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REVIEW 4 major objections 6 minor 63 references

Siblings, friends and acquaintances: Testing galaxy association methods

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Friends-of-Friends galaxy grouping, the standard percolation method for identifying groups and clusters in surveys, systematically over-associates members around massive halos in dense environments, inflating cluster-scale systems to…

desk verdict Honest FoF calibration study whose qualitative contamination result holds, but whose headline percentages lack error bars and come from in-sample tuning. read the letter →

arxiv 1908.07593 v1 pith:26DFN7LI submitted 2019-08-20 astro-ph.GA

J. P. Caso , C. A. Vega-Martínez This is my paper · ORCID
classification astro-ph.GA
keywords Friends-of-FriendsmethodpercolationgalaxygroupsclusterscontaminationMDPL2simulationhaloassociationvelocitydispersion
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 asks whether Friends-of-Friends (FoF) percolation, the standard way to assign galaxies to groups and clusters in redshift surveys, returns the right memberships when observational noise is present. Using the MDPL2 cosmological dark matter simulation at z=0, the authors add realistic radial-velocity errors and projected-distance uncertainties to the halo catalogue, run FoF with several linking-length parameter sets, and compare each output association against the simulation's own bound-halo structure. They find that FoF is reliable in low-density environments but systematically over-associates in dense ones: for cluster-like regions roughly 62% of massive main halos acquire more members than they truly have, and simulated clusters above $10^{15}\,h^{-1}M_\odot$ are inflated to about four times as many centrals and seven times as many satellites. The paper also shows that halo-mass-dependent cuts on projected distance and radial velocity, plus substructure tests, can reduce the fake-positive rate, and it applies the tuned method to the Virgo cluster region as a sanity check.

What carries the argument

The machinery is the Friends-of-Friends linking-length percolation algorithm, which links galaxies whose projected separation and radial-velocity difference both fall below thresholds $D_{\mathrm{p,max}}$ and $V_{\mathrm{R,max}}$. The central diagnostic is the ratio $\mathrm{RS/O}$: the number of satellites that the simulation's halo finder assigns to a main halo divided by the number of halos that FoF associates to it, so values below one count fake positives. The other load-bearing element is the truth definition: the halo finder's host/satellite tree in the MDPL2 simulation, taken as the correct galaxy-group membership. Around this, the paper builds empirical 95th-percentile fits for maximum projected distance and radial velocity difference as functions of main-halo mass, and uses them as post-processing cuts together with a nearest-neighbour substructure test to flag or remove contaminated systems.

What would settle it

Redo the same FoF runs on MDPL2 but replace the simulation's host/satellite tree with a different subhalo-tracking definition of true membership, then recompute the fraction of massive main halos with $\mathrm{RS/O}<1$ in the densest environmental bin; if the fraction drops from roughly 62% to below about 20%, the claimed contamination is an artefact of the chosen truth definition rather than of FoF itself.

Watch

Extended reading notes

Core claim

The central discovery is that the percolation/FoF association method, even with linking lengths optimised on the simulation, is not uniformly accurate: its success depends strongly on environment. In the densest environmental percentiles, typical of rich groups and clusters, about 62% of main halos with at least two satellites have $\mathrm{RS/O}<1$, meaning the method attaches more satellites than are gravitationally bound, with a mean ratio of 0.5 and scatter 0.22. When the FoF output is used to define $>10^{15}\,h^{-1}M_\odot$ clusters, the method returns roughly four times the true number of central galaxies and seven times the true number of satellites; the excess members are mostly low-mass field halos that contribute little mass but inflate velocity dispersions and distort conditional luminosity functions. The authors argue that these are not artefacts of the added velocity uncertainties, which change only about 1% of classifications, but consequences of the method's geometry in high-density regions, and that applying cuts derived from the simulation, such as the 95th percentile of maximum projected satellite distance and radial velocity difference as functions of main-halo mass, markedly improves the recovered group properties.

Load-bearing premise

The whole accuracy calculation assumes the simulation's own halo-finder grouping, the host/satellite labels, is the correct galaxy-group membership; if that grouping is ambiguous, especially for infalling galaxies near cluster edges, the quoted contamination fractions measure disagreement with the halo finder rather than error against physical groups.

Editorial extensions

If this is right

  • FoF-based group and cluster catalogues in dense environments carry a large fraction of fake members, so observables computed from those members, such as velocity dispersions, harmonic radii, and conditional luminosity functions, are biased even when the linking parameters are chosen for maximum overall success.
  • Counting systems with FoF-defined virial masses above $10^{15}\,h^{-1}M_\odot$ overproduces clusters by a factor of roughly four in centrals and seven in satellites, so richness- and luminosity-based cluster samples built this way are substantially contaminated at the high-mass end.
  • Applying the paper's mass-dependent cuts on maximum projected distance and radial velocity difference, together with substructure tests, can reduce but not eliminate the contamination; the substructure test only flags a third to half of the contaminated systems at moderate confidence.
  • Low-density environments are much less affected, so FoF results for field galaxies and small groups are more trustworthy than those for clusters.
  • Radial-velocity uncertainties are not the source of the contamination, since removing them changes only about 1% of classifications; the geometry of the linking thresholds in dense regions drives the fake-positive rate.

Reading between the lines

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

  • A direct test of the paper's diagnosis would be to run the same FoF parameters on the same MDPL2 halo catalogue but replace the simulation's host/satellite labels with a different subhalo-tracking definition of membership; if the dense-environment contamination fraction drops below about 20%, the reported 62% is particular to the chosen truth definition rather than to FoF itself.
  • The fake positives are mostly low-mass field halos projected near massive cluster halos, which suggests contamination concentrates in the infall region around clusters; a membership criterion based on infall dynamics or splashback radius could remove most spurious members without the paper's mass-dependent cuts.
  • Because contamination is environment-dependent and strongest exactly where cluster-versus-field comparisons are made, the paper's numbers imply that some observed environmental trends in galaxy properties could be inflated by FoF selection artefacts; testing this would require redoing those comparisons with the paper's cleaned memberships.
  • The same methodology could be applied to other association algorithms, such as Bayesian or clustering-based group finders, to see whether the contamination is a generic property of projection-based grouping or specific to percolation with fixed linking lengths.
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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

4 major / 6 minor

Summary. The paper tests the standard Friends-of-Friends (FoF) linking-length percolation method for associating galaxies into groups, using the MDPL2 dark matter simulation at z=0. The authors build a mock galaxy catalogue by assigning K-band luminosities to Rockstar halos via a simple HOD, add radial-velocity uncertainties calibrated to 2MRS, and compute projected distances in three Cartesian planes. They select two tuned FoF parameter sets (cases A and B) plus the Crook et al. (2007) set (case C), then quantify success as a function of environmental density. The central finding is that FoF association in dense, cluster-like environments is heavily contaminated: for massive main halos in the densest percentile, roughly 62% have more associated members than true satellites (RS/O<1), and for systems with virial mass above 10^15 Msun/h the method produces about four times too many centrals and seven times too many satellites relative to the Rockstar bound-halo populations. The authors also propose mass-dependent cuts on maximum projected distance and radial velocity (Eq. 3 in Section 4.6) that improve the success fraction, and they apply the method to the Virgo cluster as a sanity check.

Significance. If the central result holds, it is important: raw FoF group catalogues in dense environments are not merely incomplete but heavily contaminated, which biases velocity dispersions, harmonic radii, and conditional luminosity functions. The paper uses a large public simulation, makes its benchmark assumption explicit, and gives a transparent, reproducible analysis pipeline. The Virgo application is a useful qualitative sanity check. However, the quantitative headline is weakened by the fact that the linking-length parameters are tuned on the same catalogue used for evaluation, by the absence of uncertainty estimates on the key percentages, and by the reliance on Rockstar's host/satellite classification as the definition of true membership. These issues do not undermine the qualitative direction of the result, but they do prevent the specific contamination rates from being taken as robust, calibration-free measurements.

major comments (4)
  1. [§4.2, §4.3] Cases (A) and (B) are selected by scanning the mesh in Figure 3 and manually choosing parameters that maximize the success fraction on the very same MDPL2 halo catalogue that is then used to measure the success fractions in Figures 4–5 and the contamination statistics in Figures 6–7 and Section 4.4. Because the headline numbers (62% of massive main halos with RS/O<1 in the densest environments, and the 4x/7x central/satellite overcounting for 10^15 Msun/h systems) are measured on the same data used for tuning, they are in-sample estimates rather than independent measures of FoF performance. Please provide an out-of-sample evaluation, for example by splitting the simulation volume into independent subvolumes, using a different simulation, or withholding a subset of halos, and report how the contamination fractions vary with plausible parameter choices.
  2. [§4.3, §4.4] The key percentages and distribution properties in Section 4.3 and Section 4.4 are quoted as exact values from one Gpc/h simulation at z=0, with no error bars or sample-variance estimates. The environmental density bins are not independent draws, and the three projection planes are correlated. Please add bootstrap or jackknife uncertainties over subvolumes (or over the three projection planes) for the quoted fractions such as 62%, 7%, 25%, 4x, and 7x, and for the reported means/dispersions of the RS/O distributions. Without these, the reader cannot assess whether the differences between environmental bins are significant.
  3. [§4.6, Eq. (3)] The constraints in Equation (3) are fitted to the 95th percentiles of DMh,max and ΔVR,max measured from the same MDPL2 simulation, and then the percolation algorithm is rerun on the same halos to demonstrate the improvement in Figure 15. This is an in-sample evaluation: the fitted curves absorb noise and peculiarities of the particular simulation, so the reported improvement is likely overestimated. Please validate the constraints on an independent simulation or an independent subvolume, propagate the fit-parameter uncertainties into the classification, and report how the improvement depends on the choice of percentile (e.g., 90th versus 99th).
  4. [§4.2, §4.3] The evaluation treats Rockstar's host/satellite association as the correct group membership, as stated in Section 4.2 ('Assuming the association of halos in the simulation as the correct one'). This is an explicit and honest definitional choice, but it means the quoted contamination rates are relative to Rockstar's halo-finder classification, not directly to physical galaxy-group membership. Infalling halos near cluster outskirts are particularly ambiguous, and a different halo finder or a different definition of 'true satellite' could shift the quoted percentages. Please discuss the robustness of the contamination fractions to this definitional ambiguity, or provide a side test using a different association definition (for example, splashback-based or phase-space based membership) for a subset of halos.
minor comments (6)
  1. [Abstract] The phrase 'In order to constraint the limitations' should read 'In order to constrain the limitations'.
  2. [Figure 6] The y-axis labels 'n [Mpc−3]' appear to describe a count of neighbor halos within 1.75 Mpc/h, which is not a number density. Please relabel the axis as a count (N) or convert to a true number density.
  3. [§4.4] In the paragraph discussing Figure 9, the text states 'Dp,max = 525 Mpc, i.e., ≈ 355 Mpc h−1'; the units should be kpc, not Mpc, and the conversion as written is inconsistent.
  4. [Figure 17 caption] The caption refers to 'Section sec.param' instead of the actual section number where the linking-length parameters are defined.
  5. [§4.6] The statement that the 95th percentile 'barely matches the 2σ deviation' is imprecise; for a Gaussian distribution the 95th percentile is approximately 1.645σ, not 2σ.
  6. [References] The reference 'York D. G. S. 2000' should be formatted as York et al. (2000), and the entry for Ivezić has a typographical issue in the author name.

Circularity Check

1 steps flagged · score 4.0 of 10

The central contamination claim is benchmarked against external Rockstar labels and is not circular, but the Section 4.6 improvement claim is in-sample: the Eq. (3) cuts are fitted to the same simulation's true satellite distances and then evaluated on that same simulation, so the reported gain is partly guaranteed by construction.

  1. fitted input called prediction [Section 4.6, Eq. (3) and Figure 15]
    "For constraining the projected distances, we select as an upper limit the 95th percentile of DMh,max ... We rerun the percolation algorithm for halos more massive than 1011 M⊙ h−1 (case A), applying the restrictions in the maximum projected distance to the main halo (DMh,max) and the maximum difference in radial velocity (ΔVR,max). These restrictions resulted in an improvement in the fraction of halos accurately classified by the method."

    The function in Eq. (3) is fitted to the 95th percentiles of DMh,max and ΔVR,max taken from the same MDPL2 simulation's true host–satellite pairs used for the evaluation. Rerunning the percolation algorithm with those fitted values as hard cuts and then measuring the fraction of accurately classified halos on the same simulation is therefore not an independent test: by construction roughly 95% of real satellites lie inside each fitted bound, so the reported improvement is statistically forced by the choice of thresholds. The same in-sample logic applies to the linking-length parameters of cases (A), (B) and (C), which were selected from the success map of Figure 3 on this very catalogue before being used to measure contamination fractions.

full rationale

The paper's primary claim—that FoF association produces a large fraction of contaminants for massive halos in dense environments—is derived by comparing FoF outputs against Rockstar's host/satellite classification, which is external to the FoF algorithm. The paper explicitly states this assumption ('Assuming the association of halos in the simulation as the correct one'), so the contamination measurement is definitional rather than tautological, and the Virgo-cluster application provides an external sanity check. I find no load-bearing self-citations or imported uniqueness theorems; the cited prior work is used for context and parameter choices, not to guarantee the main result. The main circularity concern is in-sample tuning. The linking-length parameters for cases (A), (B) and (C) are chosen by maximizing success on the same MDPL2 catalogue that is later used to evaluate success and contamination, which inflates apparent performance but does not by itself force the contamination fractions. More concretely, the Section 4.6 constraints are fitted to the 95th percentiles of the true satellite distance and velocity distributions (Eq. 3), and then the algorithm is rerun and the improvement is measured on the same simulation; this improvement is partly guaranteed by construction, since the fitted thresholds are derived from the very labels used as the ground truth. The paper is candid about its limitations (indicative luminosities, lack of virial masses in surveys, future work for direct survey comparison) and does not claim external validation for the constraints. Overall, the central contamination result is independent and non-circular, but the secondary improvement result and the parameter selection are in-sample, so a moderate score is appropriate.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

All key numbers are measured relative to Rockstar's host/subhalo labels and depend on the HOD luminosity assignment and the assumed completeness. These are necessary modeling choices, not arbitrary invented entities. No new physics is postulated.

free parameters (7)
  • Dp,max (Case A) = 525 kpc
    Linking length in projected distance manually selected from a parameter mesh to maximize satellite association success for halos more massive than 1e11 Msun in the same MDPL2 catalogue used for evaluation (Section 4.2).
  • VR,max (Case A) = 980 km/s
    Linking length in radial velocity manually selected in the same mesh maximization used for Dp,max (Section 4.2).
  • Dp,max (Case B) = 975 kpc
    Linking length in projected distance chosen to maximize success for halos more massive than 1e12 Msun in the same catalogue used for evaluation (Section 4.2).
  • VR,max (Case B) = 1100 km/s
    Linking length in radial velocity chosen in the same maximization used for Dp,max in Case B (Section 4.2).
  • DMh,max constraint fit coefficients = alpha=2.66, beta=-0.75, gamma=14.93
    Fitted to the 95th percentile of simulated maximum projected satellite distance as a function of virial mass and used as the new distance cutoff in Section 4.6, Equation 3.
  • DeltaV_R,max constraint fit coefficients = alpha=1255, beta=-0.83, gamma=14.03
    Fitted to the 95th percentile of simulated maximum radial velocity difference and used as the new velocity cutoff in Section 4.6, Equation 3.
  • Environmental density radius = 1.75 Mpc/h
    Chosen by hand as the radius defining the numerical density proxy, intended to match the typical virial radius of the most massive halos (Section 4.1). This choice sets the environment percentiles used throughout the analysis.
assumptions (4)
  • domain assumption Rockstar host/satellite halo assignment is the correct definition of galaxy group membership, so any deviation by the FoF method is a misclassification.
    Used as the benchmark throughout; explicitly stated in Section 4.2: 'Assuming the association of halos in the simulation as the correct one'. If this definition is ambiguous, contamination fractions are only relative to Rockstar.
  • domain assumption Each dark matter halo hosts exactly one galaxy, and galaxy luminosity is a monotonic function of halo virial mass through HOD matching.
    Section 2.1, Equation 1 assigns magnitudes via ng(>L)=nh(>M). The authors note this ignores environmental differences between centrals and satellites but assert the effect is masked by velocity uncertainties.
  • domain assumption The mock catalogue is complete up to the adopted virial mass limit over the full redshift range, ignoring flux-limited and redshift completeness.
    Stated in Section 3: 'We assume the sample is complete up to the limiting virial mass at the entire redshift range'.
  • domain assumption The Crook et al. (2007) percolation algorithm with fixed linking lengths adequately represents FoF methods used in galaxy surveys.
    The paper deliberately follows this algorithm in Section 3 and generalizes conclusions to the percolation method as a family.

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Pith. "Pith review of Siblings, friends and acquaintances: Testing galaxy association methods." pith.science (2026). https://pith.science/paper/26DFN7LI

@misc{pith2026190807593,
  author       = {Pith},
  title        = {Pith review of: Siblings, friends and acquaintances: Testing galaxy association methods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/26DFN7LI}},
  note         = {Machine review of arXiv:1908.07593}
}
abstract

In order to constraint the limitations of association methods applied to galaxy surveys, we analysed the catalogue of halos at $z=0$ of a cosmological simulation, trying to reproduce the limitations that an observational survey deal with. We focused in the percolation method, usually called Friends of Friends method, commonly used in literature. The analysis was carried on the dark matter cosmological simulation MDPL2, from the Multidark project. Results point to a large fraction of contaminants for massive halos in high density environments. Thresholds in the association parameters and the subsequent analysis of observational properties can mitigate the occurrence of fake positives. The use of tests for substructures can also be efficient in particular cases.

Figures

Figures reproduced from arXiv: 1908.07593 by the authors.

Figure 1
Figure 1. Uncertainties in radial velocity from the 2MASS Red￾shift Survey (Huchra et al. 2012) as a function of galaxies appar￾ent magnitude in K filter. Open circles show the mean values in bins of 0.2 mag, the solid red line represent a third-order poly￾nomial fitted to data, while green dashed lines correspond to the standard deviation fit. Catalogue from 2MASS3 (Skrutskie et al. 2006). The Fig￾ure 1 shows eVR as a functi… view at source ↗
Figure 2
Figure 2. Distribution of different main halo properties as a function of their virial mass. In the four panels, the colour gradient ranges from yellow to black according to the value frequency. Upper-left panel: number of components in main halos, Upper-right panel: fraction of mass enclosed in satellite halos to main halo mass. Lower-left panel: spatial distance of satellite halos to the centre of the main halo. Grey diamon… view at source ↗
Figure 4
Figure 4. Fraction of halos (solid lines) and main halos (dashed lines) accurately classified by the method as a function of their main halo virial mass in case (A). The sample was split in several ranges of environmental density which are depicted with different line colours, so that darker colours represent denser environments. 4.3 Method success and environmental density To analyse the method success on the classification … view at source ↗
Figures from the paper (14 more)
Figure 3
Figure 3. Figure 3: Ratio of satellite halos accurately associated to their main halo to the total sample of satellite halos in terms of the virial mass for different values of linking-length parameters in projected distance Dp,max and radial velocity VR,max. The colour gradients ranges f…
Figure 5
Figure 5. Figure 5: Same as in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Smoothed distribution of the ratio between the number of satellites (S) and the number halos associated by the method from the observational constraints (O), RS/O, for these main halos as a function of the virial mass in case (A). The three panels correspond to equally…
Figure 7
Figure 7. Figure 7: Smoothed distribution of the ratio between the num￾ber of satellites and the number halos associated by the method (RS/O) for the densest percentile of halos more massive than 1012 M⊙ h −1 in cases (B) and (C), left and right panels, respec￾tively. equally populated. T…
Figure 8
Figure 8. Figure 8: Distribution of the number of satellites associated by the method for field halos (upper panel) and halos with a single satellite (lower panel) in case (A). The samples are split in six bins of mass and each one in three density bins. The colour labelled with a dash co…
Figure 9
Figure 9. Figure 9: Distribution of projected distances to the main halo as￾sociated by the method for real satellites (solid lines) and fake pos￾itives (dashed lines). The gradient in colour scheme corresponds to mass intervals for the main halos, from the least (light) to the most massi…
Figure 11
Figure 11. Figure 11: Distribution of the ratio between the velocity disper￾sion of main halos (RσVx ) derived from halos associated by the method and the obtained from the real satellite halos, for the case (A), depicted with filled coloured contours. A value larger than 1 indicates the d…
Figure 10
Figure 10. Figure 10: Left panels: Ratio between the harmonic radius as￾sociated by the method for galaxy groups, and their real harmonic radius, for the three cases analysed in this paper. Solid contour levels correspond to main halos with RS/O < 0.33, dashed ones to 0.33 < RS/O < 0.66, a…
Figure 13
Figure 13. Figure 13: shows conditional luminosity functions for clusters of galaxies. These are obtained by selecting the main halos with virial masses larger than 1015 M⊙ h −1 when the systems associations with the percolation method in the case (A) are considered (filled histograms), an…
Figure 12
Figure 12. Figure 12: Distribution of velocity dispersion ratios, analogue to [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]
Figure 14
Figure 14. Figure 14: Analogue to [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]
Figure 16
Figure 16. Figure 16: Left panel [PITH_FULL_IMAGE:figures/full_fig_p013_16.png]
Figure 15
Figure 15. Figure 15: Upper panel: Fraction of halos (solid curves) and main halos (dashed curves) accurately classified as a function of their main halo virial mass, as in [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]
Figure 17
Figure 17. Figure 17: Results from applying the percolation method with the linking length parameters calculated in Section sec.param for a sample of galaxies brighter than MK = −21 in the surroundings of the Virgo cluster. Different symbols correspond to associations of galaxies found by …

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.