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Evolution of the Physical Properties of the Most Massive Galaxies in Clusters and their Protohalos

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The most massive galaxies in clusters grow continuously from z=4 to z=0—first by in-situ star formation, later by mergers—and this growth can be traced observationally by linking clusters to equal-rank groups.

desk verdict A useful observational evolution-chain method that deserves refereeing, but the headline three-phase growth story rests on an equation the authors concede is invalid at z>2.5; the descriptive trends are fine, the phase decomposition is not yet established. read the letter →

arxiv 2509.05637 v1 pith:23IYVDRO submitted 2025-09-06 astro-ph.GA

Qingyang Li , Xiaohu Yang , Antonios Katsianis , Paola Popesso , Ilaria Marini , Y. Sophia Dai , Chengze Liu , Yipeng Jing
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Jia-Sheng Huang Marcin Sawicki
This is my paper
classification astro-ph.GA
keywords galaxyclustersmostmassivegalaxiesbrightestclusterprotoclustersprotohalosevolutionabundancematchingredshift
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 establish a coherent observational picture of how the most massive galaxies in clusters form and grow, from z=4 to today. It claims that these galaxies continuously gain stellar mass, through intense star formation at early times and then through mergers and accretion at late times, and that this two-phase history can be reconstructed purely from observations by stitching together clusters, groups, and protohalos into evolutionary chains. The value of the claim is that it offers an observational route—abundance matching of group rank plus protohalo radii—to track galaxies across cosmic time without following individual objects, connecting high-redshift protocluster galaxies to local brightest cluster galaxies.

What carries the argument

The evolution chains are built by abundance matching: groups in successive redshift bins of width Δz=0.4 are ranked by halo mass within the cumulative halo mass function, and equal-rank groups are treated as ancestors and descendants. The group finder itself is halo-based, assigning halo masses through mass-to-light abundance matching. Protohalos are defined around the main progenitor group using a simulation-derived double power-law size history, R_ph(z)=2R_c (z/2)^α / (1+(z/2)^(α−β)). The in-situ/ex-situ decomposition rests on the identity M_pi = SFR × Δt + M_i, which estimates the stellar mass that star formation alone would produce across a redshift interval.

What would settle it

Run the paper's abundance-matching chain construction on a cosmological simulation with known merger trees (for example, a mock catalog from the same simulation used in the paper) and ask how often the rank-matched high-redshift group is the true main progenitor of each z=0 cluster; if recovery is low, or if the in-situ/ex-situ split changes when using the simulated galaxies' actual SFR histories, the central claims fail.

Watch

Extended reading notes

Core claim

The paper argues that the most massive galaxy (MMG) in a cluster is not a passive fossil but grows its stellar mass all the way from z=4 to z=0. Using a halo-based group finder applied to a deep multi-band galaxy catalog, it links eight low-redshift clusters to their progenitors by matching equal ranks in the cumulative halo mass function across redshift bins, and defines surrounding protohalos by a characteristic radius from a simulation-calibrated size history. The central finding is that first MMGs in clusters and protohalos are the same objects, with stellar mass rising to about 10^11.75 M_sun by z=0, and that growth separates into three phases: in-situ star formation dominates at z>2.5

Load-bearing premise

The chains assume that in each redshift bin groups keep the same rank in the cumulative halo mass function, so equal-rank matching identifies true ancestors and descendants; a second load-bearing assumption, which the authors concede fails at z>2.5, is that a galaxy's star-formation rate stays constant between redshift bins when computing in-situ growth.

Editorial extensions

If this is right

  • MMGs at z=0 assembled most of their stellar mass at z>2, with later growth dominated by dry mergers, supporting a two-phase assembly picture over passive evolution.
  • The in-situ/ex-situ phase boundaries give quantitative targets that cosmological simulations and semi-analytic models can be tested against.
  • Second MMGs are not scaled-down first MMGs: their growth stalls around z~1.5 and they can merge into the first MMG, so rank-based tracking must account for galaxy–galaxy mergers.
  • The abundance-matching chain method is transferable to larger deep surveys, offering statistical samples of cluster evolutionary tracks.
  • Cluster MMG trajectories oscillate in the cumulative stellar mass function, unlike smooth constant-number-density predictions, implying episodic mergers and feedback rather than steady abundance evolution.

Reading between the lines

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

  • If the late-time ex-situ dominance is real, one testable prediction is that z<1 mass growth should come with extended stellar halos and tidal debris from accreted satellites; deep imaging can search for these signatures.
  • The negative ex-situ contribution at z>2.5 hints that SED-derived SFRs may be systematically overestimated at high redshift; comparing with radio or far-infrared SFR tracers in the same field would test this directly.
  • The rank-matching chain assumes monotonic halo-mass rank over time, which hierarchical merging can violate; applying the same chain construction to simulations with known merger trees would quantify how often the matched group is the true main progenitor.
  • The method could be extended beyond the first two galaxies to trace the full satellite population, potentially reconstructing the assembly histories of all cluster galaxies rather than just the most massive ones.
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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

3 major / 5 minor

Summary. The paper uses the COSMOS2020 catalog with the halo-based group finder of Yang et al. to identify galaxy groups and clusters, then constructs evolutionary chains linking eight low-redshift reference clusters (z<0.4) to higher-redshift groups via cumulative-halo-mass-function abundance matching. Protohalo envelopes are defined using the Wang et al. (2023b) characteristic-radius formula. The authors compare the physical properties of first and second most massive galaxies (MMGs) in both cluster and protohalo environments from z=4 to z=0, reporting continuous stellar mass growth, intense star formation at z>2.5 followed by quenching, reddening, and old stellar populations. Using Eq. (8), they decompose stellar mass growth into in-situ and ex-situ components and identify three phases: in-situ dominated at z>2.5, transitionary at 1<z<2.5, and ex-situ dominated at z<1. They also compare their evolutionary tracks with the evolving cumulative number-density method.

Significance. The paper addresses an important question—how the most massive cluster galaxies and their protohalo counterparts assemble over cosmic time—and extends observational studies to z~4 in a single, consistent framework. Its strengths include the use of a well-tested group finder, a cosmic-variance check against the Jiutian simulation, comparison with theoretical growth curves, and public release of the derived group/protohalo catalogs. If the phase decomposition were robust, it would provide useful observational support for the two-mode (in-situ/ex-situ) assembly picture. However, the central phase claim currently rests on an estimator whose assumptions are acknowledged by the authors to be invalid at exactly the epoch where the in-situ-dominated phase is identified. The abundance-matched chains also carry a degree of self-calibration that needs to be quantified before the word 'progenitor' can be fully justified. The significance is therefore conditional on fixing the decomposition estimator and validating the chain construction.

major comments (3)
  1. [§5.1, Eq. (8), Fig. 7] The in-situ/ex-situ decomposition is computed as M_pi = SFR×Δt + M_i, which assumes constant SFR over the full interval and ignores stellar mass loss. For a Chabrier IMF the returned-mass fraction is substantial (~40%), so SFR×Δt overestimates the net stellar mass added. The authors themselves state in §5.1 that this assumption is invalid at z>2.5 and that the COSMOS2020 smooth-SFH assumption leads to underestimated stellar masses and overestimated SFRs. Under these assumptions the red arrows exceed the observed growth, producing a negative ex-situ contribution that is interpreted as feedback. This is not an established inference; with time-varying SFR and mass-loss corrections the z>2.5 'in-situ dominated' phase could weaken or disappear. Since the three-phase claim is the paper's central result, Eq. (8) must be replaced with a decomposition that accounts for mass loss and SFR history,
  2. [§3.1–§3.2] The evolutionary chains are constructed by ranking groups by halo mass in each redshift bin using the cumulative Sheth-Tormen halo mass function. But the group finder itself assigns group halo masses from group luminosities using the same Sheth-Tormen mass function via abundance matching (§3.1). The chains therefore preserve the rank ordering of a mass estimate calibrated with the same mass function, rather than testing whether equal-rank groups are true ancestors and descendants. The Jiutian comparison in the left panel of Fig. 3 shows that the median matched mass trajectory is consistent with cosmic variance, but it does not validate individual links. A mock-catalog test with known merger trees—using the same group finder and photo-z errors—would quantify the scatter and systematics in the chain construction, particularly at z>2.5 where matched groups are few.
  3. [§4, Fig. 3, Fig. 6] The high-redshift statements rest on a very small number of systems. Only eight reference clusters are used, and the right panel of Fig. 3 shows that the number of matched groups with a second MMG declines sharply at z>1.5; the number of groups with a first MMG must also decline toward z=4. The reported medians and shaded 1σ regions do not state how many objects contribute per redshift bin. It is therefore difficult to assess whether the z>2.5 in-situ-dominated phase, the apparent second-MMG plateau, and the high-z mass trends are driven by one or two systems. Please provide the number of contributing groups per bin and bootstrap/jackknife confidence intervals for the median tracks.
minor comments (5)
  1. [Abstract and §5.1] The abstract says in-situ star formation is efficient 'at z~2', while the body and Fig. 7 label the in-situ-dominated phase as z>2.5 and the transitionary phase as 1<z<2.5. These statements should be reconciled to avoid ambiguity about when the in-situ phase peaks.
  2. [§5.1] The bullet 'In-situ dominated time' describes a negative ex-situ contribution. If this is meant to be physical feedback removing gas or stars, the mechanism should be defined more carefully: feedback expels gas and suppresses future star formation, but it does not directly remove already-formed stars in the simple M_pi = SFR×Δt + M_i accounting.
  3. [§5 title] The section title 'TWO PHASE OF STELLAR MASS GROWTH' should be 'TWO PHASES' or 'TWO-PHASE', and the text actually describes three stages, so consider retitling.
  4. [Fig. 4 caption] The caption says 'points represent the redshift position of the matched progenitors of groups at different redshift bins', but the legend says 'evolution of galaxies for a progenitor group'; this appears to be a typo.
  5. [§6, Fig. 8] The comparison with the evolving cumulative number-density method would benefit from explicit quantification of the 'oscillation' and error bars on the MMG trajectory, since Fig. 8 currently shows single median tracks without uncertainties.

Circularity Check

2 steps flagged · score 6.0 of 10

The z>2.5 'in-situ dominated' phase is not an independent finding: Eq. (8) constructs the predicted stellar mass from the same SED-fitted SFR and stellar mass, and the paper itself admits that equation's assumptions are invalid in that regime; the abundance-matched evolution chains also reuse the same CHMF used to calibrate the group masses.

  1. self definitional [Section 3.2 (and Section 3.1)]
    "we first compute the cumulative halo mass function (CHMF) in redshift bins of width Δz=0.4, consistent with the redshift interval used in our group finder. Within each redshift bin, groups are ranked by halo mass. The low redshift groups are matched to the high redshift groups with the same level of CHMF."

    The halo masses used for ranking are not independent measurements: Section 3.1 states that 'The mass-to-light ratios of the groups in each redshift bin are determined with the cumulative halo mass functions (Sheth et al. 2001) and the group luminosity functions using the abundance matching method.' Thus the same Sheth-Tormen CHMF that assigns each group's halo mass is then used to define 'the same level of CHMF' that links groups across redshift. The progenitor chains are therefore constructed to enforce constant comoving number density in that theoretical mass function, so the resulting halo-mass evolution is a restatement of the matching assumption rather than an empirical tracing. The external Jiutian simulation comparison mitigates but does not remove this definitional coupling.

  2. fitted input called prediction [Section 5.1, Eq. (8), Figure 7]
    "Specifically, the predicted stellar mass is calculated using the following equation: Mpi = SFR×Δt + M_i (8) ... Therefore, the term SFR×Δt serves as an estimate of the in-situ stellar mass formed during that interval. ... making the assumptions of Equation 8 invalid."

    The 'predicted stellar mass' M_pi is not an independent prediction; it is constructed from the same SED-fitted SFR and stellar mass that define the observed evolutionary track. The ex-situ contribution is then the residual M_obs(next) − M_pi. Because COSMOS2020 assumes a smooth star-formation history, the SFR and M_i are degenerate, and because Eq. (8) ignores stellar mass loss and assumes constant SFR, a negative ex-situ residual at z>2.5 is effectively forced by the estimator's assumptions. The paper explicitly acknowledges 'COSMOS2020 assumes a fairly smooth star formation history for stellar mass and SFR. Such an assumption would likely lead to underestimated stellar masses and overestimated SFRs' and 'making the assumptions of Equation 8 invalid,' yet still labels z>2.5 as 'in-situ do

full rationale

The paper's central claim—a three-phase in-situ/ex-situ growth history—rests on Eq. (8), which is an accounting identity M_pi = SFR×Δt + M_i, not a physical prediction. The 'ex-situ' contribution is simply the residual between the observed stellar-mass increase and this estimator, so the sign of that residual is determined by the assumed constant SFR and neglected mass loss. The authors themselves state the assumptions are invalid at z>2.5, yet they retain the phase label. This is the clearest circular step: the conclusion is built into the estimator. A second, milder circularity affects the abundance-matching chains: group halo masses are calibrated using the same Sheth-Tormen cumulative halo mass function that is then used to define 'same level' progenitors, so the match is partly self-definitional. However, the paper does include an external comparison with the Jiutian simulation and with the Katsianis et al. (2025) theoretical growth curve, which provides some independent support for the overall mass-growth trend. The self-citations (Yang et al. 2021; Li et al. 2022) are used for the group finder and are validated on mocks, so they are not the main issue. On balance, the central decomposition is partially circular because the phase boundaries are forced by the input SED/SFR assumptions, but the paper's broader empirical trends and external checks keep it from being wholly reducible to its inputs.

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

The central claims rest on four layers of external or assumed input: (1) the abundance-matching link assumes constant comoving number density and monotonic mass rank; (2) the group finder's halo masses are calibrated via the same mass function, so the chains are self-consistent but not independent; (3) the protohalo radii come from a simulation-calibrated fitting formula whose amplitude depends on the observed MMG stellar mass fraction, coupling the environment definition to the measured property; and (4) the in-situ/ex-situ decomposition treats the SFR as constant over each interval and ignores mass loss, an assumption the authors explicitly admit fails at z>2.5. No new entities are introduced.

free parameters (4)
  • Group finder background threshold B = 10
    Section 3.1; chosen based on theoretical density contrast; affects group membership and hence halo masses and the reference cluster sample.
  • Redshift bin width Δz = 0.4
    Sections 3.1-3.2; used for both group finding and abundance matching; coarser bins reduce photo-z outlier contamination but smear the evolutionary links.
  • Protohalo redshift depth = 0.1
    Section 3.3; fixed to the photometric redshift uncertainty of the faint magnitude bin; defines which galaxies enter protohalos.
  • sSFR quenched threshold = 10^-11 yr^-1
    Figure 6 caption; criterion from Katsianis et al. (2019); determines where the paper calls MMGs quenched.
assumptions (5)
  • domain assumption Groups with equal rank in the cumulative halo mass function across redshift bins are ancestors/descendants (abundance matching).
    Section 3.2; this is the backbone of the evolution chains; assumes constant comoving number density and monotonic mass evolution, validated only statistically with Jiutian simulation (left panel Fig. 3).
  • domain assumption The halo-based group finder recovers accurate halo masses from photometric redshifts.
    Section 3.1; relies on Yang et al. (2021) mock validation; any bias in mass-to-light ratios propagates into CHMF ranks and hence ancestors.
  • domain assumption Protohalo radius formula Eq. (4)-(6) from Wang et al. (2023b) is valid for these observed clusters.
    Section 3.3; the simulation-calibrated coefficients are applied to observed groups; R_c depends on r (observed MMG mass fraction), tying the protohalo definition to the measured property under study.
  • ad hoc to paper Stellar mass growth predicted by Eq. (8) treats SFR as constant over the redshift interval and ignores mass loss.
    Section 5.1; authors explicitly say this is invalid at z>2.5 where the residual becomes negative; the decomposition into in-situ/ex-situ relies on this.
  • domain assumption SED fitting (LePhare) provides unbiased stellar masses and SFRs with the assumed smooth star formation histories.
    Section 2.1; authors note COSMOS2020 assumes smooth SFH, causing underestimated M* and overestimated SFRs on rapid timescales.

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Cite this review

Pith. "Pith review of Evolution of the Physical Properties of the Most Massive Galaxies in Clusters and their Protohalos." pith.science (2026). https://pith.science/paper/23IYVDRO

@misc{pith2026250905637,
  author       = {Pith},
  title        = {Pith review of: Evolution of the Physical Properties of the Most Massive Galaxies in Clusters and their Protohalos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/23IYVDRO}},
  note         = {Machine review of arXiv:2509.05637}
}
abstract

We investigated the evolution of the physical properties of the brightest galaxies in clusters and their protohalos from $z = 4$ to $z = 0$. Galaxy clusters and groups are identified using a halo-based group finder applied to the COSMOS2020 galaxy catalog. We construct evolution chains from low redshift clusters to higher redshift groups via the abundance matching method. The region of protohalos corresponding to clusters is defined on the basis of a characteristic radius. Our analysis encompasses a wide range of physical properties, including stellar mass, luminosity, star formation rate (SFR), specific star formation rate (sSFR), color ($g - r$), and stellar age. The evolution trends of the most massive galaxies (MMGs) in higher redshift groups and their corresponding protohalos are generally consistent. The stellar mass of MMGs shows an increasing trend across the entire redshift range. By considering the stellar mass growth as in-situ and ex-situ components, we find that in-situ star formation is efficient at $z \sim 2$, while ex-situ accretion becomes the primary growth channel at later times. At $z \gtrsim 2$, MMGs undergo an intense star formation phase of approximately $10^{2}\ \rm M_{\odot}yr^{-1}$, but are generally quenched at lower redshifts. Stellar age analysis suggests that most stars in MMGs formed at $z > 2$. Our results present a coherent picture of MMG evolution across cosmic epochs, which is broadly consistent with the current theoretical framework of galaxy formation and evolution. Moreover, our work provides an intriguing way to trace galaxy evolution through the construction of cluster evolutionary chains in observations.

Figures

Figures reproduced from arXiv: 2509.05637 by the authors.

Figure 1
Figure 1. The sky coverage of the selected galaxies in the COSMOS field. The galaxy number count in each pixel with an area of about 2.8 × 10−4 deg2 is coded with the color bar. The empty circles inside the coverage of the galaxies correspond to the masked areas. |∆z| > 0.15(1 + zspec). The values of b in three mag￾nitude bins 17 < i < 22.5, 22.5 < i < 24.0, and 24.0 < i < 25.0 are −0.003, −0.004 and −0.002 with uncertainty o… view at source ↗
Figure 2
Figure 2. The number histogram of the selected galaxies as a function of photo-z. The galaxies at 4 < z < 5 marked by the shadow region are not used for MMG evolution analysis. The group finder that we used in this study is a halo￾based method developed in Yang et al. (2005, 2007). The galaxy-halo connections have been extensively stud￾ied in theory (e.g., halo occupation distribution, stellar to halo mass ratios), which prov… view at source ↗
Figure 3
Figure 3. Left: the halo mass evolution of the progenitors of reference clusters. Each blue line represents the evolution of individual reference clusters. The blue triangles show the median halo mass with shaded area indicating 1σ error. The magenta, red, and orange points show the median halo mass corresponding to the first, fourth, and eighth most massive halos within the redshift bin 0 < z < 0.4 in the same level of CHMF.… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The evolution of protohalo size for the 8 referece clusters as a function of redshift. Each line represents the evolution of galaxies for a progenitor group, with color coded by the halo mass of reference clusters. The points represent the redshift position of the matc…
Figure 5
Figure 5. Figure 5: One example of member galaxies distribution in the evolution sequence of clusters and protohalos from z = 3.78 to z = 0.35. This reference cluster (ID 7) at z = 0.35 has a halo mass of 1014.36 M⊙. The black arrows mark the evolution trend from high redshift to low reds…
Figure 6
Figure 6. Figure 6: The evolution of physical properties of MMGs, including stellar mass, luminosity, SFR, sSFR, color and stellar age. The blue triangles and red points show the medians for cluster and protohalo MMGs. The solid and hollow symbols represent the physical properties of the …
Figure 7
Figure 7. Figure 7: Comparison of stellar mass growth from SED fitting and SFR. The left and right panels show the trends for the cluster and protohalo MMGs, respectively. The top and bottom panels show the comparisons for the first and second MMGs. The black line represents the median st…
Figure 8
Figure 8. Figure 8: Cumulative stellar mass functions at different redshifts, coded with different color lines. The solid and hol￾low triangles show the evolution trajectory of cluster first and second galaxies based on the median stellar mass shown in the top left panel of [PITH_FULL_IM…

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