arxiv: 2604.03105 · v1 · submitted 2026-04-03 · 🌌 astro-ph.GA

Recognition: 2 theorem links

· Lean Theorem

The tidal evolution of satellite galaxies in cosmological simulations: insights from COLIBRE

Feihong He , Jiaxin Han , Joop Schaye , Wenting Wang , Zhaozhou Li , Sylvia Ploeckinger , Evgenii Chaikin , Robert J. McGibbon

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Filip Hu\v{s}ko Matthieu Schaller Alejandro Ben\'itez-Llambay Alexander J. Richings James W. Trayford Carlos S. Frenk Fangzhou Jiang

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Pith reviewed 2026-05-13 19:03 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords tidal strippingsatellite galaxiesdark matterstellar mass losssubhalo evolutiondark-matter-deficient galaxiescosmological simulationsmass loss rates

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The pith

Satellite galaxies lose most dark matter before significant stellar stripping begins.

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

The paper shows that satellite galaxies follow a single universal track of mass loss in which dark matter is removed first and stars only start to be stripped once the subhalo has lost nearly all of its bound mass. This two-phase behavior is captured by a simple model with one critical threshold and explains why galaxies either keep most of their stars or disappear entirely. The same track accounts for the lack of orphan galaxies in simulations and predicts a distinct population of dark-matter-deficient galaxies whose numbers peak at a particular stellar mass. It also quantifies how numerical resolution can alter the observed satellite stellar mass function.

Core claim

Satellite galaxies follow a universal tidal track that links stellar mass loss to subhalo mass loss through two clear phases. Dark matter is stripped first while the stellar component stays largely intact. Only after the bound subhalo mass fraction falls below a critical value of roughly 0.057 does stellar stripping become important. The track produces a bimodal distribution of mass-loss rates: modest-loss satellites retain frozen stellar masses, while extreme-loss satellites dissolve together with their dark matter, leaving no orphans.

What carries the argument

The universal tidal track, a two-parameter model that separates an early dark-matter stripping phase from a later stellar stripping phase once the subhalo bound mass fraction drops below approximately 0.057.

If this is right

Satellites experiencing modest mass loss keep their stellar mass largely unchanged while dark matter is removed.
Satellites in the extreme mass-loss regime dissolve rapidly, explaining the absence of orphan galaxies in hydrodynamical simulations.
Dark-matter-deficient galaxies form when stripping proceeds past the critical threshold, with their abundance peaking near 10^9.5 solar masses in stellar mass.
Numerical disruption can reduce the satellite stellar mass function by about 20 percent at 10^9 solar masses and 50 percent at 10^8 solar masses for baryonic resolution around 10^6 solar masses.

Where Pith is reading between the lines

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

Galaxy formation models must incorporate this delayed onset of stellar stripping to avoid over-predicting the survival of low-mass satellites.
The same track offers a natural formation channel for ultra-diffuse or dark-matter-poor dwarfs observed in groups and clusters.
Higher-resolution simulations could test whether the critical fraction remains fixed or shifts with improved numerical treatment of tides.

Load-bearing premise

The subhalo finder and simulation resolution capture physical tidal stripping without dominant numerical artifacts that would alter the critical mass fraction or the two-phase rates.

What would settle it

Measuring the relation between stellar mass retained and remaining subhalo mass for a large sample of observed satellite galaxies at varying distances from their hosts; systematic deviation from the predicted track below the 0.057 threshold would falsify the model.

Figures

Figures reproduced from arXiv: 2604.03105 by Alejandro Ben\'itez-Llambay, Alexander J. Richings, Carlos S. Frenk, Evgenii Chaikin, Fangzhou Jiang, Feihong He, Filip Hu\v{s}ko, James W. Trayford, Jiaxin Han, Joop Schaye, Matthieu Schaller, Robert J. McGibbon, Sylvia Ploeckinger, Wenting Wang, Zhaozhou Li.

**Figure 1.** Figure 1: The mass and orbit evolution of example satellite subhaloes after reaching their peak mass 𝑚sub,peak. The left column shows the mass evolution. Different colours represent the mass evolution of different components, while the black line indicates the total bound mass of the subhalo. The grey vertical dotted line marks the accretion time 𝑡acc, defined as the time when the subhalo falls into the host halo. T… view at source ↗

**Figure 2.** Figure 2: The stellar evolutionary (from right to left) tidal tracks of satellite galaxies in clusters with 𝑀host > 1014M⊙ from colibre L200m6. The solid line indicates the median distribution of tidal tracks, with the shaded region representing the 16th–84th percentile distribution. Blue and red colours correspond to resolved and lost subhalo populations, respectively. The black dashed line shows the tidal track … view at source ↗

**Figure 4.** Figure 4: Comparison between the raw simulation data and the extrapolated tidal stripping model for satellite galaxies in cluster-scale haloes (𝑀host > 1014 M⊙). All selected satellites have 𝑚sub,peak > 1010 M⊙. In all panels, thick solid lines and shaded regions represent the median and 16th–84th percentile ranges, while thin lines show the trajectories of 100 randomly selected individual systems. Blue and red colo… view at source ↗

**Figure 6.** Figure 6: The subhalo mass function (𝑚sub, black lines) and satellite stellar mass function (𝑚∗, blue lines) averaged over host haloes with virial masses 𝑀host > 1014 M⊙. Top Panel: Solid lines represent the resolved population directly measured from the simulation data. Dashed lines include both resolved satellites and the lost population, recovered via our extrapolation model: the black dashed line represents the… view at source ↗

**Figure 5.** Figure 5: The distribution of subhalo mass loss and rates. 10 0 10 1 10 2 10 3 10 4 d N / dln m Mhost > 10 14M m = msub(resolved data) extrapolation m = m*(resolved data) extrapolation + tidal track resolved data + tidal track 10 8 10 9 10 10 10 11 10 12 m[M ] 1.0 1.5 d N m o d el/ d N d a t a extrapolation (m = msub) extrapolation + tidal track (m = m ) resolved data + tidal track (m = m ) [PITH_FULL_IMAGE:figures… view at source ↗

**Figure 7.** Figure 7: Evolution of the normalized stellar-to-subhalo mass ratio (the tidal “amplification factor” A), as a function of the 𝑓sub. The four panels display satellite tracks binned by their best-fit tidal track parameter 𝑏 (centered at 𝑏 ≈ 0.5, 0.75, 1.0, 1.25). The red solid lines and shaded regions represent the median and the 16th–84th percentile scatter of the simulation data, respectively. The black dashed line… view at source ↗

**Figure 8.** Figure 8: The peak stellar-to-subhalo mass ratio 𝑚∗,peak/𝑚sub,peak, as a function of stellar peak mass. The colour map represents the number of satellites in each bin (𝑁sat). The white dashed line and circles trace the median relation, while the dotted lines indicate the 16th–84th percentile scatter. The thick cyan line represents the median of stellar-to-halo mass relation for central galaxies at 𝑧 = 0 for referen… view at source ↗

**Figure 9.** Figure 9: The stellar-to-subhalo-mass ratio evolved to the present day (𝑧 = 0) for the resolved (left, blue) and extrapolated lost (right, red) satellite populations. The stellar masses of the resolved population are obtained directly from the simulation data, while the masses of the lost populations are inferred using the tidal track model. The y-axis shows the ratio 𝜉 = 𝑚∗/𝑚sub at 𝑧 = 0. The colour map indicates a… view at source ↗

**Figure 10.** Figure 10: The fraction of DMDGs (satellites with a stellar-to-subhalo mass ratio 𝜉 (𝑧 = 0) > 0.5), as a function of their evolved stellar mass at 𝑧 = 0. The blue circles represent the fraction measured solely from the resolved satellite population found in the simulation. The black squares represent the total population, which combines resolved satellites with the lost population (satellites recovered via extrapola… view at source ↗

**Figure 11.** Figure 11: Top Panel: The relationship of parameter 𝑓d in Eq. (2) to the stellar half-mass radius of satellites, scaled by the virial radius of their host subhaloes. The white dashed line represents the median of the distribution, and the shaded region represents the 16th-84th percentile. Bottom Panel: The relationship of parameter 𝑏 in Eq. (2) to the stellar peak mass of satellites, scaled by the subhalo peak mass.… view at source ↗

**Figure 13.** Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗

**Figure 12.** Figure 12: Resolution convergence test for satellite galaxies in the L200 volume. Top Panel: The median stellar mass fraction 𝑓∗ as a function of the subhalo mass fraction 𝑓sub for the L200m6 (orange) and L200m7 (red) runs. The shaded areas correspond to the 16th–84th percentile scatter. Middle Panel: Comparison of the joint probability distributions of the best-fitting tidal track parameters 𝑓d and 𝑏 for the L200m6… view at source ↗

**Figure 14.** Figure 14: The evolution of gas mass for the same sample of satellites shown in [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗

read the original abstract

We investigate the co-evolution of the stellar and dark matter mass of satellite galaxies using the COLIBRE cosmological hydrodynamical simulations with subhaloes resolved by the history-based HBT-HERONS subhalo finder. We identify a universal tidal track connecting stellar mass loss to subhalo mass loss characterized by two distinct phases, which can be well described by the two-parameter model. The initial phase consists primarily of dark matter stripping, whereas stellar stripping becomes significant only after the subhalo bound mass fraction drops below a critical value ($\sim 0.057$). We find a bimodal mass loss rate distribution of subhaloes. In satellites with modest mass loss rates, the stellar mass is largely frozen. By contrast, the galaxy quickly becomes unresolved, along with the dark matter component for the extreme-mass-loss population, naturally explaining the lack of ``orphan'' galaxies in previous hydrodynamical simulations. Our model also predicts the formation condition for dark-matter-deficient galaxies (DMDGs), whose abundance peaks at $m_{*}\sim 10^{9.5}\,\rm{M}_{\odot}$. The abundance of DMDGs can be very sensitive to numerical effects, with COLIBRE resolving a much larger DMDG population than previous hydrodynamical simulations. We also estimate the influence of artificial disruption on the satellite stellar mass function, which can amount to 20 (50) per cent at $m_* \sim 10^{9} (10^{8}) \, \rm M_\odot$, given a baryonic mass resolution of $\sim 10^{6}\,\rm{M}_{\odot}$.

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

COLIBRE runs give a clean two-phase tidal track for satellite mass loss with a transition near 0.057 bound fraction, but the number and universality rest on the HBT-HERONS finder and current resolution.

read the letter

The paper's main result is a simple two-parameter model that describes how stellar mass loss tracks subhalo mass loss in satellites. It splits the process into an early phase of mostly dark-matter stripping followed by rapid stellar stripping once the bound mass fraction drops below roughly 0.057. This organizes the simulation outputs and explains both the scarcity of orphan galaxies and a formation channel for dark-matter-deficient galaxies whose abundance peaks near 10^9.5 solar masses. The bimodal mass-loss rate distribution is a concrete finding that follows directly from tracking individual objects with the history-based HBT-HERONS finder on the COLIBRE runs. The authors are explicit about the numerical limits, noting that artificial disruption can remove 20-50 percent of satellites at 10^8-10^9 solar masses given the baryonic resolution of about 10^6 solar masses. That honesty is useful. The soft spot is the dependence on the subhalo finder and resolution. The abstract itself flags that DMDG counts are very sensitive to these choices, so the exact critical fraction could move if a different finder or higher resolution were used. Without additional tests that vary the finder or push the resolution, the claim of universality stays tied to this specific setup. The work is aimed at people building models of environmental quenching or comparing simulations to cluster galaxy populations. A reader who needs a quantitative reference for tidal stripping will find the track practical, even while treating the 0.057 value as provisional. I would send it to peer review because the framework is new enough and the simulations are solid enough to merit referee input on the robustness checks.

Referee Report

3 major / 2 minor

Summary. The manuscript analyzes satellite galaxy evolution in the COLIBRE cosmological hydrodynamical simulations using the history-based HBT-HERONS subhalo finder. It identifies a universal two-phase tidal track relating stellar mass loss to subhalo mass loss, with an initial phase dominated by dark matter stripping that transitions to significant stellar stripping once the subhalo bound mass fraction drops below a critical value of ~0.057. The work reports a bimodal subhalo mass-loss rate distribution, explains the absence of orphan galaxies, predicts the abundance of dark-matter-deficient galaxies (DMDGs) peaking at m* ~ 10^9.5 M⊙, and quantifies the impact of artificial disruption on the satellite stellar mass function (20-50% at 10^8-10^9 M⊙ for baryonic resolution ~10^6 M⊙).

Significance. If the tidal track, critical fraction, and DMDG predictions hold after robustness checks, the two-parameter model would supply a compact empirical description of tidal co-evolution useful for semi-analytic models and observational interpretation of dwarf satellites. The explicit discussion of numerical sensitivities and bimodal mass-loss populations advances understanding of why hydrodynamical simulations lack orphans and how resolution affects low-mass satellite counts.

major comments (3)

[Abstract and §4] Abstract and §4 (tidal track results): The central claim of a universal track with transition at bound-mass fraction ~0.057 is derived directly from HBT-HERONS outputs, yet the abstract states that DMDG counts are 'very sensitive to numerical effects' and artificial disruption removes 20-50% of satellites at 10^8-10^9 M⊙; this raises the possibility that the reported critical value and phase transition are shifted by the finder’s mass definition or the ~10^6 M⊙ baryonic resolution limit.
[§5] §5 (DMDG abundance): The predicted peak at m* ~ 10^9.5 M⊙ and the statement that COLIBRE resolves a much larger DMDG population than prior simulations rest on the assumption that HBT-HERONS correctly tracks bound mass down to the resolution floor; without explicit convergence tests varying resolution or subhalo finder, the abundance and formation condition remain vulnerable to post-processing choices.
[§4.3] §4.3 (bimodal mass-loss distribution): The separation into 'modest' and 'extreme' mass-loss populations, used to explain the lack of orphans, is identified from the same simulation suite; a shift in the critical fraction by even 0.02 due to finder differences would alter the relative sizes of the two populations and the implied stellar-mass freezing threshold.

minor comments (2)

[Figures] Figure captions: Several panels lack explicit labels for the mass bins or resolution cuts used to construct the tidal track; adding these would improve reproducibility.
[§4] Notation: The symbol for bound mass fraction is introduced without a dedicated equation or definition box on first use in the results; a short clarifying equation would aid readers.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their careful and constructive review. We address each major comment below and have revised the manuscript to strengthen the presentation of numerical robustness where possible.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (tidal track results): The central claim of a universal track with transition at bound-mass fraction ~0.057 is derived directly from HBT-HERONS outputs, yet the abstract states that DMDG counts are 'very sensitive to numerical effects' and artificial disruption removes 20-50% of satellites at 10^8-10^9 M⊙; this raises the possibility that the reported critical value and phase transition are shifted by the finder’s mass definition or the ~10^6 M⊙ baryonic resolution limit.

Authors: We agree that the interplay between numerical resolution and the reported critical fraction merits explicit discussion. The value 0.057 is measured exclusively from subhaloes whose bound mass lies well above the resolution floor at the time of the transition; we have verified internally that the transition point remains stable across the resolved mass range. In the revised manuscript we will add a dedicated paragraph in §4 clarifying the mass range used for the fit, the definition of bound mass in HBT-HERONS, and a brief sensitivity test showing that modest changes in the mass threshold do not move the transition outside 0.05–0.06. We will also tone down the abstract wording to avoid implying that the track itself is resolution-limited. revision: yes
Referee: [§5] §5 (DMDG abundance): The predicted peak at m* ~ 10^9.5 M⊙ and the statement that COLIBRE resolves a much larger DMDG population than prior simulations rest on the assumption that HBT-HERONS correctly tracks bound mass down to the resolution floor; without explicit convergence tests varying resolution or subhalo finder, the abundance and formation condition remain vulnerable to post-processing choices.

Authors: We acknowledge that a full resolution-convergence study would be the most direct way to quantify uncertainties in the DMDG peak. Such tests would require new simulation runs at multiple resolutions, which is outside the scope of the present project. Within the existing COLIBRE suite we have performed limited checks by varying the minimum particle number and subhalo finder linking parameters; the location of the DMDG abundance peak remains stable. In the revised §5 we will present these checks, add an explicit caveat on the lack of multi-resolution convergence, and compare the DMDG formation condition against the analytic expectation from the two-parameter tidal track. revision: partial
Referee: [§4.3] §4.3 (bimodal mass-loss distribution): The separation into 'modest' and 'extreme' mass-loss populations, used to explain the lack of orphans, is identified from the same simulation suite; a shift in the critical fraction by even 0.02 due to finder differences would alter the relative sizes of the two populations and the implied stellar-mass freezing threshold.

Authors: The bimodal mass-loss-rate distribution is a direct feature of the simulation data and is not imposed by the choice of critical fraction. We have re-examined the distribution after shifting the dividing line by ±0.02 and find that the qualitative separation into a population with frozen stellar mass and a population that rapidly becomes unresolved persists; only the precise fraction of galaxies in each bin changes. In the revised §4.3 we will include this sensitivity test and show that the explanation for the absence of orphan galaxies remains robust provided a threshold exists at which stellar stripping accelerates. revision: yes

standing simulated objections not resolved

Full multi-resolution convergence tests for the DMDG abundance and critical fraction, which would require new cosmological simulations.

Circularity Check

0 steps flagged

Tidal track and critical fraction measured empirically from COLIBRE simulation data

full rationale

The paper identifies the universal tidal track and the ~0.057 critical bound-mass fraction by direct inspection of mass-loss relations in the COLIBRE runs processed with HBT-HERONS. The two-parameter model is introduced only as a descriptive fit to the observed track; no equation or claim reduces the result to a prior fitted parameter, self-definition, or self-citation chain. The DMDG abundance and mass-function corrections are likewise outputs of the same simulation analysis rather than independent predictions forced by the model inputs. This is a standard empirical extraction from simulation data with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claims rest on outputs from the COLIBRE hydrodynamical simulations and the HBT-HERONS subhalo finder. The two-parameter model and the numerical value 0.057 are extracted from those runs.

free parameters (2)

critical bound mass fraction = 0.057
Threshold (~0.057) below which stellar stripping becomes significant; identified from simulation data.
two parameters of tidal track model
Parameters chosen to describe the universal mass-loss track across the simulation sample.

axioms (1)

domain assumption Standard Lambda-CDM cosmology and hydrodynamical baryonic physics govern galaxy formation in the COLIBRE runs
Invoked throughout the simulation setup and interpretation of tidal stripping.

pith-pipeline@v0.9.0 · 5663 in / 1419 out tokens · 51394 ms · 2026-05-13T19:03:38.123232+00:00 · methodology

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 (J-cost uniqueness) and phi_golden_ratio matches

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matches
MATCHES: this paper passage directly uses, restates, or depends on the cited Recognition theorem or module.

stellar stripping becomes significant only after the subhalo bound mass fraction drops below a critical value (~0.057)
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection (bilinear branch forced by coupling combiner) echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

universal tidal track ... two distinct phases ... two-parameter model

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

The Broken Similarity: Sinking and Merging of Dark Matter Subhalos Across Hierarchical Levels
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In LambdaCDM simulations, over 90% of subhalo sinking events occur between adjacent hierarchy levels, satellite-satellite mergers can rival central-satellite rates at low masses, and the overall merger landscape devia...
The evolution of the baryonic content and mass profiles of satellite galaxies in the MTNG simulations
astro-ph.GA 2026-04 unverdicted novelty 4.0

In the MTNG simulation, satellite galaxies lose ~80% of their gas by the time their subhalos lose half their mass, while stellar mass and magnitudes evolve more slowly following v_max reduction, with inner mass loss o...

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages · cited by 2 Pith papers

[1]

AriasB.,DrakosN.E.,TaylorJ.E.,2025,arXive-prints,p.arXiv:2508.16759 Bahé Y. M., et al., 2019, MNRAS, 485, 2287 Barry M., Wetzel A., Chapman S., Samuel J., Sanderson R., Arora A., 2023, MNRAS, 523, 428 Benítez-Llambay A., et al., 2026, MNRAS, 546, stag268 Booth C. M., Schaye J., 2009, MNRAS, 398, 53 BorrowJ.,SchallerM.,BahéY.M.,SchayeJ.,LudlowA.D.,Ploeckin...

work page arXiv 2025
[2]

heavy stripping

A crucial aspect of tracking stellar mass evolution is accurately capturing the "heavy stripping" regime, where the subhalo has lost the vast majority of its dark matter mass (𝑓sub ≪1) and the stellar massbeginstodeclinesharply.Unweightedleast-squaresfittingtends to be overwhelmingly dominated by the early evolutionary phase (where both𝑓 sub and𝑓 ∗ are cl...

work page 2026
[3]

2016 10 3 10 2 10 1 100 fsub = msub(t)/msub, peak 10 2 10 1 100 f = m (t)/m , peak fd = 0.057 b = 0.99 2 = 0.004 RMSE = 0.014 COLIBRE data This work (Eq

Smith et al. 2016 10 3 10 2 10 1 100 fsub = msub(t)/msub, peak 10 2 10 1 100 f = m (t)/m , peak fd = 0.057 b = 0.99 2 = 0.004 RMSE = 0.014 COLIBRE data This work (Eq

work page 2016
[4]

2016 10 3 10 2 10 1 100 fsub = msub(t)/msub, peak 10 2 10 1 100 f = m (t)/m , peak fd = 0.091 b = 1.77 2 = 0.011 RMSE = 0.030 COLIBRE data This work (Eq

Smith et al. 2016 10 3 10 2 10 1 100 fsub = msub(t)/msub, peak 10 2 10 1 100 f = m (t)/m , peak fd = 0.091 b = 1.77 2 = 0.011 RMSE = 0.030 COLIBRE data This work (Eq

work page 2016
[5]

2016 Figure B1.Representative examples of satellite galaxy stellar mass tidal evolution tracks from L200m6 simulations

Smith et al. 2016 Figure B1.Representative examples of satellite galaxy stellar mass tidal evolution tracks from L200m6 simulations. The black circles represent the simulationdata,showingtheremainingstellarmassfraction(𝑓 ∗)asafunction oftheremainingsubhalomassfraction(𝑓 sub).Thesolidblackanddashedblue curvesdenotethebest-fitresultsusingourmodel(Eq.(2))and...

work page 2016
[6]

2016 10 3 10 2 10 1 100 fsub = msub(t)/msub, peak 10 2 10 1 100 f = m (t)/m , peak fd = 0.304 b = 0.27 2 = 0.765 RMSE = 0.230 COLIBRE data This work (Eq

Smith et al. 2016 10 3 10 2 10 1 100 fsub = msub(t)/msub, peak 10 2 10 1 100 f = m (t)/m , peak fd = 0.304 b = 0.27 2 = 0.765 RMSE = 0.230 COLIBRE data This work (Eq

work page 2016
[7]

2016 Figure B3.Examples of outlier tidal tracks, presented in the same format as Fig

Smith et al. 2016 Figure B3.Examples of outlier tidal tracks, presented in the same format as Fig. B1. These subhaloes belong to the high-𝜒2 𝜈 tail in Fig. B2. For these rare cases, both our model (Eq. (2)) and Eq. (1) struggle to reproduce the simulated data precisely. MNRAS000, 1–20 (2026)

work page 2016