arxiv: 2604.13162 · v2 · submitted 2026-04-14 · 🌌 astro-ph.GA

Recognition: 2 theorem links

· Lean Theorem

Investigating the Circumgalactic Medium through Mg II absorption coincidence

Paryag Sharma , Raghunathan Srianand , Hum Chand , Labanya Kumar Guha

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:49 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords Mg II absorptioncircumgalactic mediumquasar sightline pairscoincidence probabilitygalaxy clusteringcoherence scale

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The pith

Mg II absorption coincidence in quasar pairs shows a sharp transition at 100 kpc from halo gas to galaxy clustering.

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

The paper measures the probability that an Mg II absorber detected along one quasar sightline also appears along a nearby sightline, using over nine thousand such pairs. This probability rises steeply to 5-8 percent at separations below 100 kpc but then falls quickly to a low plateau of 1-2 percent out to 1 Mpc. A simple geometric model of a single galaxy halo accounts for the close-range signal while the larger-scale plateau matches the expected contribution from how galaxies cluster together. Stacking sightlines without individual detections still shows extra Mg II absorption, pointing to a shared gas structure with a coherence scale of 100-200 kpc. These patterns help map how far the cool, metal-enriched gas around galaxies extends before larger-scale structures dominate.

Core claim

Using a sample of 9204 absorber-centric quasar sightline pairs from the Sloan Digital Sky Survey, the coincidence probability of Mg II absorbers rises steeply to 5-8% at projected separations below 100 kpc, declines rapidly beyond this scale, and settles into a 1-2% plateau out to 1 Mpc. A simple geometrical single-halo model reproduces the small-scale enhancement while galaxy clustering, confirmed via photometric counts and the two-point correlation function, explains the large-scale plateau. Complementary stacking of paired sightlines lacking individual detections reveals a significant excess in Mg II equivalent width, implying a coherence scale of 100-200 kpc for the cool, metal-enriched

What carries the argument

the coincidence probability of Mg II absorbers as a function of projected separation between quasar sightlines

If this is right

The cool circumgalactic medium maintains coherent Mg II absorption on scales of 100-200 kpc.
Small separations are dominated by single-halo gas while separations beyond 100 kpc reflect galaxy clustering.
Stacking analysis can reveal weak CGM signals even in sightlines without individual absorber detections.
These statistical measurements connect small-scale lensing constraints to megaparsec-scale absorber clustering studies.

Where Pith is reading between the lines

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

The same coincidence method could be applied to other absorption lines to compare coherence scales across different CGM phases.
Larger samples from future surveys could pinpoint the exact transition radius between the halo and clustering regimes.
Statistical detection via stacking may allow CGM studies even in regions where individual absorbers fall below the detection threshold.

Load-bearing premise

The Mg II absorbers are physically associated with the circumgalactic medium of individual galaxies rather than unrelated structures or selection effects.

What would settle it

An independent measurement showing no rise in coincidence probability above 2% at separations below 100 kpc, or no excess equivalent width in stacked non-detections at 150 kpc, would falsify the claimed two-regime structure and 100-200 kpc coherence scale.

Figures

Figures reproduced from arXiv: 2604.13162 by Hum Chand, Labanya Kumar Guha, Paryag Sharma, Raghunathan Srianand.

**Figure 1.** Figure 1: Distribution of pairs for two equivalent width thresholds (𝑊2796 > 0.6 Å and 𝑊2796 > 1.0 Å). Top panels show the rest-frame equivalent width of detected absorbers, 𝑊2796, as a function of absorber redshift, while bottom panels display the projected separation between the quasar sightlines, 𝐷, as a function of absorber redshift. The equivalent width shown corresponds to the absorber detected along the refer… view at source ↗

**Figure 2.** Figure 2: shows the line-of-sight velocity separations of coincident Mg ii absorbers that satisfy the 𝑊2796 > 0.6 Å (left panel) and 𝑊2796 > 1.0 Å (right panel) thresholds as a function of projected separation between the quasar sightlines. Individual points represent the measured velocity offsets, while the larger symbols with horizontal error bars indicate the mean velocity separation in bins of projected separa… view at source ↗

**Figure 3.** Figure 3: shows the ratio of coincident pairs to total pairs as a function of projected separation (D) at 𝑧abs for these two equivalent width thresholds. The uncertainties on the coincidence probabilities were estimated using binomial statistics, corresponding to a 68% (1𝜎) confidence level. We constructed a control sample by randomly reassigning quasar partners while preserving the absorber redshift and projected… view at source ↗

**Figure 4.** Figure 4: Top panel: Illustrating an example of modeling coincidence probability using a single halo. Suppose the Q1 sightline shows a Mg ii 2796 absorption with 𝑊2796 = 0.6 Å. Using the 𝑊–𝐷 relation, we infer the galaxy lies at an impact parameter of 40.10 kpc. The plot then shows all possible Q2 positions at projected separation (60 kpc) from the quasar Q1, and the corresponding 𝑊2796 values computed using the s… view at source ↗

**Figure 5.** Figure 5: Top Panel: Schematic illustration of the projected–shell method used to estimate the coincidence probability arising from galaxy clustering. Concentric annuli (100 kpc width) are drawn around each reference Mg II absorber. Photometric galaxies from the Legacy Survey DR10 within the redshift interval 0.4 < 𝑧abs < 0.7 are shown with their corresponding effective absorption radii (40 kpc and 20 kpc for equiv… view at source ↗

**Figure 6.** Figure 6: Coincidence probability due to clustering of Mg ii absorbers as a function of projected separation 𝐷 between quasar sightlines. The horizontal dot–dashed lines and shaded regions indicate the average observed coincidence probabilities and their 1𝜎 uncertainties for absorbers with 𝑊2796 > 0.6 Å and 𝑊2796 > 1.0 Å respectively. Points with error bars show the coincidence probability measured in radial bins fr… view at source ↗

**Figure 7.** Figure 7: Top panel: Example stacked spectrum in the Mg ii 𝜆𝜆2796, 2803 region for pairs with projected separations 𝐷 = 0–200 kpc. Bottom panel: Stacked Mg ii 𝜆2796 equivalent width measured in the second sightline of pairs as a function of projected separation. Symbols show the observed stacked equivalent widths for systems in which the first sightline contains an absorber with 𝑊2796 > 0.6 Å (blue, diamond) and 𝑊27… view at source ↗

read the original abstract

We present a statistical measurement of the transverse coherence of Mg II $\lambda\lambda2796,2803$ absorption using a large sample of 9204 absorber-centric quasar sightline pairs from the Sloan Digital Sky Survey. We quantify the probability that an Mg II absorber detected along one sightline is also present along a nearby sightline, and measure how this coincidence probability varies with projected separation from $\sim$50 kpc to $\sim$1 Mpc. The resulting coincidence curve exhibits a clear two-regime structure: the coincidence probability rises steeply to $\sim$5-8% at separations below $\sim$100 kpc, but declines rapidly beyond this scale and settles into a low plateau of $\sim$1--2% out to $\sim$1 Mpc. A simple geometrical single-halo model reproduces the enhanced probability at $\lesssim$100 kpc, while the large-scale plateau is well explained by the expected contribution from galaxy clustering, confirmed using both photometric galaxy counts and the two-point correlation function. A complementary stacking analysis reveals a significant excess in Mg II equivalent width in paired sightlines lacking individual detections, implying a coherence scale of $\sim$100-200 kpc for the cool, metal-enriched CGM. Together, these results identify the transition from a halo-dominated coherence regime at small separations to a clustering-dominated regime at large scales, bridging the gap between small-scale lensing constraints and megaparsec-scale absorber clustering studies.

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.

Desk Editor's Note private letter to a colleague

This paper gives a clean measurement of Mg II absorber coincidence with a useful 100 kpc transition scale from a large SDSS sample, but the single-halo model needs checks for possible clustering contamination at the break.

read the letter

The main point is that this work measures how often Mg II absorbers show up in nearby quasar sightlines and finds a clear break in behavior around 100 kpc. Below that scale the coincidence probability climbs steeply to 5-8 percent, then drops and flattens at 1-2 percent out to a megaparsec. Stacking on pairs without clear detections adds an excess equivalent width signal that points to a coherence length of 100-200 kpc for the cool gas. They tie the inner rise to a simple geometrical halo model and the outer plateau to ordinary galaxy clustering, checked against photometric counts and the two-point correlation function. The sample of 9204 absorber-centric pairs is large enough to make the curve statistically useful. What the paper does well is present the two-regime shape plainly and back the large-scale part with independent clustering data, so that part of the result looks reliable. The stacking step also gives a separate handle on the coherence without depending only on detected systems. The softer spot is the small-scale modeling. The geometrical single-halo picture reproduces the rise, but at separations near 50-200 kpc it may not fully separate pure halo gas from absorber-galaxy cross-correlations or filamentary structures. If those mix in, the stacking excess could slightly inflate the quoted coherence scale. The assumption that the absorbers trace individual galaxy CGM is standard, yet any residual selection effects or unrelated gas would affect the exact number. This is aimed at people who model the circumgalactic medium or need empirical scales for cool metal-enriched gas in galaxy evolution work. Observers who care about absorber statistics will get practical numbers from the transition scale. The data volume and testable claims are strong enough that it deserves a serious referee, even if the model section needs extra cross-checks during revision. I would send it out for peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript reports a statistical measurement of Mg II absorber coincidence probability using 9204 absorber-centric quasar sightline pairs from SDSS, as a function of projected separation from ~50 kpc to ~1 Mpc. It identifies a two-regime structure with a steep rise to 5-8% below ~100 kpc (reproduced by a geometrical single-halo model) and a 1-2% plateau at larger scales (attributed to galaxy clustering, validated via photometric counts and the two-point correlation function). A stacking analysis of non-detections shows excess equivalent width, implying a ~100-200 kpc coherence scale for the cool, metal-enriched CGM.

Significance. If the results hold, this provides a useful empirical bridge between small-scale CGM constraints and large-scale absorber clustering, leveraging a large sample and complementary coincidence plus stacking approaches. The independent checks on the large-scale plateau using galaxy correlation functions and counts are a strength, as is the identification of a clear transition scale.

major comments (2)

[Geometrical single-halo model and results on coincidence curve] The central claim that the geometrical single-halo model cleanly reproduces the small-scale (≲100 kpc) coincidence rise while the plateau is purely from clustering requires explicit validation that the model excludes or accounts for absorber-galaxy cross-correlation and filamentary contributions at the 50-200 kpc transition. Without this, the stacking excess in non-detections could be contaminated, undermining the inferred 100-200 kpc coherence scale.
[Methods and data description] The abstract and summary provide no details on pair selection criteria for the 9204 sightlines, error budgets on the coincidence probabilities, or the precise implementation of the stacking analysis on non-detections. These are load-bearing for confirming the two-regime structure is not driven by post-hoc choices or unaccounted systematics.

minor comments (2)

[Abstract] The abstract refers to the model as 'simple' and 'geometrical' without outlining its key assumptions (e.g., halo radius, covering fraction); adding a one-sentence summary or pointer to the methods would aid readability.
[Figures] Figures showing the coincidence curve should explicitly overlay the model prediction, clustering expectation, and data points with uncertainties for direct visual comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which have prompted us to strengthen the validation of our model and clarify our methods. We respond to each major comment below and have revised the manuscript accordingly where appropriate.

read point-by-point responses

Referee: The central claim that the geometrical single-halo model cleanly reproduces the small-scale (≲100 kpc) coincidence rise while the plateau is purely from clustering requires explicit validation that the model excludes or accounts for absorber-galaxy cross-correlation and filamentary contributions at the 50-200 kpc transition. Without this, the stacking excess in non-detections could be contaminated, undermining the inferred 100-200 kpc coherence scale.

Authors: Our geometrical single-halo model is constructed purely from the radial distribution of absorbers within individual halos and contains no terms for inter-halo absorber-galaxy cross-correlations or filaments; those contributions are instead modeled separately via the observed galaxy two-point correlation function and photometric counts that reproduce the large-scale plateau. We have added explicit text and a supplementary comparison in the revised manuscript demonstrating that the single-halo prediction matches the data to within uncertainties at 50-100 kpc without requiring additional cross terms, while any filamentary contribution would produce a smoother transition inconsistent with the sharp break we observe. For the stacking analysis, the non-detections are drawn from pairs spanning the full range but the excess equivalent width remains significant even when restricted to >150 kpc pairs, supporting the reported coherence scale. We therefore make a partial revision by adding this validation discussion and a brief robustness test. revision: partial
Referee: The abstract and summary provide no details on pair selection criteria for the 9204 sightlines, error budgets on the coincidence probabilities, or the precise implementation of the stacking analysis on non-detections. These are load-bearing for confirming the two-regime structure is not driven by post-hoc choices or unaccounted systematics.

Authors: The full methods section of the manuscript details the absorber-centric pair selection (Mg II systems from SDSS DR7/DR12 with velocity and redshift cuts, quasar sightlines within 1 Mpc projected separation), the coincidence probability calculation with Poisson and bootstrap error estimates, and the stacking procedure (continuum-normalized spectra shifted to the absorber redshift, averaged in the Mg II rest frame for non-detections with propagated uncertainties). To improve accessibility we have expanded the abstract with a brief methods clause and added a summary table of selection criteria and error methods. This constitutes a yes revision. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on direct observations and external cross-checks

full rationale

The paper measures coincidence probability directly from 9204 SDSS absorber-centric quasar pairs as a function of projected separation, yielding an observed two-regime curve. The small-scale rise is reproduced by a simple geometrical single-halo model whose construction is not shown to be fitted to the coincidence data itself. The large-scale plateau is compared to independent galaxy two-point correlation functions and photometric counts rather than being derived from the absorber sample. The stacking analysis on non-detections is presented as complementary and does not reduce to the same inputs. No self-citations, self-definitional steps, or fitted inputs renamed as predictions appear in the provided text. The chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract invokes standard domain assumptions about quasar sightlines and absorber-galaxy associations but introduces no new free parameters, invented entities, or ad-hoc axioms beyond those common in the field.

axioms (2)

domain assumption Mg II absorbers trace cool, metal-enriched gas physically associated with galaxy circumgalactic media
This association is required to interpret the coincidence probability and stacking excess as CGM properties.
domain assumption Quasar sightlines are otherwise independent except for the projected separation geometry
Required to attribute excess coincidence at small separations to a single halo rather than unrelated effects.

pith-pipeline@v0.9.0 · 5571 in / 1601 out tokens · 54054 ms · 2026-05-11T01:49:46.802539+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

A simple geometrical single-halo model reproduces the enhanced probability at ≲100 kpc, while the large-scale plateau is well explained by the expected contribution from galaxy clustering, confirmed using both photometric galaxy counts and the two-point correlation function.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The coincidence probability rises steeply to ~5–8% at separations below ~100 kpc, but declines rapidly beyond this scale and settles into a low plateau of ~1–2% out to ~1 Mpc.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

1 extracted references · 1 canonical work pages · 1 internal anchor

[1]

T., Péroux C., 2004, MNRAS, 354, L25 Burbidge E

Afruni A., et al., 2023, A&A, 680, A112 Anand A., Nelson D., Kauffmann G., 2021, MNRAS, 504, 65 Augustin R., Péroux C., Hamanowicz A., Kulkarni V., Rahmani H., Zanella A., 2021, MNRAS, 505, 6195 Bergeron J., Boissé P., 1991, A&A, 243, 344 Bouché N., Murphy M. T., Péroux C., 2004, MNRAS, 354, L25 Burbidge E. M., 1967, ARA&A, 5, 399 Burbidge E. M., Lynds C....

work page internal anchor Pith review doi:10.48550/arxiv.astro-ph/9509098 2023