Highly Variable Quasar Candidates Selected from 4XMM-DR13 with Machine Learning

Heng Wang; Liming Dou; Wenfeng Wen; Xiangru Li; Xue-Bing Wu; Yanli Ai; Yanxia Zhang; Yuming Fu; Zhiying Huo

REVIEW 3 major objections 4 minor 51 references

Highly Variable Quasar Candidates Selected from 4XMM-DR13 with Machine Learning

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims to identify 12 quasar candidates in 4XMM-DR13 whose soft X-ray flux changed by at least a factor of 10 between XMM-Newton epochs, extending extreme X-ray variability to optically faint quasars around r ~ 22, and argues…

desk verdict Useful candidate sample, but the ROSAT-based rarity claim doesn't survive contact with the flux limits. read the letter →

arxiv 2501.15254 v2 pith:AUAZ5T2O submitted 2025-01-25 astro-ph.GA astro-ph.HE

Heng Wang , Yanli Ai , Yanxia Zhang , Yuming Fu , Wenfeng Wen , Liming Dou , Xue-Bing Wu , Xiangru Li

show 1 more author

Zhiying Huo

This is my paper · ORCID

classification astro-ph.GAastro-ph.HE

keywords quasarsX-rayvariabilityrandomforest4XMM-DR13softGaiapropermotionROSATAGN

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

The paper claims that a random forest classifier trained on spectroscopically confirmed stars, galaxies, and quasars can pick out faint, previously unclassified quasar candidates from the XMM-Newton serendipitous catalog, and that this approach finds 12 candidates whose soft X-ray flux (0.2-2 keV) changed by at least a factor of 10 between XMM-Newton epochs. These candidates are optically faint, with SDSS i-band magnitudes around 22, extending the known population of extremely X-ray-variable quasars to the faint end. The paper further argues that because none of the 12 were detected in the ROSAT All-Sky Survey, quasars with variability amplitudes above about 100 are extremely rare. The importance is that such extreme variability, previously seen mostly in bright AGNs, may also occur in faint quasars that have been missed by shallower surveys.

What carries the argument

The random forest classifier uses 15 features: X-ray flux in 0.2-12 keV, four XMM hardness ratios (hr1-hr4), X-ray-to-optical flux ratio, SDSS r magnitude and colors (u-g, g-r, r-i, i-z), WISE magnitudes W1 and W2, and infrared colors (z-W1, W1-W2). SMOTE oversampling balances the training set of 23,501 spectroscopically classified sources (16,826 quasars, 3,800 stars, 2,875 galaxies). Stellar contaminants are removed by a Gaia proper-motion probability cut using the bivariate normal of pmra and pmdec, and extreme variability is defined by the ratio of soft-band fluxes between XMM epochs exceeding 10.

What would settle it

Obtain optical spectra of the 12 candidates: if a majority lack broad emission lines or other quasar signatures, the selection is contaminated. Alternatively, a targeted search of deeper all-sky X-ray data (e.g., eROSITA) for optically faint quasars with >100-fold soft X-ray variability would directly test the claimed rarity.

Watch

Extended reading notes

Core claim

The central discovery is a sample of 12 quasar candidates in the 4XMM-DR13 catalog that each changed their 0.2-2 keV flux by a factor of at least 10 between XMM-Newton observations spanning roughly 20 years. The selection pipeline first classifies 100,183 X-ray sources with optical and mid-infrared counterparts into quasar, galaxy, and star candidates using random forest; after a Gaia proper-motion cut to remove stars and a FIRST cut to remove radio-loud objects, it isolates sources with at least two clean XMM detections, a soft-band flux ratio greater than 10, and a minimum flux of 5e-15 erg $cm^{-2}$ $s^{-1}$, followed by visual inspection of light curves and images. The 12 survivors have SDSS i-band magnitudes out to about 22, making them fainter than previously known highly variable quasars. The paper also reports that none of the 12 are detected in ROSAT, and given ROSAT's flux limit this implies that quasars with variability factors above 100 are extremely rare.

Load-bearing premise

The random forest classifier was trained on relatively bright, spectroscopically confirmed quasars, and none of the 12 final candidates has a confirming spectrum; if several are actually stars or galaxies, the sample and the rarity inference collapse.

Editorial extensions

If this is right

The population of quasars with extreme soft X-ray variability (factor >=10) extends to i-band magnitude about 22, not just the bright AGNs previously catalogued.
The ROSAT non-detections imply that variability amplitudes above 100 are very rare among these faint quasars, placing a constraint on models of changing accretion or obscuration.
The random forest pipeline can be applied to future XMM-Newton data releases to enlarge the sample and refine the rarity estimate.
The 12 candidates are prime targets for spectroscopy and multiwavelength monitoring to distinguish between changing accretion rate and obscuration as the driver.

Reading between the lines

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

If any of the 12 turn out to be flaring M dwarfs or X-ray binaries, the rarity claim would need to be revised downward; this is testable by spectroscopy.
The ROSAT non-detection may simply reflect that these quasars were in a low state during the 1990s; the true rate of >100-fold events could be higher than inferred if such events are short-lived.
Because the training set is dominated by bright quasars, the classifier's precision at the faint end is uncertain; future spectroscopic follow-up of a random subset of the 52,486 candidates would quantify the contamination rate.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper delivers what it says on the tin: a machine-learning classification of 4XMM-DR13 sources, and a hand-vetted sample of 12 quasar candidates with soft X-ray variability factors above 10, reaching r~22. That is genuinely new—previous work on extreme X-ray variable quasars was mostly limited to i<20.2. The sample construction is careful: the authors re-run a known Random Forest pipeline, apply Gaia proper-motion cuts to remove stars, cross-check against NED, and visually inspect light curves and X-ray images. They also ship the candidate table on GitHub, which is a plus.

The main caveat, which the authors themselves state, is that none of the 12 have spectroscopic confirmation. That makes them candidates, not quasars. This is a fair limitation and not fatal, but it should be flagged more prominently. The bigger problem is the ROSAT argument in Section 5. The authors note that none of the 12 are detected in RASS and then suggest that quasars with variability above a factor of 100 are 'exceedingly rare.' That inference is not supported. Table 5 gives XMM fluxes in units of 1e-14 erg/s/cm2; the brightest state among the 12 is 9.41e-14, and most are below 5e-14. The RASS sensitivity is about 1e-13 erg/s/cm2. So even in their bright states, all 12 are fainter than the RASS limit. Non-detection in RASS is exactly what you'd expect for steady sources at these fluxes. The rarity claim would require a sample with bright-state fluxes above the RASS boundary; this sample has none. The stress-test note is right, and the authors should either rephrase this as a simple statement about sensitivity or drop the quantitative rarity claim.

There are also internal inconsistencies that need cleaning: the abstract quotes 53,992 quasar candidates and 10,210 SIMBAD matches, while the body reports 52,486 and 8,410. That kind of mismatch should have been caught in proof. And Table 5 lists fluxes without uncertainties, which matters for a paper whose whole point is flux ratios.

Who is this for? Astronomers working on X-ray variability and AGN demographics. As a candidate catalog, it's useful. As a claim about the rarity of order-of-magnitude variability, it's not ready. I'd send it back for a revision that fixes the numbers, adds flux uncertainties, and rewrites the ROSAT paragraph to say 'below the RASS limit' without drawing a statistical conclusion. The core sample deserves to be published, but the current framing overreaches.

Referee Report

3 major / 4 minor

Summary. This manuscript applies a random forest classifier to 4XMM-DR13 sources cross-matched with SDSS DR18 and AllWISE photometry, using a training sample of spectroscopically classified stars, galaxies, and quasars. After Gaia proper-motion filtering and exclusion of FIRST counterparts, the authors select 12 quasar candidates that changed their 0.2–2 keV flux by a factor of at least 10 between XMM-Newton epochs, extending to r-band magnitudes around 22. The paper further reports that none of the 12 candidates is detected in ROSAT and concludes that quasars exhibiting variations of more than two orders of magnitude are extremely rare.

Significance. The sample construction is careful: the training set is built from SDSS and LAMOST spectra, the classifier is validated with cross-validation and external catalogs (SIMBAD, NED), light curves and X-ray images are visually inspected, and a comparison sample of known quasars is selected with identical criteria. The public machine-readable table and GitHub repository are useful assets. If spectroscopically confirmed, the 12 candidates would extend the known population of extreme soft-X-ray variable quasars to the optically faint end. However, two load-bearing issues remain: the ROSAT-based rarity inference is not supported by the data presented, and the reliability of the classifier for the faintest, uncataloged sources is not quantified. The paper itself acknowledges in Section 6 that spectra are needed to confirm the quasar nature of the candidates.

major comments (3)

[Abstract; Section 5, Figures 5–6] The claim that ROSAT non-detections imply that quasars with variability factors of 100 or more are 'exceedingly rare' is not supported by the data. All 12 candidates have bright-state 0.2–2 keV fluxes below 1e-13 erg/s/cm2 (Table 5; the largest is 9.41e-14 for 4XMM J122809.3+435358), while the paper itself quotes the RASS sensitivity as a few times 10^-13 erg/s/cm2. Non-detection in RASS is therefore expected even if these objects are non-variable. Constraining the occurrence rate of >100x variability would require a sample whose bright-state fluxes are above the RASS limit, or a statistical model of RASS detection probability that accounts for the sensitivity and epoch. Please remove or substantially qualify this inference.
[Section 4.2, Table 5] Table 5 reports the XMM-Newton and Chandra soft X-ray fluxes without uncertainties, and the text only states that candidates with 'large flux uncertainties' were rejected after visual inspection. Since the factor-of-10 variability claim is the central result, the reader needs the individual flux uncertainties (and ideally detection significances) for every epoch to verify that the flux ratios are statistically robust, especially for the faintest measurements near the 5e-15 erg/s/cm2 threshold.
[Section 4.1, Figure 4, Section 6] The random forest is trained on spectroscopically confirmed sources that are systematically brighter in X-rays than the 12 candidates (Figure 4), and none of the 12 has a spectrum. The paper acknowledges that spectra are needed, but to support the claim that the sample extends the highly variable quasar population, it should provide a quantitative estimate of classifier performance in the flux/magnitude regime of the candidates—for example, flux-bin precision and recall on the held-out test set, or the random-forest probability P_QSO for each of the 12 objects, which is currently omitted from Table 5.

minor comments (4)

[Section 4.2, last paragraph] The text refers to 'the relatively deeper observations in the 4XMM-DR3 catalog'; this should be 4XMM-DR13.
[Section 4.1] The proper-motion cut is described as log(fPM0) ≤ −4 in the prose and as log(fPM0) < −4 in the following sentence; please harmonize the inequality.
[Section 3.4] The sentence 'The optimal value is log 152 for max_features' is unclear; please specify whether this is log2(152) or another convention.
[Section 2.1 and Section 3] The relation among the 100,183 XMM-WISE-SDSS sources, the 23,501 training sources, and the 76,682 sources actually classified by the random forest is implicit; a brief sentence stateing that only the unclassified remainder is subject to the classifier would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the variability selection is applied after an externally validated classifier and is not used to fit any model parameter.

full rationale

The paper's derivation chain is not circular. The random forest classifier is trained on spectroscopically labeled SDSS/LAMOST sources (Table 1) with features drawn from XMM, SDSS, and AllWISE (Table 2), and its performance is evaluated by 5-fold cross-validation and external catalog checks (SIMBAD and NED). The variability selection in Section 4.2 is applied after classification: the soft-band flux ratio greater than 10 and the 5e-15 flux threshold are selection criteria, not fitted parameters, and the 12 final candidates are not used to adjust any model component. The comparison sample of 43 variable quasars is selected from the training set with the same criteria, which supports a distributional comparison rather than a circular validation. The self-citations (Y. Zhang et al. 2021 for matching radii and RF feature choices; Y. Fu et al. 2021, 2024 for the Gaia proper-motion probability cut) are methodological and are not load-bearing for the central claim of discovering faint, highly variable quasar candidates. The RASS non-detection inference in Section 5 is statistically fragile because all 12 candidates have bright-state fluxes below the ROSAT sensitivity of about 1e-13 erg cm-2 s-1, but this is an evidential-support problem rather than a circularity: the ROSAT non-detection is not used to define, train, or fit the selection, and no equation in the paper reduces the rarity conclusion to an input by construction. Therefore no circular step can be quoted, and the paper is self-contained against external benchmarks.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central sample rests on a chain of catalog and modeling assumptions rather than on new physics. The random forest classification generalizes to faint sources, the 4XMM flux conversion is adequate for variability work, the training set is representative, and the ROSAT nondetection constrains historical bright states. The selection thresholds (variability factor 10, flux cut 5e-15) are free choices that shape the final sample. No new particles, forces, or physical entities are introduced.

free parameters (5)

Random forest max_features = log 152 (as stated in text; ambiguous)
Selected by grid search with 5-fold cross-validation; affects which sources are classified as quasars.
Random forest n_estimators = 151
Selected by grid search; number of trees in the ensemble.
Soft X-ray flux threshold = 5e-15 erg s^-1 cm^-2
Chosen as the median soft-band flux of 4XMM-DR13; candidates with fainter fluxes are rejected to reduce uncertainties, and this cut shapes the final 12-object sample.
Variability ratio threshold = 10
Author-defined selection threshold for 'highly variable'; sources must change soft X-ray flux by more than this factor between epochs.
Gaia proper-motion cut = log10(f_PM0) < -4
Adopted from Fu et al. (2021, 2024) to remove stellar contaminants; a fixed threshold applied to quasar candidates.

assumptions (4)

domain assumption The random forest classifier trained on SDSS/LAMOST spectroscopically classified sources generalizes to all unclassified sources in the XMM-WISE-SDSS sample, including optically faint ones around r ~ 22.
Invoked in Section 4.1 when 52,486 sources are classified; none of the final 12 candidates has a confirming spectrum, and the Summary explicitly says spectra are needed to confirm their quasar nature.
domain assumption The 4XMM-DR13 soft-band fluxes, derived assuming an absorbed power law with photon index 1.7 and N_H = 3e20 cm^-2, yield flux ratios accurate enough to establish factor-of-10 variability.
Section 4.2; the authors cite Saxton et al. (2011) and Li et al. (2022) to argue the fixed spectral slope introduces negligible errors, but heavily absorbed or intrinsically varying spectra could bias the ratios.
domain assumption The training set of 3,800 stars, 2,875 galaxies, and 16,826 quasars is representative of the unclassified XMM-WISE-SDSS population.
Implied in Section 3.4 and Section 5; if unclassified sources occupy parts of feature space not covered by the training set, the classifier's probability estimates may be miscalibrated.
domain assumption The ROSAT All-Sky Survey would have detected any of the 12 objects if they had been in a bright state above the RASS flux limit during the survey era.
Section 5 uses the RASS nondetections to conclude extreme variability above a factor of 100 is extremely rare; this requires that the historical bright states were not missed due to incomplete sky coverage or higher local RASS sensitivity limits.

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Cite this review

Pith. "Pith review of Highly Variable Quasar Candidates Selected from 4XMM-DR13 with Machine Learning." pith.science (2026). https://pith.science/paper/AUAZ5T2O

@misc{pith2026250115254,
  author       = {Pith},
  title        = {Pith review of: Highly Variable Quasar Candidates Selected from 4XMM-DR13 with Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AUAZ5T2O}},
  note         = {Machine review of arXiv:2501.15254}
}

abstract

We present a sample of 12 quasar candidates with highly variable soft X-ray emission from the 4th XMM-newton Serendipitous Source Catalog (4XMM-DR13) using random forest. We obtained optical to mid-IR photometric data for the 4XMM-DR13 sources by correlating the sample with the SDSS DR18 photometric database and the AllWISE database. By cross-matching this sample with known spectral catalogs from the SDSS and LAMOST surveys, we obtained a training data set containing stars, galaxies, and quasars. The random forest algorithm was trained to classify the XMM-WISE-SDSS sample. We further filtered the classified quasar candidates with $\it{Gaia}$ proper motion to remove stellar contaminants. Finally, 53,992 quasar candidates have been classified, with 10,210 known quasars matched in SIMBAD. The quasar candidates have systematically lower X-ray fluxes than quasars in the training set, which indicates the classifier is helpful to single out fainter quasars. We constructed a sample of 12 sources from these quasars candidates which changed their soft X-ray fluxes by a factor of 10 over $\sim$ 20 years in the 4XMM-newton survey. Our selected highly variable quasar candidates extend the quasar sample, characterized by extreme soft X-ray variability, to the optically faint end with magnitudes around $r \sim 22$. None of the 12 sources were detected in ROSAT observations. Given the flux limit of ROSAT, the result suggests that quasars exhibiting variations of more than two orders of magnitudes are extremely rare.

Figures

Figures reproduced from arXiv: 2501.15254 by the authors.

**Figure 1.** The classification flowchart for the 4XMM-DR13 sources. 5 The Astrophysical Journal, 985:23 (12pp), 2025 May 20 Wang et al [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Color–color diagrams of quasar candidates (blue contours), galaxy candidates (green contours), and star candidates (red-shaded density plots) [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Light curves of the 12 quasar candidates with highly variable X-ray emission. All error bars are 3σ. 7 The Astrophysical Journal, 985:23 (12pp), 2025 May 20 Wang et al [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Distribution of the broadband X-ray flux for classified quasar candidates and known quasars in training data. 9 The Astrophysical Journal, 985:23 (12pp), 2025 May 20 Wang et al [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Soft X-ray flux vs. SDSS i-band magnitude for the 12 highly variable quasar candidates. As a comparison, we also present the distribution of highly variable quasars in training data and in D. Bi et al. (2015). For clarity, only the brightest (larger symbols) and fainte…

**Figure 6.** Figure 6: , which presents the distribution of the maximum soft X-ray variability flux ratio of quasars in TD and quasar candidates [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

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Fu, Y., Wu, X.-B., Li, Y., et al. 2024, ApJS, 271, 54

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