Fitting trends in quasar emission and absorption line redshifts

Netra K Subramanian; Nimisha G Kantharia; Prasad Subramanian

REVIEW 3 major objections 5 minor 16 references

Fitting trends in quasar emission and absorption line redshifts

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A quasar's lowest MgII absorption redshift rises linearly with its emission redshift, a correlation the authors use to argue the absorption lines form in the quasar itself rather than in intervening gas.

desk verdict The MgII lower envelope matches the Lyα forest selection boundary, so the paper's central physical claim is unsupported despite the fits being reproducible. read the letter →

arxiv 2608.10945 v1 pith:ORNTNMCY submitted 2026-08-11 astro-ph.CO astro-ph.HE

Netra K Subramanian , Prasad Subramanian , Nimisha G Kantharia This is my paper · ORCID

classification astro-ph.COastro-ph.HE

keywords quasarabsorptionlinesMgIIabsorbersCIVemission-lineredshiftlower-envelopefitcosmologicalspectra

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 tries to show that a quasar's absorption lines carry information about the quasar itself, not just about gas along the line of sight. Plotting the redshifts of MgII absorption doublets against the emission-line redshift of more than 36,000 systems produces a wedge-shaped scatter plot, and the authors fit its lower edge with $z_{\rm MgII,model}=(0.418\pm 0.008)\,z_{\rm em}-(0.482\pm 0.02)$, with $R^2=0.99$. They find a similar lower envelope for CIV absorption, $z_{\rm CIV,model}=0.845\,z_{\rm em}-0.153$, and verify the MgII line against higher-redshift samples. If this is right, the lowest absorption redshift is predictable for any quasar, the usual assumption that the emission redshift is the cosmological redshift fails, and the standard picture of intervening absorption is ruled out. That matters because emission-line redshifts are the distance measure behind most quasar cosmology.

What carries the argument

The carrying object is the lower envelope of the scatter plot of absorption redshift against emission redshift, defined by a convex-hull fit to the data boundary. The envelope is what converts a dense cloud of points into a falsifiable statement: any straight, nonzero-slope lower edge contradicts the null picture of unrelated intervening absorbers, whose lowest redshift should be the same for every $z_{\rm em}$. The argument then uses the two-component redshift composition law $(1+z)=(1+z_1)(1+z_2)$ to interpret the gap between $z_{\rm em}$ and $z_{\rm MgII,model}$ as an upper-bounded difference redshift, roughly constant near $\Delta z\approx 1.3$.

What would settle it

Forward-model the SDSS selection function for MgII detection, including the quoted $0.35<z_{\rm MgII}<2.3$ window and signal-to-noise limits, and ask whether the observed lower envelope is exactly the selection boundary; if it is, the intrinsic trend is not established. Alternatively, a single clean MgII absorption system with $z_{\rm MgII}<0.418\,z_{\rm em}-0.482$ in a high-$z_{\rm em}$ quasar would falsify the predictive model.

Watch

Extended reading notes

Core claim

The central claim is that the lower boundary of the $(z_{\rm em}, z_{\rm abs})$ distribution is a real physical relation, not a selection effect: as the emission redshift grows, the smallest MgII absorption redshift seen in any quasar grows linearly according to $z_{\rm MgII,model}=(0.418\pm 0.008)\,z_{\rm em}-(0.482\pm 0.02)$, and the analogous CIV relation is $z_{\rm CIV,model}=0.845\,z_{\rm em}-0.153$. Because an intervening-medium origin would leave the lowest absorption redshift independent of $z_{\rm em}$, the authors read the rising envelope as proof that the absorption and emission lines are formed together in the quasar and its environs. They conclude that the observed emission redshift is the largest redshift in the spectrum, not the cosmological redshift, and that every line shares one cosmological component plus a variable component, expressed through $(1+z)=(1+z_1)(1+z_2)$.

Load-bearing premise

The diagonal lower envelope is treated as a real physical boundary, but the catalogue only records MgII absorption with $0.35<z_{\rm MgII}<2.3$; if the line merely traces where the survey could detect absorption, the conclusion that $z_{\rm abs}$ and $z_{\rm em}$ are coupled collapses.

Editorial extensions

If this is right

The model predicts the lowest MgII absorption redshift for any quasar; for $z_{\rm em}=7$ it gives $z_{\rm MgII,model}\approx 2.45$, and the authors note this combination has not yet been observed.
If the envelope is intrinsic, the intervening-medium explanation for these absorption lines is ruled out, because it cannot produce a lowest absorption redshift that rises with $z_{\rm em}$.
The emission-line redshift $z_{\rm em}$ is not the cosmological redshift; the spread in absorption redshifts implies one common cosmological component and a second, variable component.
The analogous CIV fit gives a predictive floor for carbon absorption, $z_{\rm CIV,model}=0.845\,z_{\rm em}-0.153$, and other species (FeII, SiIV) fall between the same two bounding lines.

Reading between the lines

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

Editorial inference: a forward model of the SDSS selection function could test whether the diagonal boundary is an artifact of the catalog's $0.35<z_{\rm MgII}<2.3$ window; if the window alone reproduces the line, the intrinsic-coupling conclusion would not follow.
Editorial inference: applying the same envelope analysis to other ions with full surveys should produce slopes ordered by ionisation state, linking the model to the temperature and density structure of the absorbing gas.
Editorial inference: if $z_{\rm em}$ is not cosmological, distance indicators that assume it is would need to be recalibrated; a direct check would compare emission-redshift distances against redshift-independent anchors for the same quasars.

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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

Quick take: the paper fits straight lines to the lower envelopes of MgII and CIV absorption redshifts and then argues the very existence of these envelopes rules out intervening absorbers, implying quasar emission redshifts are not cosmological. The fits are straightforward and reproducible, but the interpretation is almost certainly wrong: the MgII envelope coincides with the Lyα forest boundary, so it is a selection effect, not a physical relation.

What's new: the specific linear fits for the MgII and CIV lower envelopes (Equations 4 and 6) are not in Kantharia (2016). That is a narrow quantitative novelty. The paper also checks the MgII fit against higher-redshift data and finds those points lie above the line, which is consistent with the selection-boundary reading. The analysis is transparent and uses public catalogs.

Where it falls apart: the physical inference. For MgII, the lower envelope corresponds almost exactly to the condition that the MgII line falls shortward of Lyα in the quasar frame. Rest wavelength 2796 Å needs 2796(1+z_MgII) > 1216(1+z_em), i.e. (1+z_MgII)/(1+z_em) > 0.435. The fitted line gives roughly 0.43 across the relevant range. That is not an unexpected diagonal; it is precisely where MgII lines can still be seen against quasar continuum that has not been absorbed by the Lyα forest. Intervening absorbers below the line can exist but are invisible. The paper never models this selection function and never tests a null hypothesis of intervening absorbers with the same boundary. The CIV fit is less clean, but the same selection logic applies, and the hand-chosen fitting range (2 < z_CIV < 4) weakens any claim of a universal trend.

So the summary claim that the trend "effectively rules out the intervening medium origin" and that z_em is not cosmological is not supported. The descriptive fits are fine as descriptions of a boundary, but they do not carry the physical weight the authors attach to them.

Who this is for: someone interested in a cautionary example of a survey boundary being mistaken for a physical signal. Not a paper to build on.

Recommendation: I would not accept this as is. A serious editor could send it to a referee because the claim is important, but the referee would need to evaluate the selection function—and the result would almost certainly be rejection. I would not cite it as evidence for quasar-intrinsic absorption. For our reading group, it is a maybe: a quick look at how selection effects masquerade as physics could be instructive.

Referee Report

3 major / 5 minor

Summary. The paper analyzes the distribution of MgII and CIV absorption-line redshifts against quasar emission-line redshifts in large SDSS-based catalogs. It fits the lower envelope of the z_em–z_abs distribution with linear relations (Eqs. 4 and 6), presents these fits as predictive models for the lowest detectable z_abs, and interprets the increasing lower envelope as evidence that absorption and emission lines form in the quasar environment, that the lowest detected z_abs is the cosmological redshift, and that z_em is not the cosmological redshift.

Significance. If the trend were physical, the conclusion would overturn the standard interpretation of quasar absorption lines as intervening systems and would have broad implications for quasar physics and cosmology. The paper has some strengths: it is transparent about the catalog redshift limits, uses large samples, provides concrete linear fits with uncertainties, and checks the MgII fit against higher-redshift data. However, the central inference is not supported, because the fitted lower envelope is quantitatively consistent with an observational selection boundary (Ly-alpha forest suppression of the quasar continuum), and the paper neither models this selection function nor tests a null model of intervening absorbers.

major comments (3)

[§2.1, Fig. 3, Eq. (4)] The lower envelope is not demonstrated to be a physical boundary. For a MgII line at z_abs, the observed wavelength is 2796(1+z_abs), and the quasar continuum at that wavelength was emitted at rest wavelength 2796(1+z_abs)/(1+z_em). When this rest wavelength is below the Ly-alpha wavelength of 1216 Å, the quasar continuum is heavily suppressed by the Ly-alpha forest and Lyman-limit absorption, so the MgII line can be detected only when (1+z_abs)/(1+z_em) > 1216/2796 = 0.435. Equation (4) gives (1+z_MgIImodel)/(1+z_em) ≈ 0.43 across the fitted range (e.g. 0.438 at z_em=4 and 0.431 at z_em=7), matching the selection threshold. The fitted line also intersects the catalog limits z_MgII=0.35 and 2.3 at z_em≈2 and ≈6.65, so the apparent diagonal may simply trace the edge of the detectable parameter space. The paper never models this selection function and never tests a null hypothesis of intervening absorbers; the conclusion in §3 that the trend 'effectively rules out the intervening medium origin' therefore does not follow.
[§2.2, Eq. (4)] The validation in §2.2 is not an independent test of the model. The additional data from Matejek and Simcoe (2012) and Chen et al. (2017) are said to lie above the red line 'as expected from the model', but under the Ly-alpha selection interpretation every detectable MgII line must also lie above that line. The test therefore cannot distinguish the paper's physical interpretation from the selection effect, and no quantitative comparison or goodness-of-fit against a null model is provided. The statement that the model is 'applicable' to higher-redshift systems is accordingly unsupported.
[§2.3, Eq. (6)] The CIV model is constructed from a hand-chosen subset (2<z_CIV<4) of a catalogue whose stated selection range is 1.5<z_CIV<4.5, and no justification is given for the truncation. The reported uncertainties (±0.0002 and ±0.0006) are implausibly small for a fit to a scattered envelope of convex-hull vertices and suggest overfitting. Moreover, the same Ly-alpha selection argument applies to CIV: with a rest wavelength of 1548 Å, the threshold ratio is 1216/1548 ≈ 0.785, whereas Eq. (6) implies (1+z_CIVmodel)/(1+z_em) ≈ 0.85; the paper does not explain this discrepancy or model the CIV selection function. The CIV 'trend' is therefore not established as physical.

minor comments (5)

[§2.3, Fig. 6 caption] The text and caption refer to 'SIV' and 'SiVI'; the intended ion is triply ionized silicon, SiIV, and these spellings should be corrected.
[§2.1, Eq. (4)] The intercept is written as 0.48(±0.02) in Eq. (4) but as 0.482(±0.02) in the abstract and §2.3; the inconsistency should be fixed.
[§2.1, R² statement] The R²=0.99 is quoted for a fit to the lower envelope obtained from the convex-hull algorithm; with only a handful of hull points, R² is not a meaningful measure of how well the line describes the scatter of the full data distribution, and this should be stated.
[§2.1, Eq. (5)] The quantity Δz introduced in Eq. (5) is called the 'difference redshift' but its relation to the component redshifts z1 and z2 of Eq. (3) is not clarified; the notation should be defined more carefully.
[Abstract and §2.1] The word 'predict' is used for the output of Equations (4) and (6), but these equations are fits to the same data from which the envelopes are defined; 'describe' or 'interpolate' would be more accurate unless independent validation is provided.

Circularity Check

2 steps flagged · score 6.0 of 10

Predictions are just the fitted lower-envelope lines, and the physical conclusion imports a self-cited uniqueness claim.

fitted input called prediction [Section 2.1, Eq. (4); Section 2.3, Eq. (6); Section 3 summary]
"Since we are interested in the lower side of the envelope in Figure 3, we considered only that data from the algorithm. The best fit to the lower envelope was found to be the straight line given by zMgIImodel= 0.418(±0.008)zem −0.48(±0.02) ... From Equation 4, the lowest redshift at which MgII doublet will be detected in a quasar spectrum for a given emission line redshift z_em can be predicted."

z_MgIImodel is introduced as 'the lowest redshift detected for a z_em' and then defined by the best-fit line to the lower envelope. Any 'prediction' of the lowest MgII or CIV absorption redshift for a given z_em is therefore just the fitted line evaluated at that z_em; it is not produced by an independent physical model or held-out data. The same holds for Eq. (6), fitted to the CIV lower envelope. Thus the paper's headline predictions reduce by construction to the fits that generated them, so they cannot independently confirm the model.
uniqueness imported from authors [Section 2.1 and Section 3 summary]
"As pointed out by Kantharia (2016), the nature of the lower envelope can only be explained if all the emission and absorption features detected in a quasar spectrum arise in the quasar or its host galaxy. If the emission features were formed in the quasar and the absorption features were formed in the medium between us and the quasar then no relation between z_em and z_abs can be expected."

The sentence asserts, on the authority of the authors' own earlier arXiv paper Kantharia (2016), that the envelope 'can only be explained' by quasar-associated absorption. No derivation of uniqueness is given here, and no alternative (e.g., survey selection) is modeled. The paper's final conclusions — intervening origin is 'effectively rule[d] out', all lines form in the quasar, and z_em is not cosmological — are loaded onto that self-cited uniqueness claim. Since the cited work is by one of the present authors and is not independently verified in this paper, the central physical inference reduces to a self-citation.

full rationale

Most of the paper is an empirical curve fit: Eq. (4) describes the lower envelope of the MgII z_abs-z_em distribution and Eq. (6) does the same for CIV. Fitting an envelope is not circular, and the paper honestly states that z_MgIImodel is the fitted lowest value. However, the paper then calls evaluations of these fitted lines 'predictions' and uses the existence of the fitted lower envelope, combined with a uniqueness interpretation imported from the authors' own prior arXiv preprint, to rule out the intervening-medium model and to declare z_em non-cosmological. Those uses are circular or self-citation load-bearing: the 'predicted' lowest redshifts are the fit by construction, and the 'can only be explained' premise is taken from Kantharia (2016) rather than derived. The higher-redshift check in Section 2.2 only verifies that external points lie above the lower-bound line, which is a necessary condition but not an independent confirmation; it does not break the circularity. A separate (non-circularity) concern is that the lower diagonal may trace the Ly-alpha forest selection boundary, but that is a validity issue rather than a circularity step and is noted here only to show the uniqueness claim is not forced. Overall score 6: the empirical fits have independent content, but the paper's predictions reduce by construction and the central physical conclusion leans on a self-cited uniqueness claim.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The load-bearing inputs are the fitted envelope lines, the assumption that the lower boundary is physical rather than a survey selection edge, and the assumption that a correlation rules out intervening absorbers. No new physical constants are introduced, but a variable redshift component is postulated without independent evidence.

free parameters (4)

MgII lower-envelope slope = 0.418 +/- 0.008
Fitted by linear regression to the convex-hull lower envelope of z_em vs z_MgII data; central to Equation (4).
MgII lower-envelope intercept = -0.482 +/- 0.02
Same regression as the MgII slope; anchors the line in Equation (4).
CIV lower-envelope slope = 0.845 +/- 0.0002
Fitted to Cooksey et al. data restricted to 2<z_CIV<4; central to Equation (6).
CIV lower-envelope intercept = -0.153 +/- 0.0006
Same CIV regression as the CIV slope; anchors the line in Equation (6).

assumptions (4)

domain assumption The lower envelope of the plotted z_em-z_abs distribution reflects the true minimum detectable absorption redshift, not the survey selection function.
This is the load-bearing premise. Section 2.1 interprets the diagonal lower boundary as a physical trend without modeling SDSS wavelength coverage or the Raghunathan et al. search limits.
domain assumption If absorption lines were formed in intervening material, z_em and z_abs would be independent, so any correlation rules out that origin.
Section 2.1 states that if absorption features were formed in the medium between us and the quasar, no relation between z_em and z_abs can be expected. This ignores large-scale structure correlations and survey selection effects.
standard math ConvexHull and linear regression provide a meaningful and stable estimate of the lower envelope.
The scipy ConvexHull algorithm is standard, but the fit to 'only that data from the algorithm' in Section 2.1 is not specified, so the number of points and the fit method are not auditable.
domain assumption Catalog redshifts and identifications from Raghunathan et al. (2016) and Cooksey et al. (2013) are complete and accurate across the full plotted range.
The analysis uses these catalogs as ground truth without propagating their completeness limits or error rates.

invented entities (1)

Variable redshift component
purpose: Proposed to explain why z_abs differs from z_em within a common cosmological frame; the sum of a common cosmological redshift and a variable component produces the observed spread.
No independent measurement or falsifiable prediction is provided for this component; it is introduced to accommodate the fitted trend in Sections 1 and 3.

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Cite this review

Pith. "Pith review of Fitting trends in quasar emission and absorption line redshifts." pith.science (2026). https://pith.science/paper/ORNTNMCY

@misc{pith2026260810945,
  author       = {Pith},
  title        = {Pith review of: Fitting trends in quasar emission and absorption line redshifts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ORNTNMCY}},
  note         = {Machine review of arXiv:2608.10945}
}

abstract

The spectrum of a quasar consists of a few emission lines whose wavelengths are shifted by similar redshifts and numerous absorption lines whose wavelengths are shifted by different redshifts. Hence each quasar is characterised by an emission line redshift and the absorption lines redshifts are all less than the emission line redshift. The distribution of observed absorption line redshifts ($z_{abs}$) with respect to emission line redshift ($z_{em}$) for a large sample of quasars shows a systematic trend as pointed out by \citet{2016arXiv160901593K}. They noticed that increase in $z_{em}$ is accompanied by a monotonic increase in the lowest detected value of $z_{abs}$ and inferred that the emission and absorption lines were all formed in the quasar. This study focuses on modeling the systematic trend in the observed $z_{em} \rightarrow z_{abs}$ distribution. We considered the redshift data of absorption lines of singly ionized magnesium (denoted by MgII) and triply ionized carbon (denoted by CIV) for a large sample of quasars. We find that the envelope of data points defining the lowest value of the MgII absorption line redshift (which we denote by $z_{MgIImodel}$) for a given $z_{em}$ satisfies $z_{MgIImodel} = (0.418 \pm 0.008) z_{em} - (0.482 \pm 0.02)$ with an $R^2$ value of 0.99. The model can be used to predict the lowest expected MgII absorption line redshift for any $z_{em}$. We find a similar model for the lowest expected redshift of triply ionized carbon lines for any $z_{em}$ which is $z_{CIVmodel} = 0.845 (\pm 0.0002) z_{em} - 0.153 (\pm 0.0006)$.

Figures

Figures reproduced from arXiv: 2608.10945 by the authors.

**Figure 1.** (a) A typical spectrum recorded between wavelengths of ∼ 3900 Angstroms and ∼ 5000Angstroms is shown in this figure taken from Sargent et al. (1988a). This spectrum is of quasar Q0013-004. (b) The emission line features are identified and their redshift is listed in this snapshot from Sargent et al. (1988a). The emission line redshift of the quasar Q0013-004 is zem = 2.086. the most luminous active galactic nuclei (… view at source ↗

**Figure 2.** The absorption features in the spectrum of quasar Q0013-004 ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The redshift distribution of redshift of MgII doublet lines detected in absorption is plotted against the emission line redshift of the quasar for a large sample of quasars. The data have been taken from the catalogue based on SDSS DR12 (Raghunathan et al., 2016). Notice the horizontal bounds at zM gII = 0.35 and zM gII = 2.3 which defines the range of MgII redshifts in the catalogue. The upper diagonal line is for … view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: The model fitted to the lower envelope of the redshift distribution is plotted in red. The blue line is plotted for x=y. Notice how all the detected redshifts of MgII absorption lines in all quasar spectra lie between the two bounding lines. While the x=y bound is expe…

**Figure 5.** Figure 5: Redshift data from three databases are plotted along with the model from Equation 4. The blue line is for zM gII = zem. Notice how all the data lie between these two lines. not be a single quasar with a MgII feature displaced by a redshift less than 2.446. Let us consi…

**Figure 6.** Figure 6: (a) Redshifts of absorptions lines MgII taken from Sargent et al. (1988b), redshifts ofFeII and SiVI taken from Sargent et al. (1988a) are plotted against the emission line redshift for a small sample of quasars. The red line is the best fit model obtained for zem → zM…

**Figure 7.** Figure 7: The redshift data on CIV doublet lines taken from catalogue of Cooksey et al. (2013) is plotted. The best model fit to the lower diagonal estimated using data in the range 2 < zCIV < 4 is zCIVmodel = 0.845zem − 0.153 which is shown by the red line. The blue line is zCI…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 9 canonical work pages

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

The Astrophysical Journal Letters , year = 1971, month = mar, volume =

`The Absorption-Line Spectrum of 4c 05.34'. The Astrophysical Journal Letters , year = 1971, month = mar, volume =. doi:10.1086/180695 , adsurl =

doi:10.1086/180695 1971

[2] [2]

The Astrophysical Journal , keywords =

`MG II absorption in the spectra of high and low redshift QSOs'. The Astrophysical Journal , keywords =. doi:10.1086/166814 , adsurl =

work page doi:10.1086/166814

[3] [3]

The Astrophysical Journal Supplement Series , keywords =

`C IV absorption in a new sample of 55 QSOs - Evolution and clustering of the heavy-element absorption redshifts'. The Astrophysical Journal Supplement Series , keywords =. doi:10.1086/191300 , adsurl =

doi:10.1086/191300

[4] [4]

Monthly Notices of the Royal Astronomical Society , keywords =

`Intervening Mg II absorption systems from the SDSS DR12 quasar spectra'. Monthly Notices of the Royal Astronomical Society , keywords =. doi:10.1093/mnras/stw2095 , archivePrefix =. 1608.05112 , primaryClass =

arXiv

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`Mg II Absorption at 2 < Z < 7 with Magellan/Fire. III. Full Statistics of Absorption toward 100 High-redshift QSOs'. The Astrophysical Journal , keywords =. doi:10.3847/1538-4357/aa9707 , archivePrefix =. 1612.02829 , primaryClass =

arXiv

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`Precious Metals in SDSS Quasar Spectra. I. Tracking the Evolution of Strong, 1.5 < z < 4.5 C IV Absorbers with Thousands of Systems'. The Astrophysical Journal , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/763/1/37 , adsurl =

doi:10.1088/0004-637x/763/1/37

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Decoding quasars: gravitationally redshifted spectral lines !

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work page Pith review arXiv doi:10.48550/arxiv.1609.01593

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Machine Learning Uncovers the Universe's Hidden Gems: A Comprehensive Catalogue of CIV Absorption Lines in SDSS DR12

`Machine learning uncovers the universe's hidden gems: A comprehensive catalogue of C IV absorption lines in SDSS DR12'. Monthly Notices of the Royal Astronomical Society , keywords =. doi:10.1093/mnras/stad2940 , archivePrefix =. 2305.00023 , primaryClass =

work page Pith review arXiv