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Galaxy bias of radio AGN and star-forming galaxies from MIGHTEE and CMB lensing

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Joel Hamlett, Catherine L. Hale, Matt J. Jarvis, David Alonso, S. Lyla Jung, Natalia Stylianou, Rohan G. Varadaraj

Cosmology and Nongalactic Astrophysics · Submitted 16 Oct 2026 · 168 references

Pith's verdict: Solid measurement of radio source bias from MIGHTEE+ACT with a novel AGN/SFG decomposition, but the large errors and untested selection assumptions keep the constraints from being discriminating.

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arXiv ID2610.23567 (version 1)
Pith IDF7CELHM6, Pith's permanent record of this paper and its review
CitationCatherine L. Hale, David Alonso, Joel Hamlett, Matt J. Jarvis, Natalia Stylianou, Rohan G. Varadaraj, S. Lyla Jung. "Galaxy bias of radio AGN and star-forming galaxies from MIGHTEE and CMB lensing." arXiv:2610.23567 (2026). https://pith.science/paper/F7CELHM6
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The paper

The paper claims

Cross-correlation of MIGHTEE radio sources with CMB lensing yields a 4.3σ detection and separates the bias of AGNs and star-forming galaxies without individual classifications.

The reading

This paper establishes that the cross-correlation between faint radio sources (40 μJy at 1.4 GHz) from the MIGHTEE survey and CMB lensing maps from ACT can be measured at 4.3σ significance over 20 square degrees. By combining this cross-spectrum with auto-spectra of low- and high-redshift subsamples, the authors constrain the redshift evolution of the effective galaxy bias. Using radio luminosity functions to estimate the fraction of active galactic nuclei (AGNs) as a function of redshift, they then decompose the total bias into separate contributions from AGNs and star-forming galaxies (SFGs) without needing to classify individual sources. The result is a clean measurement of how each population traces dark matter, with AGNs consistently more biased than SFGs, and with statistical uncertainties that already distinguish the two components.

What carries the argument

The central object is the galaxy bias parameter b(z), defined by the linear relation Δ_g = b(z) Δ_m on large scales (k<0.15 $Mpc^{{-1}}$). The analysis uses three angular power spectra: the cross-spectrum $C^{{full,κ}}$_ℓ between the full radio sample and CMB lensing convergence, and the auto-spectra $C^{{low-z,low-z}}$_ℓ and $C^{{high-z,high-z}}$_ℓ of subsamples selected by Spitzer IRAC colour. The key machinery for separating populations is the number-weighted decomposition b_radio(z)=f_AGN(z) b_AGN(z) + [1-f_AGN(z)] b_SFG(z), where f_AGN(z) is derived from radio luminosity functions. The power spectra are estimated via the pseudo-C_ℓ method with transfer-function corrections, and parameters are inferred through nested sampling with Gaussian likelihood and analytic covariance.

Extended reading notes

Core claim

The authors measure the angular cross-power spectrum between 64,776 MIGHTEE radio sources above 40 μJy at 1.4 GHz and ACT DR6 CMB lensing convergence maps, detecting the signal at 4.3σ. Jointly fitting this cross-spectrum with auto-spectra of low-redshift (z_eff≈0.68) and high-redshift (z_eff≈1.46) samples, they find that the effective bias of the combined population is best described by a constant-amplitude model b(z)=1.63/D(z) or a linear model b(z)=0.49+1.62z, with both fitting comparably. Using the 1.4 GHz radio luminosity functions of Thykkathu et al. (2026) to estimate the AGN fraction f_AGN(z), they further model the AGN and SFG contributions separately, obtaining b_AGN(z)=2.60/D(z) and b_SFG(z)=0.52/D(z) for the constant-amplitude model. Incorporating an external prior on SFG bias from Hale et al. (2025b) tightens these to b_AGN(z)=1.96/D(z) and b_SFG(z)=0.90/D(z). The key insight is that the redshift evolution of the effective bias largely reflects the changing mixture of AGNs and SFGs with redshift, rather than intrinsic evolution of a single population.

Load-bearing premise

The AGN fraction as a function of redshift, derived from the 1.4 GHz radio luminosity functions of Thykkathu et al. (2026), accurately represents the composition of the MIGHTEE sample down to 40 μJy, despite the fact that the luminosity functions were derived from a different (Early Science) dataset and have steeper faint-end slopes than alternative models.

Editorial extensions

If this is right

  • Radio AGNs inhabit more massive dark matter haloes than SFGs at all redshifts probed (z∼0.2–2.5), consistent with AGN feedback models that place AGNs in dense environments.
  • The method of decomposing bias using luminosity functions can be applied to future wide-area radio surveys such as LoTSS and EMU, where deep multi-wavelength data for individual classifications are unavailable.
  • The measured AGN and SFG biases provide input for multi-tracer techniques that reduce cosmic variance in large-scale structure constraints.
  • The weak Bayesian evidence favouring constant-amplitude over linear evolution means that larger survey areas or deeper data are required to distinguish intrinsic bias evolution from population-mix evolution.

Reading between the lines

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

  • If the luminosity function slopes are revised by deeper source counts, the inferred AGN bias could shift: a flatter faint-end slope (as in Novak et al. 2018) produces a lower AGN bias, as the authors already test in Appendix D.
  • The steep linear model for the effective bias (b_1=1.62) implies that at z>2, the radio population may be dominated by the rarest, most massive haloes; this prediction could be tested with deeper spectroscopic follow-up.
  • The technique could be extended to split AGN bias into HERG and LERG components by using excitation-class luminosity functions, potentially revealing different halo mass trends.
  • The small sky coverage (20 deg^2) limits the constraining power on models beyond constant amplitude; a full-sky survey like SKA would reduce uncertainties by an order of magnitude, enabling decisive model selection.
Original abstract

Radio galaxies play a significant role in galaxy evolution through feedback mechanisms, making it important to characterize the environments in which they reside. We measure the cross-correlation between the positions of radio sources in the MIGHTEE survey and cosmic microwave background lensing measurements from the Atacama Cosmology Telescope over $20\ {\rm deg}^2$ to flux densities $S_{\rm 1.4\,GHz}>40\ {\rm \mu Jy}$, detecting the signal at $\sim4\sigma$ significance. By combining this with auto-correlation measurements of low- and high-redshift radio samples, we constrain the redshift evolution of the galaxy bias parameter, $b(z)$. Fitting different models for the redshift evolution of the bias, we find that both a model inversely proportional to the linear growth factor, $b(z) = (1.63^{+0.19}_{-0.22})/D(z)$, and a model where bias grows linearly with redshift, $b(z) = (0.49^{+0.44}_{-0.32}) + (1.62^{+0.37}_{-0.51})z$, provide comparably good fits to the data, with the current measurements unable to distinguish between them. Using a radio luminosity function, we estimate the fraction of sources that are active galactic nuclei (AGNs) or star-forming galaxies (SFGs) as a function of redshift, and model the individual contributions of AGNs and SFGs to the total bias. This approach allows us to measure the bias of AGNs and SFGs without individual source classifications. Though no single model is favoured significantly, the best-fitting model gives $b_{\rm AGN}(z) = (2.60^{+0.65}_{-0.91})/D(z)$ compared to $b_{\rm SFG}(z) = (0.52^{+0.47}_{-0.34})/D(z)$. Incorporating SFG bias measurements from previous work as a prior tightens these constraints to $b_{\rm AGN}(z) = (1.96^{+0.37}_{-0.40})/D(z)$ and $b_{\rm SFG}(z) = (0.90^{+0.06}_{-0.06})/D(z)$.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-20: 1 request, 7,083 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Radio galaxies play a significant role in galaxy evolution through feedback mechanisms, making it important to characterize the environments in which they reside. We measure the cross-correlation between the positions of radio sources in the MIGHTEE survey and cosmic microwave background lensing measurements from the Atacama Cosmology Telescope over $20\ {\rm deg}^2$ to flux densities $S_{\rm 1.4\,GHz}>40\ {\rm \mu Jy}$, detecting the signal at $\sim4\sigma$ significance. By combining this with auto-correlation measurements of low- and high-redshift radio samples, we constrain the redshift evolution of the galaxy bias parameter, $b(z)$. Fitting different models for the redshift evolution of the bias, we find that both a model inversely proportional to the linear growth factor, $b(z) = (1.63^{+0.19}_{-0.22})/D(z)$, and a model where bias grows linearly with redshift, $b(z) = (0.49^{+0.44}_{-0.32}) + (1.62^{+0.37}_{-0.51})z$, provide comparably good fits to the data, with the current measurements unable to distinguish between them. Using a radio luminosity function, we estimate the fraction of sources that are active galactic nuclei (AGNs) or star-forming galaxies (SFGs) as a function of redshift, and model the individual contributions of AGNs and SFGs to the total bias. This approach allows us to measure the bias of AGNs and SFGs without individual source classifications. Though no single model is favoured significantly, the best-fitting model gives $b_{\rm AGN}(z) = (2.60^{+0.65}_{-0.91})/D(z)$ compared to $b_{\rm SFG}(z) = (0.52^{+0.47}_{-0.34})/D(z)$. Incorporating SFG bias measurements from previous work as a prior tightens these constraints to $b_{\rm AGN}(z) = (1.96^{+0.37}_{-0.40})/D(z)$ and $b_{\rm SFG}(z) = (0.90^{+0.06}_{-0.06})/D(z)$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Radio galaxies play a significant role in galaxy evolution through feedback mechanisms, making it important to characterize the environments in which they reside. background 1.00 0.04 0.02 asserted 1.00
s1 We measure the cross-correlation between the positions of radio sources in the MIGHTEE survey and cosmic microwave background lensing measurements from the Atacama Cosmology Telescope over $20\ {\rm deg}^2$ to flux densities $S_{\rm 1.4\,GHz}>40\ {\rm \mu Jy}$, detecting the signal at $\sim4\sigma$ significance. method 0.46 0.98 0.07 asserted 1.00
s2 By combining this with auto-correlation measurements of low- and high-redshift radio samples, we constrain the redshift evolution of the galaxy bias parameter, $b(z)$. method 0.56 0.96 0.09 asserted 1.00
s3 Fitting different models for the redshift evolution of the bias, we find that both a model inversely proportional to the linear growth factor, $b(z) = (1.63^{+0.19}_{-0.22})/D(z)$, and a model where bias grows linearly with redshift, $b(z) = (0.49^{+0.44}_{-0.32}) + (1.62^{+0.37}_{-0.51})z$, provide comparably good fits to the data, with the current measurements unable to distinguish between them. result 1.00 0.97 0.38 asserted 0.99
s4 Using a radio luminosity function, we estimate the fraction of sources that are active galactic nuclei (AGNs) or star-forming galaxies (SFGs) as a function of redshift, and model the individual contributions of AGNs and SFGs to the total bias. method 0.94 0.96 0.04 asserted 0.99
s5 This approach allows us to measure the bias of AGNs and SFGs without individual source classifications. method 0.53 0.84 0.05 asserted 0.95
s6 Though no single model is favoured significantly, the best-fitting model gives $b_{\rm AGN}(z) = (2.60^{+0.65}_{-0.91})/D(z)$ compared to $b_{\rm SFG}(z) = (0.52^{+0.47}_{-0.34})/D(z)$. result 1.00 0.95 0.28 asserted 0.91
s7 Incorporating SFG bias measurements from previous work as a prior tightens these constraints to $b_{\rm AGN}(z) = (1.96^{+0.37}_{-0.40})/D(z)$ and $b_{\rm SFG}(z) = (0.90^{+0.06}_{-0.06})/D(z)$. result 1.00 0.89 0.28 asserted 1.00

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from analysis of existing data 0.52.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. 3.6 − 4.5 𝜇m colour against redshift for radio sources cross￾matched with Spitzer sources that overlap with the multi-wavelength data. Orange points are sources with spectroscopic redshifts, and blue points are the peak redshift PDF values for sources with photometric data. The black horizontal line is the divide used to select the low- and high-redshift samples. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 z 0 1 2 3 4 N(z) = 1 0 4 / W full low-z high-z
Figure 2. Redshift distributions of radio sources overlapping with the multi-wavelength data (full), and for the low- and high-redshift subsamples (low/high-𝑧). The shaded regions show the 16th and 84th percentiles of the redshift distribution realizations. The dashed black line is proportional to the CMB lensing kernel, 𝑊𝜅 , which peaks at 𝑧 ∼ 1.9. using a combination of the automated Likelihood Ratio method (de Ruiter et al. 1977; Sutherland & Saunders 1992, see Section 3.1.1 for further discussion of this method), and manual host identification by MIGHTEE team members using the MIGHTEE zoo…
Figure 3. Various maps for the full 𝑆1.4 GHz > 40 𝜇Jy radio sample used in this analysis. From left to right, the columns show the radio galaxy number count maps, 𝑁g, the masks, the galaxy weights maps, Wg, and the galaxy overdensity maps, 𝛿g, for each of the MIGHTEE fields (rows). The numbers on the axes are the right ascensions and declinations of the fields in degrees. All colour bars are linear in scale. NaMASTER), with the input convergence field, 𝜅𝑖 (masked with 𝑤g). Averaging over all simulations, we compute the transfer function: 𝑇 (ℓ) = 1 𝑁sim Í𝑁sim 𝑖=1 𝐶 𝜅ˆ𝑖 𝜅𝑖 ℓ 𝐶 𝜅 𝜅 ℓ,th , (19)…
Figure 4. To correct the measured cross-spectrum, we simply divide by 𝑇 (ℓ). We do not propagate the uncertainties on 𝑇 (ℓ) as they are much smaller than those on the measured spectra and contribute ≲ 0.1 per cent to the total uncertainty. 4.4 Noise bias The measured auto-spectra contain additive noise contributions that must be removed to obtain the underlying clustering signal. For the galaxy auto-spectra, the dominant contribution is Poissonian shot￾noise arising from the discrete sampling of the density field. This contribution predominantly affects small angular scales (high ℓ), where…
Figure 5. Correlation matrix, Corr𝑖 𝑗, for the cross-spectrum between radio sources and the CMB lensing convergence map (full-𝜅), and the auto-spectra of the low- and high-redshift samples. 4.5.2 Covariance We estimate the analytic Gaussian covariance using NaMaster, fol￾lowing García-García et al. (2019). This approach models both the CMB lensing convergence and the galaxy overdensities as Gaussian random fields, which has been shown to be a good approximation for the scales studied here (Barreira et al. 2018; Nicola et al. 2020). The covariance calculation requires an input model for the…
Figure 6. shows the measured cross-spectrum between the full radio sample and CMB lensing convergence,𝐶ˆ full,𝜅 ℓ , and the auto-spectra of the low- and high-redshift sub-samples, 𝐶ˆ low-𝑧,low-𝑧 ℓ and 𝐶ˆ high-𝑧,high-𝑧 ℓ . In order to establish the statistical significance of the cross￾spectrum detection, we fit a single parameter model of the form 𝐶ˆ full,𝜅 ℓ = 𝑏𝐶full,𝜅 ℓ |𝑏0=1, (32) as in Allison et al. (2015); Alonso et al. (2021). Here, 𝑏 is a free amplitude parameter and 𝐶 full,𝜅 ℓ is the predicted cross-spectrum for the constant bias model with 𝑏0 = 1. The null hypothesis of no…
Figure 7. Measured angular power spectrum of the cross-correlation between radio sources and a rotated lensing convergence map. The shaded grey region represents the 1𝜎 uncertainties when fitting a constant amplitude, 𝐴null, to these measurements which is consistent with zero (dashed black line). 5.3 Measurement robustness tests In this section, we perform a series of sanity checks described in Alonso et al. (2021) to assess the stability of the measured power spectra against analysis choices and potential residual systematics. First, we verify that the results are robust against the choice…
Figure 9. Galaxy bias constraints obtained from fitting to the low- and high￾redshift radio auto-power spectra under different systematic tests. The fiducial measurement is compared to fits excluding the lowest multipole bin (to test for large-scale systematics associated with survey pointings) and fits where a constant offset in the power spectrum is marginalized over to account for potential mis-estimation of the shot-noise contribution. where 1 is a vector of ones with length equal to the number of band powers. The resulting galaxy bias values for the fiducial fit, the low-ℓ truncated fit,…
Figure 10. shows the evolution of the best-fitting bias models against redshift. The linear model favours a steeper slope than the constant amplitude model with a gradient 𝑏1 = 1.62+0.37 −0.51 and a low normalization 𝑏0 = 0.49+0.44 −0.32. The constant amplitude model corre￾sponds to a galaxy overdensity that remains fixed on linear scales, so interpreted physically, a steeper evolution corresponds to a radio population whose overdensity decreases towards later times. This suggests that the radio sources at high redshift inhabit rarer and more massive dark matter haloes. However, this…
Figure 11. Best-fitting bias evolution for AGNs (pink and red) and SFGs (green and blue) for the four models considered: constant bias (top left), constant amplitude (top right), passive (bottom left) and linear (bottom right). Solid curves show the posterior median predictions, with shaded bands indicating the 1𝜎 uncertainties, when fitting without using the SFG bias values of Hale et al. (2025b) (blue diamonds) as a prior. The dashed and dotted lines are the median posterior predictions and 1𝜎 uncertainties from fitting with the prior. Also shown are the bias values for LERGs (dark grey…

Showing 10 of the paper's 11 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.23567 by the authors.

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