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REVIEW 3 major objections 4 minor 11 references

The Three Hundred Project: The relationship between the shock and splashback radii of simulated galaxy clusters

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Using 324 simulated galaxy clusters, this paper shows that the accretion shock radius is systematically larger than the splashback radius, with median ratios of 1.38 and 1.91 and a linear relation $r_\mathrm{shock} \simeq…

desk verdict Solid, useful calibration of the shock–splashback relation in full-physics clusters; the entropy-proxy validation gap is real but addressable. read the letter →

arxiv 2412.09864 v1 pith:CV333ETW submitted 2024-12-13 astro-ph.CO astro-ph.GA

M. Zhang , K. Walker , A. Sullivan , C. Power , W. Cui , Y. Li , X. Zhang This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords splashbackradiusaccretionshockintraclustermediumentropygalaxyclusteroutskirtscosmologicalhydrodynamicalsimulationsthermalSunyaev-Zeldovicheffectmasshistoryboundary
topics Dark Matter
open problems Dark Matter
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 sets out to quantify how the accretion shock radius of a galaxy cluster's gas, $r_\mathrm{shock}$, relates to the splashback radius, $r_\mathrm{splash}$, where dark matter and galaxies complete their first orbit. Using 324 clusters from full-physics cosmological simulations that include cooling, star formation, and black-hole feedback, it finds that the shock radius is almost always outside the splashback radius. Depending on how the shock is defined from the gas entropy profile, the median ratio is about 1.38 or 1.91, and the best-fit relation is $r_\mathrm{shock} \simeq 0.65\,r_\mathrm{splash}$ plus a constant offset. Both radii shrink relative to $R_{200}$ for more massive and more recently accreting clusters, while the ratio $r_\mathrm{shock}/r_\mathrm{splash}$ grows with recent accretion rate. The result matters because it gives observers a quantitative target: searches for shocks in radio, X-ray, and thermal Sunyaev-Zeldovich data should expect the boundary to lie well beyond the splashback radius.

What carries the argument

The load-bearing objects are the two boundary radii and the gas-entropy feature used to define one of them. The entropy $K \equiv k_\mathrm{B}T/n_\mathrm{e}^{2/3}$ is computed from the simulated gas temperature and electron density; the shock radius is identified either where $K$ reaches its maximum ($r_\mathrm{shock,p}$) or where its logarithmic slope $\mathrm{d}\ln K/\mathrm{d}\ln r$ reaches its minimum ($r_\mathrm{shock,m}$). The splashback radius is identified, by convention, where the logarithmic slope of the spherically averaged dark-matter density profile reaches its minimum. To make these identifications reliable in the presence of substructure, profiles are built from angular median filtering within each of 100 logarithmic radial bins, then smoothed with a Gaussian filter; the reported uncertainties and correlations come from bootstrap resampling and Spearman rank coefficients.

What would settle it

If, in the same simulated clusters, direct shock diagnostics such as temperature jumps or velocity discontinuities fail to coincide with $r_\mathrm{shock,p}$ or $r_\mathrm{shock,m}$ within the scatter, then the entropy-extremum definition does not trace the physical shock and the calibrated relations would not describe the shock boundary. Observationally, a stacked thermal Sunyaev-Zeldovich or X-ray profile of clusters with weak-lensing splashback measurements would test the claim: a shock feature appearing at $r_\mathrm{splash}$ rather than near $1.4$–$1.9\,r_\mathrm{splash}$ would falsify the predicted offset.

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Extended reading notes

Core claim

The paper's central claim is that the accretion shock and the splashback boundary are not the same surface. In the median cluster, the dark-matter splashback radius is $r_\mathrm{splash}=1.87\,R_{200}$, while the shock radius from the entropy maximum is $r_\mathrm{shock,p}=2.58\,R_{200}$ and from the minimum entropy slope $r_\mathrm{shock,m}=3.54\,R_{200}$. This gives median ratios $r_\mathrm{shock,p}/r_\mathrm{splash}=1.38$ and $r_\mathrm{shock,m}/r_\mathrm{splash}=1.91$, and the best-fit relations $r_\mathrm{shock,p}=0.64\,r_\mathrm{splash}+1.39\,h^{-1}\mathrm{Mpc}$ and $r_\mathrm{shock,m}=0.65\,r_\mathrm{splash}+2.38\,h^{-1}\mathrm{Mpc}$. Both radii, normalized by $R_{200}$, anticorrelate with virial mass and with the fractional mass increase since $z=0.5$, while the ratio $r_\mathrm{shock}/r_\mathrm{splash}$ is larger for clusters with higher recent accretion rates. The authors take this as evidence that the shock radius is a separate, outer boundary whose location in observations can be predicted from a measured splashback radius and an estimate of recent accretion.

Load-bearing premise

The load-bearing premise is that the entropy maximum (or minimum slope) actually marks the accretion shock in these full-physics runs, an identification imported from non-radiative simulations and not checked against direct temperature or velocity jumps in this paper.

Editorial extensions

If this is right

  • For a typical cluster, the accretion shock should be sought at about $1.38$–$1.91$ times the splashback radius, i.e. near $2.6$–$3.5\,R_{200}$, not at the splashback radius itself.
  • Because both $r_\mathrm{shock}/R_{200}$ and $r_\mathrm{splash}/R_{200}$ decrease with $M_{200}$ and with recent accretion, stacks used to detect the shock should be split by mass and accretion rate; mixing populations will blur the signal.
  • The ratio $r_\mathrm{shock}/r_\mathrm{splash}$ is not universal: it grows for clusters that have accreted a larger fraction of their mass since $z=0.5$, and this dependence is dominated by how strongly $r_\mathrm{splash}/R_{200}$ responds to accretion history.
  • Observational splashback measurements from galaxy density or weak lensing, combined with these relations, give a predicted radial window for non-thermal radio, X-ray, and thermal Sunyaev-Zeldovich shock searches.

Reading between the lines

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

  • If the entropy feature truly marks the accretion shock, then combining a measured splashback radius with the accretion-rate dependence of the ratio gives an observational prior: a cluster with a given $r_\mathrm{splash}$ and recent accretion history has a predictable radius where shock emission should appear.
  • A natural next test inside the same simulation volume would compare the entropy-defined shock radii against direct temperature-jump and velocity-jump shock finders; the paper does not run that comparison, so the physical interpretation of $r_\mathrm{shock}$ remains an open question.
  • The consistency of the relation across different galaxy formation implementations suggests the offset may be a generic feature of cluster accretion, but verifying it against observed stacked thermal Sunyaev-Zeldovich profiles with measured splashback radii would connect the prediction to data.
  • Since $r_\mathrm{splash}$ can be measured from galaxy density and weak lensing, the ratio could in principle serve as a dynamical-age indicator, tagging clusters that have recently accreted a large fraction of their mass.
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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 / 4 minor

Summary. The paper uses 324 galaxy clusters from The Three Hundred GIZMO-Simba-7k simulations to measure the shock radius, defined by an entropy maximum (rshock,p) or a minimum of the entropy logarithmic slope (rshock,m), and the dark-matter splashback radius (rsplash). The authors find median ratios rshock,p/rsplash = 1.38 and rshock,m/rsplash = 1.91, best-fit linear relations rshock ~ 0.65 rsplash + offset (Eqs. 5-6), and weak-to-moderate anti-correlations of rshock/R200 and rsplash/R200 with M200 and recent accretion rate. The results are compared with non-radiative simulations and observational tSZ/X-ray studies, and the paper discusses implications for locating the accretion shock in observations.

Significance. If the entropy-based shock radius is a faithful tracer of the physical accretion shock in full-physics simulations, this is a valuable statistical calibration: it is the largest sample (324 clusters) used for such a measurement, it spans multiple simulation codes and resolutions, and it provides quantitative relations that can guide stacking searches in tSZ, X-ray, and radio data. The agreement with Aung et al. (2021) in the median ratio (1.91 vs 1.89) is a useful cross-check, and the explicit bootstrap uncertainties and the sensitivity appendix are strengths. However, the physical interpretation of the central relations hinges on the unvalidated assumption that the entropy extremum marks the accretion shock in the presence of cooling, star formation, and AGN feedback.

major comments (3)
  1. [Section 2, Figure 3] The identification of rshock with the maximum of K or the minimum of d lnK/d lnr is imported from non-radiative simulations (Lau et al. 2015; Shi 2016) and is applied to GIZMO-Simba-7k without validation against direct shock diagnostics. Since this run includes radiative cooling, star formation, and AGN feedback, processes that can alter the entropy profile in cluster outskirts, the paper should demonstrate that the entropy extremum actually coincides with a genuine gas shock. A concrete check would be to measure temperature or velocity jumps, or to compare with a shock-finding algorithm, in a subset of clusters. Without such validation, Eqs. 5-12 and the median ratios are measurements of an entropy-feature radius, and their physical interpretation as the accretion-shock radius is not secured.
  2. [Section 2, radial-profile construction] The description of the angular-segment binning is ambiguous and could introduce a systematic bias in rshock. The text states that the median density and median mass-weighted temperature are evaluated in each radial bin and used to estimate the entropy via Eq. 1. Because K = k_B T / n_e^{2/3} is nonlinear, the entropy of the median temperature and median density is not generally equal to the median of the per-segment entropy values. If the latter was not used, the location of the entropy maximum or slope minimum can be shifted. The authors should clarify the exact procedure and test the sensitivity of rshock,p and rshock,m to whether the median is taken before or after computing K.
  3. [Appendix 1, Eq. 11 coefficients] The sensitivity check for Eq. 11 (rshock,m/R200 versus ΔM/M) lists the GIZMO-Simba-7k coefficients as (-1.05, 3.13), which is identical to the pair quoted for Eq. 10 and inconsistent with the fiducial values (-1.34, 4.27) stated in the main text. This appears to be a transcription error, but it undermines the reader's ability to assess the robustness of the rshock,m versus accretion-rate relation. The authors should correct the appendix and re-check the listed coefficients for all runs.
minor comments (4)
  1. [Abstract and Section 5] The abstract and conclusions quote rshock,m/R200 = 3.54, while the text around Figure 3 reports 3.58; these values should be reconciled.
  2. [Abstract, Eqs. 5-6] The phrase 'the best-fit linear relation increases as rshock ∝ 0.65 rsplash' is misleading because Eqs. 5 and 6 have non-zero intercepts (1.39 and 2.38 h^-1 Mpc); a proportional relation would have zero intercept. Please refer to the slope rather than using the proportionality symbol.
  3. [Section 2] The Gaussian smoothing applied to the density and entropy profiles is mentioned but its width is not specified; since the location of maxima and minima can depend on the smoothing scale, the authors should state the smoothing length and test its impact on the measured radii.
  4. [Section 3, Figure 4] The Spearman correlation coefficients for Eqs. 5 and 6 are reported, but the corresponding p-values, although described as 'vanishingly small', are not given; please provide numeric values.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the shock and splashback radii are measured from independent components, and the fitted relations are empirical and externally benchmarked; only minor self-citations to the collaboration's simulation papers appear.

full rationale

The paper's central claim—that rshock is generally larger than rsplash, with median ratios 1.38 and 1.91 and best-fit slopes around 0.65—is not forced by construction. rshock is an operational definition tied to the gas entropy profile (K maximum or minimum d lnK/d lnr; Section 2, Eqs 1-2), imported from Lau et al. (2015) and Shi (2016), while rsplash is measured from the minimum logarithmic slope of the dark matter density profile. These are independent physical components; the paper explicitly reports scatter and clusters where rshock,p is close to or not larger than rsplash, so the ordering is a measured outcome, not a definitional identity. Equations 5-12 are best-fit characterizations of the simulated data, not predictions derived from the fits, and the paper checks them against external non-radiative and full-physics results (Aung et al. 2021; O'Neil et al. 2021; Towler et al. 2024; Anbajagane et al. 2024). The main self-citations are to The Three Hundred collaboration's simulation suite, including the in-preparation GIZMO-Simba-7k description (Cui et al., In Preparation; Section 2) and earlier Cui et al. (2018, 2022). These are data sources rather than load-bearing theorems: the measurements are made directly from simulation outputs, and the consistency with Aung et al.'s independent rshock,m/rsplash ≈ 1.89 versus the present 1.91 provides an external anchor. The unvalidated entropy-maximum/minimum-slope proxy for the physical accretion shock (no direct check against temperature or velocity jumps) is a substantive assumption and correctness risk, but it is not circular because the proxy is not defined in terms of rsplash and the relation is not used to define either radius. The score of 2 reflects only the presence of minor, non-load-bearing self-citations; no circular step was found.

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

The paper is an empirical calibration on an existing simulation suite. No new physical entities are introduced and no ad hoc parameters are needed to force the result; the fitted coefficients listed above are the results themselves. The main hidden inputs are the operational definitions of the two radii and the fidelity of the simulation, both inherited from prior work.

free parameters (4)
  • slope of rshock,p vs rsplash (Eq 5) = 0.64 +/- 0.06
    Best-fit slope from bootstrapped linear regression of the simulated data; this is an empirical result, not an input assumption.
  • intercept of rshock,p vs rsplash (Eq 5) = 1.39 +/- 0.11 h^-1 Mpc
    Best-fit intercept; the large value means rshock is not simply proportional to rsplash.
  • slope of rshock,m vs rsplash (Eq 6) = 0.65 +/- 0.07
    Best-fit slope from the minimum-entropy-slope shock definition.
  • intercept of rshock,m vs rsplash (Eq 6) = 2.38 +/- 0.14 h^-1 Mpc
    Best-fit intercept for the rshock,m relation.
assumptions (5)
  • domain assumption The shock radius is identified with the radius at which the entropy profile K is maximal (rshock,p) or its logarithmic slope is minimal (rshock,m).
    Adopted from Lau et al. (2015) and Shi (2016); used throughout Section 3. The paper does not validate this against direct shock detection in the full-physics GIZMO-Simba-7k runs.
  • domain assumption The splashback radius is the minimum of d ln rho / d ln r for the spherically averaged dark matter density profile.
    Standard definition (More et al. 2015; Mansfield et al. 2017); applied in Section 2 to simulated profiles.
  • domain assumption The GIZMO-Simba-7k simulations reproduce the ICM properties needed to define meaningful entropy and density profiles.
    Relied on throughout; Appendix 1 compares across codes and resolutions but does not compare directly to observed entropy profiles.
  • domain assumption The 324 clusters are a mass-complete, representative sample of massive clusters at z=0.
    The sample is drawn from the MultiDark Planck 2 simulation (Section 2); cosmic variance from the single 1 h^-1 Gpc box is not quantified.
  • domain assumption Gaussian smoothing of the profiles does not bias the locations of the extrema used to define rshock and rsplash.
    Used in Section 2 to enable identification of maxima/minima; no smoothing-scale sensitivity test is reported.

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Cite this review

Pith. "Pith review of The Three Hundred Project: The relationship between the shock and splashback radii of simulated galaxy clusters." pith.science (2026). https://pith.science/paper/CV333ETW

@misc{pith2026241209864,
  author       = {Pith},
  title        = {Pith review of: The Three Hundred Project: The relationship between the shock and splashback radii of simulated galaxy clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CV333ETW}},
  note         = {Machine review of arXiv:2412.09864}
}
abstract

Observations of the intracluster medium (ICM) in the outskirts of galaxy clusters reveal shocks associated with gas accretion from the cosmic web. Previous work based on non-radiative cosmological hydrodynamical simulations have defined the shock radius, $r_\text{shock}$, using the ICM entropy, $K \propto T/{n_\mathrm{e}}^{2/3}$, where $T$ and $n_\text{e}$ are the ICM temperature and electron density respectively; the $r_\text{shock}$ is identified with either the radius at which $K$ is a maximum or at which its logarithmic slope is a minimum. We investigate the relationship between $r_\text{shock}$, which is driven by gravitational hydrodynamics and shocks, and the splashback radius, $r_\text{splash}$, which is driven by the gravitational dynamics of cluster stars and dark matter and is measured from their mass profile. Using 324 clusters from {\small The Three Hundred} project of cosmological galaxy formation simulations, we quantify statistically how $r_\text{shock}$ relates to $r_\text{splash}$. Depending on our definition, we find that the median $r_\text{shock} \simeq 1.38 r_\text{splash} (2.58 R_{200})$ when $K$ reaches its maximum and $r_\text{shock} \simeq 1.91 r_\text{splash} (3.54 R_{200})$ when its logarithmic slope is a minimum; the best-fit linear relation increases as $r_\text{shock} \propto 0.65 r_\text{splash}$. We find that $r_\text{shock}/R_{200}$ and $r_\text{splash}/R_{200}$ anti-correlate with virial mass, $M_{200}$, and recent mass accretion history, and $r_\text{shock}/r_\text{splash}$ tends to be larger for clusters with higher recent accretion rates. We discuss prospects for measuring $r_\text{shock}$ observationally and how the relationship between $r_\text{shock}$ and $r_\text{splash}$ can be used to improve constraints from radio, X-ray, and thermal Sunyaev-Zeldovich surveys that target the interface between the cosmic web and clusters.

Figures

Figures reproduced from arXiv: 2412.09864 by the authors.

Figure 1
Figure 1. Projected dark matter, gas, and stellar densities (top to bottom) at z=0 in the most massive cluster in our sample within a cubic region 20 h –1Mpc, centred on the density-weighted centred of AHF’s adaptive mesh refinement grid. The dark matter halo’s mass and radius are M200 = 2.82 × 1015h –1M⊙ and R200,crit = 2.298h –1Mpc, and it has accreted 75% of its present day mass since z=0.5 [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 2
Figure 2. Density (top) and gas entropy (bottom) radial profiles, along with their logarithmic slopes (lower panels) for the cluster shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. The relationship between the shock radius rshock and splashback radius rsplash for each of the 324 clusters in our sample. Upper panels correspond to rshock,p identified with the maximum of K, while the lower panels correspond to rshock,m identified with the minimum of its logarithmic slope. The points are colour coded by the virial mass M200 (left panels) and the fractional increase in M200 since z = 0.5, ∆M/M (rig… view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: The relationship between the shock and splashback radii, rshock, p, rshock, m, and rsplash as a function of virial mass, M200 (upper panel) and recent mass accretion history (lower panel) for each of the 324 clusters in our sample. The shaded bands indicate the 1-σ var…
Figure 6
Figure 6. Figure 6: The relationship between the shock and splashback radii, rshock, m, rshock, p and rsplash as a function of virial mass, M200 and recent mass accretion history ∆M/M in the GIZMO-Simba-3k (left two panels) and GadgetX (right two panels) runs for each of the 324 clusters …

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Works this paper leans on

11 extracted references · 5 canonical work pages

  1. [68]

    arXiv: 1411.5361 [astro-ph.CO]

    https://doi.org/10.1088/0004-637X/806/1/68. arXiv: 1411.5361 [astro-ph.CO]. Lebeau, Théo, Stefano Ettori, Nabila Aghanim, and Jenny G. Sorce. 2024. Can the splashback radius be an observable boundary of galaxy clusters? A&A 689 (September): A19. https://doi.org/10.1051/0004-6361/202450146. arXiv: 2403.18648 [astro-ph.CO]. Li, Yun, H. J. Mo, and L. Gao. 20...

    arXiv 2024

  2. [441]

    Suzaku Observation of Abell 1689: Anisotropic Temperature and Entropy Distributions Associated with the Large-Scale Structure

    https://doi.org/10.1088/0004-637X/714/1/423. arXiv: 1002.4811 [astro-ph.CO]. Klypin, Anatoly, Gustavo Y epes, Stefan Gottlöber, Francisco Prada, and Stef- fen Heß. 2016. MultiDark simulations: the story of dark matter halo concentrations and density profiles. MNRAS 457, no. 4 (April): 4340–

    work page Pith review arXiv 2016

  3. [996]

    \textsc{The Three Hundred} project: The \textsc{Gizmo-Simba} run

    https://doi.org/10.1093/mnras/stac1402. arXiv: 2202.14038 [astro-ph.GA]. Cui, Weiguang, Alexander Knebe, Gustavo Y epes, Frazer Pearce, Chris Power, Romeel Dave, Alexander Arth, et al. 2018. The Three Hundred project: a large catalogue of theoretically modelled galaxy clusters for cosmological and astrophysical applications. MNRAS 480, no. 3 (November): 2898–

    work page Pith review arXiv 2018

  4. [1787]

    arXiv: 2101.04179 [astro-ph.CO]

    https://doi.org/10.1093/mnras/stab2720. arXiv: 2101.04179 [astro-ph.CO]. Bianconi, Matteo, Riccardo Buscicchio, Graham P. Smith, Sean L. McGee, Chris P. Haines, Alexis Finoguenov, and Arif Babul. 2021. LoCuSS: The Splashback Radius of Massive Galaxy Clusters and Its Dependence on Cluster Merger History. ApJ 911, no. 2 (April): 136. https://doi.org/ 10.384...

    arXiv 2021

  5. [1815]

    Locations of Accretion Shocks around Galaxy Clusters and the ICM properties: insights from Self-Similar Spherical Collapse with arbitrary mass accretion rates

    https://doi.org/10.1093/mnras/stw1418. arXiv: 1603.07183 [astro-ph.CO]. Simionescu, Aurora, Stefano Ettori, Norbert Werner, Daisuke Nagai, Franco Vazza, Hiroki Akamatsu, Ciro Pinto, et al. 2021. V oyage through the hidden physics of the cosmic web. Experimental Astronomy 51, no. 3 (June): 1043–1079. https://doi.org/10.1007/s10686- 021- 09720- 0. arXiv: 19...

    work page Pith review arXiv 2021

  6. [2007]

    MNRAS 375, no

    Properties of dark matter haloes in clusters, filaments, sheets and voids. MNRAS 375, no. 2 (February): 489–499. https://doi.org/10.1111/ j.1365-2966.2006.11318.x. arXiv: astro-ph/0610280 [astro-ph]. Hogan, M. T., B. R. McNamara, F. Pulido, P. E. J. Nulsen, H. R. Russell, A. N. Vantyghem, A. C. Edge, and R. A. Main. 2017. Mass Distribution in Galaxy Clust...

    work page arXiv 2006

  7. [2017]

    The Splashback Radius of Halos from Particle Dynamics. II. De- pendence on Mass, Accretion Rate, Redshift, and Cosmology. ApJ 843, no. 2 (July): 140. https://doi.org/10.3847/1538-4357/aa79ab. arXiv: 1703.09716 [astro-ph.CO]. Ghirardini, V., D. Eckert, S. Ettori, E. Pointecouteau, S. Molendi, M. Gaspari, M. Rossetti, et al. 2019. Universal thermodynamic pr...

    arXiv

  8. [2021]

    MNRAS 504, no

    The splashback boundary of haloes in hydrodynamic simulations. MNRAS 504, no. 3 (July): 4649–4666. https://doi.org/10.1093/mnras/ stab1221. arXiv: 2012.00025 [astro-ph.GA]. Panagoulia, E. K., A. C. Fabian, J. S. Sanders, and J. Hlavacek-Larrondo. 2014. A volume-limited sample of X-ray galaxy groups and clusters - II. X- ray cavity dynamics. MNRAS 444, no....

    arXiv 2012

Show all 11 references
  1. [2915]

    arXiv: 1809.04622 [astro-ph.GA]

    https://doi.org/10.1093/mnras/sty2111. arXiv: 1809.04622 [astro-ph.GA]. Davé, Romeel, Daniel Anglés-Alcázar, Desika Narayanan, Qi Li, Mika H. Rafieferantsoa, and Sarah Appleby. 2019. SIMBA: Cosmological simula- tions with black hole growth and feedback. MNRAS 486, no. 2 (June)...

    2019 arXiv

  2. [4192]

    arXiv: 2010.02937 [astro-ph.GA]

    https://doi.org/10.1093/mnras/staa3590. arXiv: 2010.02937 [astro-ph.GA]. Diemer, Benedikt, Philip Mansfield, Andrey V. Kravtsov, and Surhud More

    2010 arXiv

  3. [4359]

    org / 10

    https : / / doi . org / 10 . 1093 / mnras / stw248. arXiv: 1411 . 4001 [astro-ph.CO]. Knollmann, Steffen R., and Alexander Knebe. 2009. AHF: Amiga’s Halo Finder. ApJS 182, no. 2 (June): 608–624. https://doi.org/10.1088/0067- 0049/182/2/608. arXiv: 0904.3662 [astro-ph.CO]. Koba...

    2009 arXiv

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