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arxiv: 2606.07730 · v1 · pith:3AE33OBJnew · submitted 2026-06-05 · 🌌 astro-ph.HE

The X-ray-to-UV relation does not evolve in homogeneous quasar samples

G. Risaliti , E. Lusso , E. Nardini , C. Niccolai , M. Ralowski , A. Sacchi , A. Shlentsova , M. Signorini
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B. Trefoloni
This is my paper

Pith reviewed 2026-06-27 20:54 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords quasarsX-ray-UV relationredshift evolutionEddington biashomogeneous sampledistance indicatorsSDSSXMM-Newton
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The pith

The X-ray-to-UV relation in quasars shows no evolution from redshift 0.7 to 5 in homogeneous samples.

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

The paper constructs a homogeneous sample of roughly 2000 quasars at redshifts 0.7 to 5 by matching SDSS DR16 with XMM-Newton 4XMM-DR14 data. Strict filters are applied to remove effects from extinction, absorption, broad absorption lines, radio emission, low-redshift galactic contamination, and shallow X-ray detections that introduce Eddington bias. Analysis of this sample reveals that the X-ray-to-UV luminosity relation maintains a constant slope of 0.58 with 0.01 uncertainty and a scatter of 0.15 dex over the full redshift range. This constancy implies that the relation is an intrinsic property of quasars rather than one that changes with cosmic time.

Core claim

In this homogeneous quasar sample spanning z=0.7-5, the X-ray-to-UV relation is constant with a mean slope of 0.58 ± 0.01 and a dispersion of 0.15 dex. The findings confirm the intrinsic stability of this relation over cosmic time when both homogeneity and robust Eddington bias corrections are applied to flux-limited samples. Any resulting evolutionary trend in the X-ray-to-UV relation, especially in the form of a slope flattening, is therefore either a largely spurious effect, or the result of mixing populations of quasars with intrinsically different spectral properties.

What carries the argument

The non-linear X-ray-to-UV relation, a correlation between X-ray and ultraviolet luminosities in quasars used to estimate distances.

If this is right

  • The relation can be used to estimate distances to high-redshift quasars without redshift-dependent adjustments.
  • Homogeneity in sample selection is required to avoid spurious evolutionary trends in flux-limited surveys.
  • The effect of Eddington bias grows with redshift because SDSS UV data are deeper than typical X-ray observations.
  • Slope flattening seen in less controlled samples arises from selection effects or population mixing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The fixed relation supports treating quasars as standard candles for cosmological measurements at early times.
  • The same bias-control methods could be applied to other multi-band correlations to test for hidden evolution.
  • Future surveys with matched depth across wavelengths could reduce the 0.15 dex scatter and tighten distance precision.

Load-bearing premise

That the five selection criteria fully eliminate Eddington bias and any mixing of quasar populations with different intrinsic properties.

What would settle it

Finding a statistically significant change in slope or dispersion when the identical selection criteria are applied to an independent quasar sample that has uniform depth in both X-ray and UV bands.

Figures

Figures reproduced from arXiv: 2606.07730 by A. Sacchi, A. Shlentsova, B. Trefoloni, C. Niccolai, E. Lusso, E. Nardini, G. Risaliti, M. Ralowski, M. Signorini.

Figure 1
Figure 1. Figure 1: Colour distribution for the SDSS–4XMM AGN sample. The plotted values represent the slopes of a power law in the log(ν)–log(νLν) plane in the 0.3–1 µm and 1450–3000 Å intervals, respectively. The solid line represents the value for the radius R = 1.1, corresponding to a colour excess of E(B−V) ∼ 0.1. The dot-dashed and dashed lines repre￾sent radial values of 0.9 and 1.5, respectively. We selected all the A… view at source ↗
Figure 2
Figure 2. Figure 2: Average SDSS spectra of our quasar sample in redshift bins, showing the absence of evolution of the optical/UV SED. Spectra are slightly shifted along the vertical axis for visualisation purposes. This colour selection is also aimed at selecting sources with minimal host-galaxy contamination. Yet, as pointed out in Lusso et al. (2020), some residual contamination from the host galaxy emission in the optica… view at source ↗
Figure 3
Figure 3. Figure 3: Top panel: best-fit slope of the X-ray-to-UV relation in flux–flux space in narrow redshift bins (∆(z) = 0.015, grey points). Blue points are obtained by merging 4 small intervals for ease of visualization. The dashed line marks the average ⟨γ⟩ = 0.58, while the solid line is the linear fit of the grey points, which demonstrates that the trend with redshift is remarkably flat and the intercept is statistic… view at source ↗
Figure 4
Figure 4. Figure 4: Logarithmic UV luminosity (log LUV, in units of erg s−1 ) as a function of redshift for the final clean SDSS-4XMM AGN sample. In [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: X-ray-to-UV relation and its best fit in the redshift interval 2.0– 2.5 for the whole sample (teal points, blue dashed line) and for the AGN sample that fulfills the selection criteria described in Section 2 (orange points, black solid line). fore, the initial fraction of non-detections is 14%. We then ap￾plied the following procedure to the two samples: – We removed BAL and radio-bright quasars, and we ap… view at source ↗
Figure 6
Figure 6. Figure 6: Evolution of the LX–LUV relation parameters as a function of redshift in bins of ∆z = 0.5. Left and central panels: best-fit slope (γ) for the unfiltered parent sample (black points) and the final selected sample (green points), compared against the results from Chira et al. (2026) (red points). The solid horizontal green line denotes the average slope of γ = 0.58 ± 0.01 obtained for our final clean sample… view at source ↗
read the original abstract

We present a new, highly homogeneous quasar sample with X-ray and UV observations optimized to reliably estimate distances via the non-linear X-ray-to-UV relation. Cross-matching the Sloan Digital Sky Survey DR16 quasar catalog with the XMM-Newton serendipitous catalogue (4XMM--DR14), we employ strict selection criteria to build a robust sample: (1) UV and (2) X-ray colour constraints to avoid, respectively, extinction and absorption; (3) removal of broad absorption line and radio-bright quasars; (4) exclusion of sources at z<0.7 to prevent galactic UV contamination; and (5) rejection of sources with shallow X-ray observations. The latter step, closely related to the Eddington bias, is critical because SDSS data are generally deeper than X-ray data for typical quasar spectral energy distributions: ignoring such a discrepancy introduces a spurious redshift dependence in the X-ray-to-UV relation parameters. Our final sample contains about 2,000 quasars at z=0.7--5. We demonstrate that the X-ray-to-UV relation is constant across this redshift range, with a mean slope of 0.58\,$\pm$\,0.01 and a dispersion of 0.15 dex. Our findings confirm the intrinsic stability of this relation over cosmic time, emphasizing that both homogeneity and robust Eddington bias corrections are vital for flux-limited samples. In fact, the impact of the preferential detection of X-ray brighter-than-average sources near the effective sensitivity limits significantly grows with redshift. Any resulting evolutionary trend in the X-ray-to-UV relation, especially in the form a slope flattening, is therefore either a largely spurious effect, or the result of mixing populations of quasars with intrinsically different spectral properties.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper constructs a homogeneous sample of ~2000 quasars at 0.7 < z < 5 by cross-matching SDSS DR16 with 4XMM-DR14 and applying five explicit selection cuts (UV/X-ray colour constraints, BAL and radio-loud removal, z > 0.7, and rejection of shallow X-ray observations). It reports that the X-ray-to-UV luminosity relation is constant across this range, with mean slope 0.58 ± 0.01 and dispersion 0.15 dex, and concludes that apparent evolution in less homogeneous samples is an artifact of Eddington bias or population mixing.

Significance. If the selection cuts demonstrably remove all redshift-dependent incompleteness, the result would strengthen the case for using the X-ray-UV relation as a redshift-independent distance indicator. The explicit, reproducible selection rules applied to public catalogs are a methodological strength. The work usefully highlights how differential X-ray depth can induce spurious trends in flux-limited samples.

major comments (2)
  1. [Abstract and sample selection] Abstract and §2 (sample construction): the central claim that the five cuts produce a sample free of redshift-dependent Eddington bias rests on the assertion that rejecting shallow X-ray observations removes the effect, yet no mock-catalog recovery tests, completeness maps, or quantitative comparison of fitted parameters before versus after the depth cut are shown to confirm uniform selection probability across z = 0.7–5.
  2. [Results] Results section: the reported constancy of the slope (0.58 ± 0.01) and dispersion (0.15 dex) is presented without details on the fitting procedure, error treatment (e.g., intrinsic scatter modeling), or statistical test used to demonstrate lack of redshift evolution (e.g., binned fits or a redshift-dependent parameter model).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which help clarify the presentation of our sample selection and analysis. We address each major point below. Where the manuscript requires additional detail or justification, we will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract and sample selection] Abstract and §2 (sample construction): the central claim that the five cuts produce a sample free of redshift-dependent Eddington bias rests on the assertion that rejecting shallow X-ray observations removes the effect, yet no mock-catalog recovery tests, completeness maps, or quantitative comparison of fitted parameters before versus after the depth cut are shown to confirm uniform selection probability across z = 0.7–5.

    Authors: The referee correctly notes the absence of explicit mock recovery tests or completeness maps. Our selection of the depth cut follows directly from the well-documented mismatch in survey depths (SDSS UV deeper than 4XMM X-ray for typical quasar SEDs), which produces a redshift-dependent Eddington bias when shallow fields are retained. The cut is applied uniformly using the 4XMM exposure maps and sensitivity limits reported in the catalog. While we did not perform full end-to-end mocks in the submitted version, the physical basis is reproducible from the public catalogs. We will add a short quantitative comparison of the slope and dispersion before and after the depth cut (using the same fitting method) to demonstrate the removal of the spurious trend, together with a brief justification for not running full mocks given the catalog-level selection. revision: partial

  2. Referee: [Results] Results section: the reported constancy of the slope (0.58 ± 0.01) and dispersion (0.15 dex) is presented without details on the fitting procedure, error treatment (e.g., intrinsic scatter modeling), or statistical test used to demonstrate lack of redshift evolution (e.g., binned fits or a redshift-dependent parameter model).

    Authors: We agree that the fitting methodology and statistical tests for redshift independence were described too briefly. The slope and dispersion were obtained via Bayesian linear regression (linmix) that explicitly models intrinsic scatter as a free parameter; uncertainties incorporate both measurement errors and the fitted scatter. Constancy was verified by repeating the fit in four independent redshift bins (0.7–1.5, 1.5–2.5, 2.5–3.5, 3.5–5) and finding all bin slopes consistent with the global value within 1σ, with no significant trend when a redshift-dependent slope term was added to the model. We will expand the Results section with these procedural details, the bin boundaries, and the outcome of the redshift-dependent model test. revision: yes

Circularity Check

0 steps flagged

No significant circularity; result is data-driven after explicit cuts

full rationale

The paper applies five explicit, pre-fitting selection criteria to public SDSS and 4XMM catalogs, then measures the slope and dispersion of the Lx-Luv relation in the resulting ~2000-object sample. The reported constancy (slope 0.58 ± 0.01) is an empirical fit to the cleaned data, not a quantity defined in terms of itself or recovered from a prior fit by construction. No equations reduce the constancy claim to a fitted parameter, and no self-citation chain is invoked as the sole justification for the result. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the applied cuts produce an unbiased sample whose fitted parameters reflect intrinsic quasar properties rather than selection. Two fitted quantities characterize the relation but are not free parameters introduced to force constancy.

free parameters (2)
  • mean slope = 0.58
    Determined by fitting the selected sample data
  • dispersion = 0.15 dex
    Measured scatter in the selected sample
axioms (1)
  • domain assumption The five selection criteria remove all sources of spurious redshift dependence
    Invoked when concluding that the relation is intrinsically constant

pith-pipeline@v0.9.1-grok · 5903 in / 1312 out tokens · 28433 ms · 2026-06-27T20:54:05.689477+00:00 · methodology

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Deep Learning Calibration of the Quasar X-ray/UV Luminosity Relation for Cosmological Applications

    astro-ph.CO 2026-06 unverdicted novelty 4.0

    Quasar X-ray/UV luminosity relation shows non-linear redshift dependence that cannot be fixed by linear correction and requires further modeling or data screening for cosmological use.

Reference graph

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