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Assembly bias from nuisance to probe I: the relation between galactic conformity and the linear matter clustering

T0 review · 2 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The paper shows that two-halo galactic conformity is a double-difference statistic whose radial shape follows the linear matter correlation function, with assembly bias setting its amplitude.

desk verdict A useful analytic repackaging of two-halo conformity as a linear-response statistic, with a plausible assembly-bias amplitude claim that is not yet fully closed by the tests presented. read the letter →

arxiv 2607.04022 v2 pith:US55PW5V submitted 2026-07-04 astro-ph.GA astro-ph.CO

Nelson Padilla , Ivan Lacerna , Dante Paz This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords galaxies:evolutionhaloesstatisticslarge-scalestructureofUniversecosmology:theorygalacticconformityassemblybias
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 tries to establish that two-halo galactic conformity—the excess quenching of neighbours around quenched galaxies versus star-forming ones—is not a nuisance contaminant of clustering measurements but a compact probe of cosmology and galaxy formation. It shows the standard statistic Δf_Q(r) can be written exactly as a combination of correlation functions, and that in the weak-clustering limit its scale dependence reduces to a single amplitude times the linear matter correlation function ξ_mm^lin(r). Measured in the IllustrisTNG300 simulation at z=0, this template describes Δf_Q(r) over roughly 2–40 h^-1 Mpc, with an amplitude larger than halo-mass bias alone predicts and strongly suppressed when galaxies are shuffled at fixed halo mass. The authors conclude that the amplitude of two-halo conformity is set by galaxy assembly bias, while its radial shape traces the linear matter clustering, turning a former nuisance into a probe.

What carries the argument

The central object is the double-difference ratio form of the conformity statistic, Δf_Q(r) = f̄_Q [ (1+ξ_QQ)/(1+ξ_QN) − (1+ξ_SFQ)/(1+ξ_SFN) ]. In the weak-clustering limit the difference of ratios collapses to f̄_Q (b_Q−b_SF)(b_Q−b_N) ξ_mm^lin(r), which cancels the constant term and, more generally, the ratio-and-difference structure suppresses nonlinear and transition-scale terms common to the selected and total neighbour profiles when the compared primary populations have similar halo masses. The transformed family G_n = f^n_{X|H} − f^n_{X|L}, especially cubic conformity n=3, reweights the same signal to preserve the linear template to smaller separations.

What would settle it

Build a mass-only mock from the same TNG300 halo catalogue by assigning quenched status as a deterministic function of halo mass alone; if the resulting Δf_Q matches the Tinker-based prediction and the full simulation's signal, the assembly-bias interpretation fails. Alternatively, fit Δf_Q(r) with a nonlinear matter template (e.g., halofit) over 2–40 h^-1 Mpc: if the nonlinear template fits significantly better with the same amplitude structure, the linear-response interpretation is wrong.

Watch

Extended reading notes

Core claim

Δf_Q(r) is a definite function of auto- and cross-correlations of quenched, star-forming, and neighbour samples (Eq. 3). Expanding each correlation as a biased linear template b_i b_j ξ_mm^lin gives Δf_Q ≈ f̄_Q (b_Q − b_SF)(b_Q − b_N) ξ_mm^lin(r). Measurements in TNG300-1 confirm that this single-amplitude linear template holds from ~2 to 40 h^-1 Mpc, and that the fitted amplitude exceeds the halo-mass-only prediction computed from Tinker et al. (2010) bias–mass relation. Shuffling galaxies between haloes in 0.1 dex mass bins suppresses the signal, so in TNG300 the amplitude is dominated by galaxy assembly bias at fixed halo mass; quenching, colour, and concentration splits share the same re

Load-bearing premise

The amplitude decomposition rests on the Tinker et al. (2010) bias–mass relation being the correct halo-mass-only prediction for TNG300 galaxies and on 0.1-dex fixed-mass shuffling erasing only assembly-bias correlations; if either fails, the claim that assembly bias dominates the amplitude is not established.

Editorial extensions

If this is right

  • Two-halo conformity, measured as Δf_Q(r), is a compact real-space statistic whose radial shape directly traces the linear matter correlation function over ~2–40 h^-1 Mpc.
  • Because halo-mass bias alone underpredicts the amplitude and fixed-mass shuffling removes it, the statistic is a direct measure of galaxy assembly bias at fixed halo mass.
  • The double-difference construction suppresses nonlinear and baryonic scale dependence, so the linear template extends to smaller separations than the individual correlation functions.
  • Assembly-bias-linked observables (quenching, colour, concentration) share a common rescaled template, providing a selection criterion for which galaxy splits are clean assembly-bias probes.
  • The transformed family G_n, especially cubic conformity n=3, reweights the signal to preserve the template deeper into the nonlinear regime with a modest gain in information.

Reading between the lines

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

  • If the template survives projection to a line-of-sight statistic, the same double-difference construction could yield an assembly-bias amplitude for galaxy surveys that is largely independent of the assumed mass-bias relation.
  • The factorized amplitude (b_Q−b_SF)(b_Q−b_N) implies a consistency check: measuring Δf_Q for two different neighbour selections over-constrains the bias differences and can test whether one assembly-bias field drives all observables.
  • A testable extension is to correlate the amplitudes of Δf for quenching, colour, and concentration across environments or redshifts; a single rescaled shape is consistent with a common assembly field, but a correlation of amplitudes would confirm it.
  • Combining Δf_Q with the full correlation-function vector in a joint likelihood could sharpen the Ω_m shape information while keeping the assembly-bias amplitude as a free parameter.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper derives a correlation-function expression for the two-halo galactic conformity statistic Δf_Q(r) (Eq. 3), shows in the weak-clustering limit that it reduces to a bias-factorisation amplitude times the linear matter correlation function (Eqs. 4–6), and tests the single-template form Δf_Q(r) = A_fit ξ_mm^lin(r) against IllustrisTNG300-1 at z=0 over ~2–40 h^-1 Mpc (Eq. 7, Fig. 1). It reports that the linear template describes the measured signal, that a halo-mass-only bias estimate based on Tinker et al. (2010) underpredicts the amplitude, and that fixed-mass shuffling strongly suppresses the signal. The paper concludes that the amplitude of two-halo conformity in TNG300 is dominated by galaxy assembly bias at fixed halo mass, while the radial shape traces linear matter clustering. Supporting tests include Ω_m shape recovery, common-shape comparisons for quenching, colour, and concentration, and the transformed G_n family, including the cubic statistic G_{n=3}.

Significance. If the central claim holds, this is a useful conceptual advance: it turns an often ad hoc conformity diagnostic into a compact statistic whose scale dependence is tied to linear clustering and whose amplitude is tied to galaxy assembly bias. The derivation in Sec. 2 is clean, and the internal consistency checks (Ω_m recovery, shuffling suppression, common-shape tests among quenching/colour/concentration, and the G_n family) are thoughtful and appropriate. The paper is also honest about the limits of the Ω_m test and about the stress-test nature of the mass-split comparisons. However, the central amplitude decomposition is not yet closed: the shuffled signal is never directly compared with the halo-mass-only prediction. That comparison is required to justify Eq. (9)'s identification of the residual amplitude with assembly bias rather than with a mis-estimated mass-only bias or with shuffle-induced destruction of physical correlations. With that closure test supplied, the paper would provide a credible route to using galaxy assembly bias as a probe rather than a nuisance.

major comments (2)
  1. [Sec. 4, Fig. 2, Eq. (9)] The decomposition Δb_eff = Δb_mass + Δb_AB rests on a two-legged argument: (i) the Tinker et al. (2010) mass-only prediction is smaller than the measured signal, and (ii) fixed-mass shuffling suppresses the signal. These two legs are jointly sufficient only if the shuffled signal agrees with the mass-only prediction. The text states only that both are 'smaller amplitudes than the original signal' but never reports whether the shuffled amplitude equals, exceeds, or falls below the mass-only curve. If the shuffled amplitude is below the mass-only prediction, the shuffle destroys correlations beyond assembly bias; if it is above, either the shuffle fails to erase all fixed-mass correlations or the Tinker relation does not correctly describe the mass-only bias for TNG300 galaxies. Please overplot the shuffled Δf_Q(r) with the Tinker-based mass-only prediction, with jackknife errors, so that
  2. [Sec. 4, Fig. 1, Eq. (7)] The main shape claim—that Δf_Q(r) is 'well described' by A_fit ξ_mm^lin(r) over ~2–40 h^-1 Mpc—is presented visually, but no quantitative goodness-of-fit is reported. Since A_fit is fitted to the same data, a visual claim is not sufficient to distinguish a genuinely linear template from a one-parameter approximation to a mildly curved signal. Please report a χ²/dof (or equivalent) over the fitted range, the jackknife uncertainty on A_fit, and a residual plot with error bars. This also affects the common-shape test in Fig. A.1: normalising each signal by its own best-fit amplitude removes amplitude information, so the claim of a common rescaled shape is only as strong as the per-signal fit quality. Without these numbers, the common-shape agreement is partly by construction.
minor comments (4)
  1. [Sec. 2.1, Eqs. (10)–(11)] The definition of G_n and the factorised form for G_{n=3} should be written more explicitly. In particular, the notation f_{X|H} and f_{X|L} is introduced quickly; a short sentence defining H/L and the meaning of 'cubic conformity' before Eq. (11) would help the reader verify the algebra.
  2. [Sec. 3 and Fig. 2] The caption of Fig. 2 should clearly identify the model curves (Tinker mass-only prediction, bias-factorisation, etc.) and specify whether the open symbols are the fully shuffled sample or one of the variants discussed in the footnote. Currently the reader must infer this from the text and legend description.
  3. [Sec. 3] Please clarify how the 'effective biases' used in the bias-factorisation model are measured from the correlations and how they differ from the Tinker-based halo-mass-only biases. In particular, state explicitly whether the effective biases are free parameters or fixed by measured clustering amplitudes.
  4. [Appendix A] The stellar-mass and halo-mass split thresholds are only given in the appendix text; consider stating them in the main text or in the Fig. A.1 caption, since these stress tests are discussed in Sec. 5 as supporting the claim that near-linearity is not generic.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the shape claim is tested against an external linear template and the mass-only amplitude uses an external bias calibration; only minor in-sample bias-factorisation comparisons and the shuffle-based assembly-bias definition create small non-independent elements.

full rationale

The paper's central derivation is self-contained. Equation (3) is an exact rewriting of the quenched-neighbour fraction in terms of correlation functions, not a result that presupposes the conclusion. The linear-template claim (Eq. 7) fits only the amplitude A_fit and compares the radial shape against ξlin_mm(r) computed externally from CAMB for the TNG cosmology, so agreement in shape is not manufactured by the fit; residuals are shown. The weak-clustering expansion (Eqs. 4-6) is a standard linear-bias derivation from an external factorization assumption (Zehavi et al. 2011), and the mass-only amplitude (Eqs. 8-9 with Tinker et al. 2010) is an external calibration. The claim that halo-mass bias alone predicts lower amplitudes is therefore not circular. The shuffle test is an operational definition of assembly bias at fixed halo mass; the paper does not report a closure test comparing the shuffled amplitude with the mass-only prediction, which is a robustness/correctness concern rather than a circular step. Self-citations (Contreras et al. 2019; Lacerna et al. 2025) provide supporting context and are not load-bearing for the derivation. The only mildly non-independent element is that the bias-factorisation comparison uses effective biases measured from the same correlations used to build Δf_Q, making that particular model comparison a repackaging of the same data rather than a fully external prediction; however, it is not the central evidence for the paper's conclusions, which rest on the external Tinker calibration and the fitted-template shape test. Overall, no load-bearing circularity is present; the score of 2 reflects the minor in-sample determination of effective biases in one auxiliary comparison, not a defect in the main derivation chain.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim requires one fitted amplitude (A_fit), the linear-bias factorisation assumption, the external Tinker mass-bias calibration, and a particular interpretation of the shuffling test. No new physical entities are introduced; the G_n family is a family of statistics, not a new entity.

free parameters (1)
  • A_fit = Not reported in text (best-fit amplitude of the linear template)
    Eq. (7): the single amplitude fitted directly to the measured ∆f_Q is used to test the linear-template shape. The amplitude itself is not predicted from first principles or from an independent calibration.
assumptions (5)
  • domain assumption Large-scale linear bias factorisation ξ_ij ≃ b_i b_j ξ_mm^lin
    Used in Sec. 2.1 (Eq. 5 and the bias-factorisation model) to derive the expected template and amplitude. This is standard in the field but assumed to hold for TNG300 galaxies over the fitted range.
  • domain assumption Tinker et al. (2010) bias–mass relation is valid for TNG300 host haloes
    Eq. (8) and Sec. 4: the mass-only amplitude estimate relies on this external calibration. If the relation misestimates bias for TNG300 haloes, the inferred assembly-bias fraction changes.
  • ad hoc to paper Fixed-mass shuffling removes only assembly-bias correlations
    Fig. 2 and Sec. 4: the shuffle test is the primary evidence that the amplitude is dominated by assembly bias; the interpretation assumes that shuffling galaxies in 0.1-dex mass bins erases fixed-mass secondary correlations without destroying other physical correlations.
  • standard math Weak-clustering expansion captures the leading large-scale behaviour
    Eq. (4) and Sec. 2.2: the linear-response form follows from a Taylor expansion in |ξ| ≪ 1. The paper argues the exact ratio form extends the range, but the formal derivation starts from this assumption.
  • domain assumption TNG300-1 is representative of galaxy formation at z=0
    All measurements and conclusions are drawn from a single hydrodynamical simulation volume; cosmic variance is not fully accounted, and the paper notes its jackknife errors are internal only.

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Cite this review

Pith. "Pith review of Assembly bias from nuisance to probe I: the relation between galactic conformity and the linear matter clustering." pith.science (2026). https://pith.science/paper/US55PW5V

@misc{pith2026260704022,
  author       = {Pith},
  title        = {Pith review of: Assembly bias from nuisance to probe I: the relation between galactic conformity and the linear matter clustering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/US55PW5V}},
  note         = {Machine review of arXiv:2607.04022}
}
abstract

Two-halo galactic conformity is commonly interpreted as a manifestation of galaxy assembly bias, but its statistical structure and physical origin remain unclear. We aim to write the quenched-neighbour statistic in correlation-function form, test whether its scale dependence follows the linear matter correlation function $\xi_{\rm mm}^{\rm lin}(r)$, and separate the contributions of halo-mass bias and assembly bias to its amplitude. Using galaxies in IllustrisTNG300-1 at $z=0$, we measure the two-halo galactic conformity statistic of quenched neighbours at distance $r$, $\Delta f_{Q}(r)$, and related quantities in real space, compute the required correlations, perform shuffling tests at fixed halo mass, compare several $\Delta f$ observables, and explore the transformed family $G_n$. We show explicitly that $\Delta f_{Q}(r)$ can be written directly in terms of correlation functions and that, over $\sim 2$--$40\,h^{-1}\,\mathrm{Mpc}$, it is well described by $A_{\rm fit}\,\xi_{\rm mm}^{\rm lin}(r)$. Thus nonlinear and baryonic terms do not dominate the residual scale dependence isolated by this statistic. Halo-mass bias alone predicts lower amplitudes than measured, while fixed-mass shuffling strongly suppresses the signal; in TNG300 the amplitude is therefore dominated by galaxy assembly bias at fixed halo mass. Quenching, colour, and concentration share a common rescaled shape, whereas stellar-mass and halo-mass splits do not. These results suggest that galaxy assembly bias sets the amplitude of two-halo conformity, while the double-difference structure of the statistic suppresses nonlinear residuals when the compared populations have similar halo-mass and transition-scale structure.

Figures

Figures reproduced from arXiv: 2607.04022 by the authors.

Figure 1
Figure 1. Fractions of quenched galaxies and galactic conformity. Top: quenched-neighbour fractions around quenched and star-forming cen￾tral primaries, together with the corresponding bias-factorisation and linear template predictions; colours identify the primary samples and line styles identify the models. The bottom subpanel shows ratios be￾tween models and data; error bars are obtained from 64 jackknife re￾gions. Bottom:… view at source ↗
Figure 2
Figure 2. Shuffling test. The original conformity signal (solid symbols) is strongly suppressed in the sample obtained by shuffling galaxies be￾tween halos in 0.1 dex mass bins (open squares). This demonstrates that the amplitude of ∆fQ is dominated by galaxy assembly bias rather than by halo-mass selection (see the legend for description of different model lines). Article number, page 3 of 7 [PITH_FULL_IMAGE:figures/full_fi… view at source ↗

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