Figure 7: Confusion matrix comparing the spectroscopic classifications with >90 per cent confidence between this work (rows) and Dr24 (columns) for the common DESI and SDSS LOFAR sources. Each cell represents the level of agreement based on Dr24 in percentages, where the number of sources in each cell is also included. The percentages in brackets are calculated for the subset of sources with classifications (that is… view at source ↗
Figure 8
Figure 8. Figure 8: The distributions of sources classified using our > 90 per cent reliability threshold (solid lines and step histograms) and those from Dr24 (dashed lines and filled histograms) as a function of redshift (top left), 144 MHz flux density (top right), radio luminosity (bottom left), and stellar mass (bottom right). Each panel shows the distributions for the different classes: SFGs (blue), radio-quiet AGN (ora… view at source ↗
Figure 9
Figure 9. Figure 9: The influence of optical selection criteria on the sampling of the faint radio source population, illustrated by the distributions of sources classified above our > 90 per cent reliability threshold in the Bright Galaxy Survey (BGS; solid lines and step histograms) and the Luminous Red Galaxy sample (LRG; dashed lines and filled histograms). Panel layout, line styles, and shading are the same as in [PITH_… view at source ↗
Figure 10
Figure 10. Figure 10: The log Eddington-scaled accretion rate distributions for LERGs (blue), HERGs (orange), and radio-excess sources (grey; including objects that cannot be confidently assigned to either class) that satisfy our > 90 per cent threshold. For the LERG population, the distributions are additionally sepa￾rated by classification method: the dashed line indicates sources classified via the BPT/MEx diagnostics, whil… view at source ↗
Figure 11
Figure 11. Figure 11: The stacked spectra of LERGs (top panel), HERGs (second panel), radio-excess sources that cannot be classified at > 90 per cent confidence into the two classes (or RX_Unc, third panel) and the whole radio excess population (bottom panel) shown as a function of log Eddington-scaled accretion rate, as indicated by the colourbar. Each stack represents the median of all spectra within a given accretion-rate b… view at source ↗
Figure 12
Figure 12. Figure 12: The BPT diagram for the stacked spectra of LERGs (squares), HERGs (diamonds), radio-excess sources that remain unclassified (or RX_Unc; cross), and the total radio-excess sources (circles), colour coded by the log Eddington-scaled accretion rate. The diagnostic lines delineating the SFG, LINER and Seyfert region are from Kauffmann et al. (2003b) and Cid Fernandes et al. (2010) and are denoted in the legen… view at source ↗
Figure 13
Figure 13. Figure 13: The radio excess (left), BPT (middle) and MEx diagnostic diagrams (right) for the high-accreting LERGs (𝜆Edd>-1.5), as denoted by the colour bar. The grey contours encompass 10, 50 and 90 per cent of the low-accreting LERGs. The demarcation lines are the ones used in the classification scheme discussed in section 4, and are denoted by the legend in each panel. For reference, the total number of high-accre… view at source ↗
Figure 1
Figure 1. Figure 1: The Eddington-scaled accretion rate distributions for LERGs (blue), HERGs (orange), and all radio-excess sources (grey), separated into the sub￾samples belonging to the DESI BGS (top) and LRG (bottom) survey selec￾tions. The arrows indicate that the LERG accretion rates should be considered upper limits due to the 3𝜎 upper limit on the [Oiii] emission, while the shaded regions indicate binomial uncertainti… view at source ↗

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