Pith. sign in

REVIEW 2 major objections 4 minor 2 cited by

Numerical convergence of hydrodynamical simulations of galaxy formation: the abundance and internal structure of galaxies and their cold dark matter haloes

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Hydrodynamical galaxy simulations are far more sensitive to the gravitational softening length than dark-matter-only runs are, and this paper derives analytic thresholds that tell when a chosen softening will distort the results.

desk verdict A strong, useful convergence study whose headline feedback criterion (eq. 13) is off by a factor of about two — the qualitative message survives, the quantitative recommendation does not. read the letter →

arxiv 1908.05019 v3 pith:553BPOJZ submitted 2019-08-14 astro-ph.GA astro-ph.CO

Aaron D. Ludlow (ICRAR/UWA) , Joop Schaye , Matthieu Schaller (Leiden) , Richard Bower (ICC/Durham) This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords gravitationalsofteningnumericalconvergenceSPHsimulationsgalaxyformationdarkmatterhaloesreionizationstellarfeedbacksizes
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 establishes that the gravitational softening length is a first-order numerical parameter in hydrodynamical galaxy formation simulations, not a small detail. In a suite of cosmological smoothed-particle-hydrodynamics runs that keep particle masses and subgrid physics fixed and vary only softening, the star formation history, the abundance of low-mass galaxies, galaxy sizes, and the inner structure of dark-matter haloes all shift systematically as softening is changed by factors of two. The authors derive two analytic thresholds that mark where the damage begins: a minimum resolved escape speed set by gas self-binding, and a critical softening below which thermal feedback radiatively overcools. These thresholds matter because they give simulators concrete numbers to choose softening by, and they warn that a higher-resolution run is not automatically a more trustworthy one.

What carries the argument

The central machinery is a pair of analytic thresholds written in terms of the Plummer-equivalent softening $\epsilon$ and gas particle mass $m_g$: the minimum resolved escape speed $v_\epsilon = \sqrt{2G m_g/\epsilon}$ (Eq. 8) and the feedback-efficiency softening $\epsilon_{\rm eFB}$ that keeps the maximum resolved gas density, $n_{\rm H}^{\rm max}\propto \epsilon^{-3}$, below the critical density $n_{\rm H,tc}$ required for thermal feedback to act before cooling (Eq. 13). These thresholds connect force resolution to gas physics, and the paper verifies them against two distinct diagnostics: the baryon fractions of low-mass haloes at $z=10$ and the distribution of gas densities at the moment stars are born.

What would settle it

Keep particle masses and subgrid physics fixed and rerun one cosmological volume with present-day softening below $19\,{\rm pc}$ and above $156\,{\rm pc}$, the paper's $v_\epsilon$ bounds for its high-resolution case: if the median baryon fraction of $\sim10^8\,\mathrm{M}_\odot$ haloes at $z=10$ does not jump from near the cosmic mean to a small fraction of it, the minimum-resolved-escape-speed mechanism fails. The same experiment should also show a high-redshift star-formation peak and late-time suppression for the small softening; their absence would falsify the over-cooling story.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that hydrodynamical simulations of galaxy formation are far more sensitive to gravitational softening than dark-matter-only simulations, and that the sensitivity is predictable. Softening sets a minimum resolved escape speed $v_\epsilon = \sqrt{2 G m_g / \epsilon}$ for gas particles; once $v_\epsilon$ exceeds roughly $10\,{\rm km\,s^{-1}}$, the photo-heating associated with reionization is suppressed, low-mass haloes retain baryons, and stars form in systems that should have been quenched. Softening also caps the maximum resolved gas density roughly as $n_{\rm H}^{\rm max}\propto \epsilon^{-3}$; when that cap pushes gas past the critical density $n_{\rm H,tc}$ for efficient thermal feedback, a large share of star-forming gas radiates away feedback energy before it can act. In addition, because dark-matter particles are more massive than star particles, small softening accelerates two-body mass segregation, which inflates galaxy sizes and contracts dark-matter haloes even after the baryons responsible for the contraction have been scattered away. The paper's recommended softening---about $0.05$ times the mean inter-particle spacing in comoving units at early times and $0.022$ times that spacing in physical units at late times---keeps circular velocity profiles converged to roughly 10 per cent outside the dark-matter convergence radius.

Load-bearing premise

The quantitative thresholds are derived and tested for smoothed-particle-hydrodynamics runs with a single calibrated subgrid model, equal numbers of dark-matter and gas particles, and identical softening for all particle species; other numerical setups may shift the numbers or weaken the effects.

Editorial extensions

If this is right

  • Runs with softening below the $v_\epsilon$ threshold overproduce stars in small haloes after reionization, so their low-mass galaxy stellar mass functions become too steep.
  • Runs with softening below $\epsilon_{\rm eFB}$ convert a large part of star formation into numerically over-cooled events with weak feedback, producing galaxies that are initially too compact.
  • Runs with softening too large suppress dwarf-galaxy formation because the maximum resolved gas density falls below the star-formation threshold.
  • At the recommended optimal softening, cosmic star formation histories and stellar mass functions converge across two mass resolutions, and dark-matter circular velocity profiles agree to within about 10 per cent outside the dark-matter convergence radius.
  • Small softening also alters dark-matter structure: haloes that are baryon-free at $z=0$ can still contain steep central cusps left by baryons that were later scattered away, so dark-matter-only convergence criteria do not carry over to hydrodynamical runs.

Reading between the lines

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

  • The same two thresholds should apply, at least approximately, to any subgrid feedback model that heats gas to roughly $10^{7.5}\,\mathrm{K}$, because the over-cooling criterion depends only on particle mass, softening, and post-heating temperature.
  • A testable extension of the mass-segregation result: runs with equal-mass dark-matter and star particles should show much weaker softening-driven size inflation, since the paper ties the effect to the mass ratio $\mu = m_{\rm DM}/m_{\rm gas}$.
  • The softening-dependent star-formation peak near $z_{\rm reion}$ implies that high-redshift star formation rates from simulations with very small softening deserve suspicion even when their $z=0$ galaxy populations look reasonable.
  • If these criteria generalize to moving-mesh or adaptive-mesh codes, simulators would gain a common vocabulary for choosing force resolution across methods; the paper does not test this, but the criteria are phrased in resolution-element terms that carry over.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper uses a suite of cosmological SPH simulations with EAGLE-like subgrid physics, run in a 12.5 cMpc box at two mass resolutions (Np = 188 and 376 per side), to study how the gravitational softening length affects galaxy formation and dark matter halo structure. Softening is varied by factors of two around the fiducial EAGLE values, and the runs include both non-radiative and full-physics cases. The authors derive analytic criteria for choosing the softening: an upper limit from resolving low-mass haloes, a lower limit from two-body collisional heating of gas, a minimum resolved escape velocity (Eq. 8), and a feedback-efficiency threshold (Eqs. 12-13) that prevents numerical over-cooling of supernova-heated gas. They then test these criteria against baryon fractions, cosmic star formation histories, galaxy stellar mass functions, galaxy sizes, and DM circular velocity profiles. The central qualitative conclusion is that hydrodynamical simulations are far more sensitive to softening than dark-matter-only simulations, with too-small softening suppressing photo-heating, promoting over-cooling, and exacerbating mass segregation, sometimes causing galaxy sizes to increase as softening decreases.

Significance. If the quantitative criteria are correct, this is an important contribution: it provides simple, physically motivated rules of thumb for a community that routinely adopts softening lengths without such tests, and it demonstrates the non-trivial coupling between numerical force resolution and subgrid feedback. The study is strengthened by the systematic factor-of-two coverage of softening, by the use of two mass resolutions, and by direct diagnostics such as baryon fractions and stellar birth densities that make the claimed effects falsifiable. The qualitative results, especially the v_epsilon criterion and the identification of mass segregation as a softening-dependent effect, are valuable and likely robust. However, the central feedback-efficiency threshold contains an arithmetic error of a factor of about 1.9, which directly affects the paper's quantitative statements and its recommended 'optimal' softening. The paper therefore requires a major revision before the practical guidance can be accepted.

major comments (2)
  1. [Section 3.3, Eqs. (10)-(13)] The coefficient in Eq. (12) does not follow from equating Eqs. (10) and (11). With the stated normalizations, n_H,tc = n_max^H implies epsilon_eFB = 350 pc x (180/26)^(1/3) x (Nngb/58)^(1/3) x (X/0.75)^(1/3) x (f/0.1)^(-1) x (T/10^7.5 K)^(-1/2) x (mg/10^5 Msun)^(1/2), approximately 667 pc x (mg/10^5 Msun)^(1/2). The missing factor (180/26)^(1/3) is about 1.9 and is not a convention effect: Eq. (10) already refers to the Plummer-equivalent softening, with the eps_sp = 2.8 eps conversion folded into the 180 cm^-3 calibration. Consequently, the values quoted in Section 3.3 (epsilon_eFB about 0.5 kpc and 1.5 kpc for the Np = 376 and Np = 188 runs) should be about 1.0 kpc and 2.8 kpc. This is not a cosmetic issue: Sections 5.1(iii) and 5.2 use these values to state that EAGLE's high-resolution run falls short of epsilon_eFB by only a factor of 1.4 and that the recommended softening 'ensure[s] that feedback will be maximally efficient.' Under the corrected criterion, 700 pc is below epsilon_eFB, and the shortfall is about 2.9, not 1.4. Please recompute the threshold, revise the numerical statements throughout, and reassess the practical recommendations.
  2. [Section 5.2, optimal softening recommendation] The recommendation epsilon_opt about 0.022 L/Np (approximately 700 pc for Np = 376 and 1400 pc for Np = 188) is presented as ensuring efficient feedback, but with the corrected epsilon_eFB from the previous comment it falls below the paper's own feedback-efficiency threshold for both resolutions. The statement in Section 5.2 that 'these criteria ensure that feedback will be maximally efficient' is therefore not supported by the corrected algebra. Because epsilon_eFB and the DM-only convergence radius rconv about 0.055 L/Np (about 1.8 kpc for Np = 376) are both constraints, the paper should discuss the resulting allowed window (roughly 1.0-1.8 kpc for the high-resolution runs) and explain whether any of the simulated configurations actually satisfies both requirements, rather than simply doubling the fiducial softening.
minor comments (4)
  1. [Section 4.1.3, first paragraph] The text quotes 'about 27 per cent for epsilon = 700 pc' for stars formed at z above about 11.5 and then, in the same paragraph, quotes 'only about 9 per cent of all stars' for the same run; please state explicitly that these refer to different stellar populations (pre-reionization versus all epochs) to avoid an apparent contradiction.
  2. [Figure 7 caption] The phrase 'the upper middle-right panel' is ambiguous; please specify the panel corresponding to epsilon0 = 700 pc.
  3. [Section 2.2 and Acknowledgements] There are minor language errors: 'effected' should be 'affected' in Section 2.2, and 'we also with to acknowledge' should be 'we also wish to acknowledge' in the Acknowledgements.
  4. [Section 3.3] The derivation of n_H,tc in Eq. (11) is quoted from Dalla Vecchia & Schaye (2012), but the text would benefit from a brief statement of the adopted cooling function and the kernel-volume normalization, since the coefficient 26 cm^-3 enters directly into the corrected feedback threshold.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: analytic softening thresholds are derived from independent physical estimates and validated by the simulations, not fitted from them.

full rationale

The derivation chain in Section 3 is not circular. Equations (4), (7), (8), (10), and (11)-(13) are obtained from independent physical estimates: virial scaling, two-body encounter heating, the self-binding energy of a particle pair, SPH kernel normalization, and the cooling-time versus sound-crossing-time comparison imported from Dalla Vecchia & Schaye (2012). None of these formulas is fitted to the EAGLE simulation outputs that later confirm them (Figures 1-3); the simulations are used as validation, not as the source of the coefficients. The EAGLE subgrid parameters are acknowledged prior calibrations (Section 2.2), and the paper's softening tests hold that calibration fixed while varying only epsilon, so the measured softening sensitivity is not a renamed fit. Self-citations to Ludlow et al. (2019) (Paper I) supply the DM-only convergence radius rconv and mass-segregation physics from independent collisionless simulations; the present paper also shows its own mu = 1 comparison and its own Vc(r) convergence tests, so the argument does not reduce to those citations. The recommended 'optimal' softening is explicitly empirical ('At present we lack a detailed analytic framework that can guide our choices, but the results shown in Figure 7 suggest ...'), anchored to observed size-mass data rather than presented as a derived first-principles prediction. A genuine internal consistency problem does exist in the quoted numbers: substituting the stated normalizations into eqs. (10) and (11) gives epsilon_eFB = 350 pc x (180/26)^(1/3) x (mg/10^5 Msun)^(1/2) ~ 667 pc x (mg/10^5 Msun)^(1/2), roughly 1.9 times larger than the 350 pc coefficient quoted in eq. (12). Consequently, the quoted thresholds (0.5 kpc and 1.5 kpc) and the 'optimal' 700 pc recommendation are not self-consistent with the paper's own equations. This is a correctness defect, not circularity, because the qualitative over-cooling conclusion is independently evidenced by the simulated birth-density distributions in Figure 3 and the surrounding analysis.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper's criteria depend on the EAGLE subgrid model, the Dalla Vecchia & Schaye (2012) feedback efficiency criterion, and an assumed physical mechanism (mass segregation) for interpreting size and DM profile changes. These are domain assumptions inherited from prior work or stated as speculative in the text.

free parameters (2)
  • epsilon_opt (optimal physical softening) = ~0.022 x (L/Np) at z=0, ~0.05 x (L/Np) in comoving units
    Recommended in Section 5.2 as a compromise that suppresses 2-body scattering and matches the observed size-mass relation; effectively calibrated to Shen et al. (2003) observations rather than derived independently.
  • f, minimum smoothing length factor = 0.1
    Chosen by hand as lmin_hsml = 0.1 x spline softening; robustness tested in Appendix A3 but the value itself is an input selection, not derived.
assumptions (4)
  • domain assumption The EAGLE subgrid model (stochastic thermal feedback with Delta T = 10^7.5 K, pressure-based star formation, AGN feedback) adequately represents unresolved physics.
    Central to interpreting softening-induced changes as numerical artifacts; stated in Section 1 and inherited from Schaye et al. 2015 and Crain et al. 2015.
  • domain assumption The cooling-time criterion of Dalla Vecchia & Schaye (2012) (eq. 11) characterizes numerically efficient thermal feedback.
    Used to derive epsilon_eFB (eq. 13); applies to stochastic thermal feedback implementations, not necessarily momentum injection (Section 3.3).
  • domain assumption Two-body scattering and energy equipartition between DM and stellar particles cause the observed mass segregation.
    Invoked to explain size increase and DM cusp formation; acknowledged as speculative in Sections 4.2.3 and 4.3.2.
  • domain assumption Statistics from a single 12.5 Mpc box per parameter set are representative despite chaotic galaxy-by-galaxy divergence.
    Rely on statistical properties; single realization per resolution/softening; chaos studies (Keller et al. 2019; Genel et al. 2019) discussed in Section 1.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Numerical convergence of hydrodynamical simulations of galaxy formation: the abundance and internal structure of galaxies and their cold dark matter haloes." pith.science (2026). https://pith.science/paper/553BPOJZ

@misc{pith2026190805019,
  author       = {Pith},
  title        = {Pith review of: Numerical convergence of hydrodynamical simulations of galaxy formation: the abundance and internal structure of galaxies and their cold dark matter haloes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/553BPOJZ}},
  note         = {Machine review of arXiv:1908.05019}
}
abstract

We address the issue of numerical convergence in cosmological smoothed particle hydrodynamics simulations using a suite of runs drawn from the EAGLE project. Our simulations adopt subgrid models that produce realistic galaxy populations at a fiducial mass and force resolution, but systematically vary the latter in order to study their impact on galaxy properties. We provide several analytic criteria that help guide the selection of gravitational softening for hydrodynamical simulations, and present results from runs that both adhere to and deviate from them. Unlike dark matter-only simulations, hydrodynamical simulations exhibit a strong sensitivity to gravitational softening, and care must be taken when selecting numerical parameters. Our results--which focus mainly on star formation histories, galaxy stellar mass functions and sizes--illuminate three main considerations. First, softening imposes a minimum resolved escape speed, $v_\epsilon$, due to the binding energy between gas particles. Runs that adopt such small softening lengths that $v_\epsilon \gt 10\,{\rm km s^{-1}}$ (the sound speed in ionised $\sim 10^4\,{\rm K}$ gas) suffer from reduced effects of photo-heating. Second, feedback from stars or active galactic nuclei may suffer from numerical over-cooling if the gravitational softening length is chosen below a critical value, $\epsilon_{\rm eFB}$. Third, we note that small softening lengths exacerbate the segregation of stars and dark matter particles in halo centres, often leading to the counter-intuitive result that galaxy sizes {\em increase} as softening is reduced. The structure of dark matter haloes in hydrodynamical runs respond to softening in a way that reflects the sensitivity of their galaxy populations to numerical parameters.

Figures

Figures reproduced from arXiv: 1908.05019 by the authors.

Figure 1
Figure 1. Halo baryon fractions as a function of virial mass for adiabatic (i.e. non-radiative) runs. We show results for N3 p = 1883 with softening lengths that vary from /(L/Np) ≈ 0.67 to ≈ 0.0013 in units of the mean inter-particle spacing (for all runs zphys = 0, which enforces fixed co-moving softening at all times). Dashed curves show results for haloes at z = 10 and solid curves at z = 0. Blue curves distinguish value… view at source ↗
Figure 2
Figure 2. Halo baryon fractions as a function of virial mass for N3 p = 3763 runs at z = 10. Different panels show results for different softening lengths; the physical values are quoted at both z = 0 (0) and at zreion = 11.5 in each panel. Points show results for individual galaxies in our full-physics runs; solid lines show, for comparison, the median trends from the same runs but without photo-heating from reionization (t… view at source ↗
Figure 3
Figure 3. Differential mass distribution of fluid element densities at the moment they were converted into star particles. Results are shown for our N3 p = 3763 runs, with softening decreasing from top-left to bottom-right (softening lengths at z = 0 and zreion = 11.5 are quoted in each panel). Densities are normalized to nH,tc, the maximum density for numerically efficient feedback (eq. 11). In all panels, shaded regions cor… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Cosmic star formation histories (SFH) for runs with different z = 0 softening lengths. Thin (faint) lines distinguish our N3 p = 1883 Reference runs from the higher resolution ones (heavy lines). Downward pointing arrows mark the reionization redshift, zreion = 11.5. A…
Figure 4
Figure 4. Figure 4: Decreasing  results in a systematic increase in the SFR at early times, eventually leading to a “peak” in the cosmic SFH at z ≈ zreion = 11.5 (marked by a downward pointing arrow). This initial burst of star formation–clearly numer￾ical in origin–is first noticeable i…
Figure 5
Figure 5. Figure 5: Comparison of the cumulative z = 0 galaxy stellar mass functions for all models. Different panels correspond to runs carried out with different maximum physical softening lengths, colour coded as in previous figures. Solid lines show runs with N3 p = 1883 particles and…
Figure 6
Figure 6. Figure 6: Upper panels: Cumulative galaxy stellar mass functions at z = 0 (left), z = 1 (middle) and z = 2 (right) for our N3 p = 3763 runs carried out with different softening lengths, . The total number of galaxies resolved by these simulations increases systematically with d…
Figure 7
Figure 7. Figure 7: Projected (physical) half stellar-mass radii as a function of galaxy stellar mass at z = 0 (solid lines) and z = 2 (dashed lines) for our N3 p = 3763 (thick lines) and N3 p = 1883 runs (thin lines). The shaded coloured regions indicate the 20th and 80th percentiles of …
Figure 8
Figure 8. Figure 8: Maximum circular velocity, Vmax/V200, versus virial mass, M200, for central galaxies and DM haloes in our N3 p = 3763 runs. Dots show results for main haloes that contain no stellar component; circles show haloes that contain at least one star particle. The solid lines…
Figure 9
Figure 9. Figure 9: As in [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Top panels: Average (z = 0) circular velocity profiles for DM haloes and galaxies in three separate bins of virial mass: M200 = 109 M (left), 1010 M (middle) and 1011 M (right). Results are shown for N3 p = 3763 . Solid curves show the mean DM Vc(r) profiles for all h…
Figure 11
Figure 11. Figure 11: Circular velocity profiles (upper panels) and mass accretion histories (MAHs; lower panels) for dark matter main haloes that contain no baryons at z = 0. Haloes are selected to lie in a narrow mass bin centred on M200 = 5 × 108 M of width ∆ log M200 = 0.4. Results are…
Figure 12
Figure 12. Figure 12: A summary of results from intermediate- (N3 p = 1883 ) and high-resolution (N3 p = 3763 ) runs that used our fiducial softening length, fid (blue curves), or the “optimal” softening length, opt (orange curves), described in Section 5.2. Top panels, from left to righ…
Figure 7
Figure 7. Figure 7: J. T. V., eds, Clusters of Galaxies and the High Red￾shift Universe Observed in X-rays Modelling the UV/X￾ray cosmic background with CUBA. p. 64 Haas M. R., Schaye J., Booth C. M., Dalla Vecchia C., Springel V., Theuns T., Wiersma R. P. C., 2013a, MN￾RAS, 435, 2931 Haa…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. The complex stellar system M 22: constraining the chemical enrichment from AGB stars using magnesium isotope ratios

    astro-ph.GA 2026-07 conditional novelty 6.0 of 10

    First Mg isotope measurements at [Fe/H]≈-2 in a globular cluster show no difference tied to s-process enrichment, favoring ~2.75 M_sun AGB polluters and a 280–480 Myr age gap.

  2. The complex stellar system M 22: confirming abundance variations with high precision differential measurements

    astro-ph.GA 2026-07 conditional novelty 6.0 of 10

    High-precision differential abundances confirm M 22 hosts a >0.24 dex iron spread and ~0.65 dex s-process spread, and reveal new internal abundance variations within each population.

Reference graph

Works this paper leans on

104 extracted references · 70 canonical work pages · cited by 2 Pith papers

  1. [1]

    write newline

    " 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.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...

  2. [2]

    @esa ( ) , n @biblabelnum##1 ##1

    \@ifclassloaded aguplus natbib The aguplus class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command natbib from the document \@ifclassloaded nlinproc natbib The nlinproc class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later r...

  3. [3]

    @stdbsttrue NAT@ctr \@lbibitem[ NAT@ctr ] \@lbibitem[#1]#2 \@ifundefined b@#2\@extra@b@citeb @num @parse #2 [ @natanchorstart #2 \@biblabel @num @natanchorend] @ifcmd#1()()\@nil #2 \@ifpackageloaded showkeys @lbibitem\@lbibitem \@lbibitem[#1]#2 @lbibitem[#1] #2 @ @@label #2 @stdbst @stdbstfalse @stdbst @filesw \@auxout @numberstrue [2] \@ifundefined b@#1\...

  4. [4]

    @open @close @open @close and [1] URL: ##1 \@ifundefined chapter * \@mkboth \@ifundefined NAT@sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifundefined bib@heading @heading NAT@ctr thebibliography [1] @ \@biblabel NAT@ctr \@bibsetup #1 NAT@ctr 0 @openbib .11em \@plus.33em \@minus.07em 4000 4000 `\.=1000 \...

  5. [5]

    V., Leitner S

    Agertz O., Kravtsov A. V., Leitner S. N., Gnedin N. Y., 2013, , 770, 25

    2013

  6. [6]

    Agertz, et al 2007, , 380, 963

    2007

  7. [7]

    M., Barnes D

    Bah \'e Y. M., Barnes D. J., Dalla Vecchia C., Kay S. T., White S. D. M., McCarthy I. G., Schaye J., Bower R. G., Crain R. A., Theuns T., Jenkins A., McGee S. L., Schaller M., Thomas P. A., Trayford J. W., 2017, , 470, 4186

    2017

  8. [8]

    S., Ludlow A

    Ben \' tez-Llambay A., Frenk C. S., Ludlow A. D., Navarro J. F., 2019, , 488, 2387

    2019

Show all 104 references
  1. [9]

    Binney J., Knebe A., 2002, , 333, 378

    2002

  2. [10]

    Princeton, NJ, Princeton University Press, 1987, 747 p

    Binney J., Tremaine S., 1987, Galactic dynamics . Princeton, NJ, Princeton University Press, 1987, 747 p

    1987

  3. [11]

    R., Faber S

    Blumenthal G. R., Faber S. M., Flores R., Primack J. R., 1986, , 301, 27

    1986

  4. [12]

    M., Schaye J., 2009, , 398, 53

    Booth C. M., Schaye J., 2009, , 398, 53

    2009

  5. [13]

    B., Stinson G., Gibson B

    Brook C. B., Stinson G., Gibson B. K., Ro s kar R., Wadsley J., Quinn T., 2012, , 419, 771

    2012

  6. [14]

    B., Stinson G., Gibson B

    Brook C. B., Stinson G., Gibson B. K., Wadsley J., Quinn T., 2012, , 424, 1275

    2012

  7. [15]

    E., Kay S

    Bryan S. E., Kay S. T., Duffy A. R., Schaye J., Dalla Vecchia C., Booth C. M., 2013, , 429, 3316

    2013

  8. [16]

    et al 2014, , 211, 19

    Bryan, G. et al 2014, , 211, 19

    2014

  9. [17]

    V., Dutton A

    Buck T., Macci \`o A. V., Dutton A. A., Obreja A., Frings J., 2019, , 483, 1314

    2019

  10. [18]

    Chabrier G., 2003, , 115, 763

    2003

  11. [19]

    A., Schaye J., Bower R

    Crain R. A., Schaye J., Bower R. G., Furlong M., Schaller M., Theuns T., Dalla Vecchia C., Frenk C. S., McCarthy I. G., Helly J. C., Jenkins A., Rosas-Guevara Y. M., White S. D. M., Trayford J. W., 2015, , 450, 1937

    2015

  12. [20]

    Cui et al 2018, , 480, 2898

    2018

  13. [21]

    Dalla Vecchia C., Schaye J., 2012, , 426, 140

    2012

  14. [22]

    H., Appleby S., 2019, , 486, 2827

    Dav \'e R., Angl \'e s-Alc \'a zar D., Narayanan D., Li Q., Rafieferantsoa M. H., Appleby S., 2019, , 486, 2827

    2019

  15. [23]

    Dolag K., Borgani S., Murante G., Springel V., 2009, , 399, 497

    2009

  16. [24]

    Dolag K., Komatsu E., Sunyaev R., 2016, , 463, 1797

    2016

  17. [25]

    R., Schaye J., Kay S

    Duffy A. R., Schaye J., Kay S. T., Dalla Vecchia C., Battye R. A., Booth C. M., 2010, , 405, 2161

    2010

  18. [26]

    A., Macci \`o A

    Dutton A. A., Macci \`o A. V., Buck T., Dixon K. L., Blank M., Obreja A., 2019, , 486, 655

    2019

  19. [27]

    S., White S

    Efstathiou G., Frenk C. S., White S. D. M., Davis M., 1988, , 235, 715

    1988

  20. [28]

    A., Everitt M

    El-Zant A. A., Everitt M. J., Kassem S. M., 2019, , 484, 1456

    2019

  21. [29]

    J., Korista K

    Ferland G. J., Korista K. T., Verner D. A., Ferguson J. W., Kingdon J. B., Verner E. M., 1998, , 110, 761

    1998

  22. [30]

    Gaburov E., Nitadori K., 2011, , 414, 129

    2011

  23. [31]

    L., Springel V., Hernquist L., Nelson D., Pillepich A., Weinberger R., Pakmor R., Marinacci F., Vogelsberger M., 2019, , 871, 21

    Genel S., Bryan G. L., Springel V., Hernquist L., Nelson D., Pillepich A., Weinberger R., Pakmor R., Marinacci F., Vogelsberger M., 2019, , 871, 21

    2019

  24. [32]

    A., Monaghan J

    Gingold R. A., Monaghan J. J., 1977, , 181, 375

    1977

  25. [33]

    Governato F., Brook C., Mayer L., Brooks A., Rhee G., Wadsley J., Jonsson P., Willman B., Stinson G., Quinn T., Madau P., 2010, , 463, 203

    2010

  26. [34]

    M., Tran J

    Haardt F., Madau P., 2001, in Neumann D. M., Tran J. T. V., eds, Clusters of Galaxies and the High Redshift Universe Observed in X-rays Modelling the UV/X-ray cosmic background with CUBA . p. 64

    2001

  27. [35]

    R., Schaye J., Booth C

    Haas M. R., Schaye J., Booth C. M., Dalla Vecchia C., Springel V., Theuns T., Wiersma R. P. C., 2013a, , 435, 2931

  28. [36]

    R., Schaye J., Booth C

    Haas M. R., Schaye J., Booth C. M., Dalla Vecchia C., Springel V., Theuns T., Wiersma R. P. C., 2013b, , 435, 2955

  29. [37]

    F., 2015, , 450, 53

    Hopkins P. F., 2015, , 450, 53

    2015

  30. [38]

    Hopkins et al 2018, , 480, 800

    2018

  31. [39]

    A., Falle S

    Hubber D. A., Falle S. A. E. G., Goodwin S. P., 2013, , 432, 711

    2013

  32. [40]

    D., 2007, Computing In Science & Engineering, 9, 90

    Hunter J. D., 2007, Computing In Science & Engineering, 9, 90

    2007

  33. [41]

    S., White S

    Jenkins A., Frenk C. S., White S. D. M., Colberg J. M., Cole S., Evrard A. E., Couchman H. M. P., Yoshida N., 2001, , 321, 372

    2001

  34. [42]

    C., Cole S., Frenk C

    Jiang L., Helly J. C., Cole S., Frenk C. S., 2014, , 440, 2115

    2014

  35. [43]

    Jones E., Oliphant T., Peterson P., et al.,, 2001, SciPy : Open source scientific tools for Python

    2001

  36. [44]

    H., Hernquist L., 1996, , 105, 19

    Katz N., Weinberg D. H., Hernquist L., 1996, , 105, 19

    1996

  37. [45]

    W., Wadsley J

    Keller B. W., Wadsley J. W., Wang L., Kruijssen J. M. D., 2019, , 482, 2244

    2019

  38. [46]

    Kennicutt Jr. R. C., 1989, , 344, 685

    1989

  39. [47]

    Knebe A., Green A., Binney J., 2001, , 325, 845

    2001

  40. [48]

    V., 1999, PhD thesis, NEW MEXICO STATE UNIVERSITY

    Kravtsov A. V., 1999, PhD thesis, NEW MEXICO STATE UNIVERSITY

    1999

  41. [49]

    I., Yepes G., Knebe A., Gottl \"o ber S., Hoffman Y., Knollmann S

    Libeskind N. I., Yepes G., Knebe A., Gottl \"o ber S., Hoffman Y., Knollmann S. R., 2010, , 401, 1889

    2010

  42. [50]

    D., Bose S., Angulo R

    Ludlow A. D., Bose S., Angulo R. E., Wang L., Hellwing W. A., Navarro J. F., Cole S., Frenk C. S., 2016, , 460, 1214

    2016

  43. [51]

    D., Navarro J

    Ludlow A. D., Navarro J. F., Angulo R. E., Boylan-Kolchin M., Springel V., Frenk C., White S. D. M., 2014, , 441, 378

    2014

  44. [52]

    D., Schaye J., Bower R., 2019, , 488, 3663

    Ludlow A. D., Schaye J., Bower R., 2019, , 488, 3663

    2019

  45. [53]

    D., Schaye J., Schaller M., Richings J., 2019, , 488, L123

    Ludlow A. D., Schaye J., Schaller M., Richings J., 2019, , 488, L123

    2019

  46. [54]

    V., Stinson G., Brook C

    Macci \`o A. V., Stinson G., Brook C. B., Wadsley J., Couchman H. M. P., Shen S., Gibson B. K., Quinn T., 2012, , 744, L9

    2012

  47. [55]

    Madau P., Dickinson M., 2014, , 52, 415

    2014

  48. [56]

    J., 1992, , 30, 543

    Monaghan J. J., 1992, , 30, 543

    1992

  49. [57]

    F., Eke V

    Navarro J. F., Eke V. R., Frenk C. S., 1996, , 283, L72

    1996

  50. [58]

    F., Ludlow A., Springel V., Wang J., Vogelsberger M., White S

    Navarro J. F., Ludlow A., Springel V., Wang J., Vogelsberger M., White S. D. M., Jenkins A., Frenk C. S., Helmi A., 2010, , 402, 21

    2010

  51. [59]

    Ogiya G., Mori M., 2014, , 793, 46

    2014

  52. [60]

    W., Nagamine K., Springel V., Hernquist L., Norman M

    O'Shea B. W., Nagamine K., Springel V., Hernquist L., Norman M. L., 2005, , 160, 1

    2005

  53. [61]

    E., 2007, Computing in Science and Engineering, 9, 21

    P\'erez F., Granger B. E., 2007, Computing in Science and Engineering, 9, 21

    2007

  54. [62]

    P., Marinacci F., Vogelsberger M., 2018, , 475, 648

    Pillepich A., Nelson D., Hernquist L., Springel V., Pakmor R., Torrey P., Weinberger R., Genel S., Naiman J. P., Marinacci F., Vogelsberger M., 2018, , 475, 648

    2018

  55. [63]

    Planck Collaboration Ade P. A. R., Aghanim N., Alves M. I. R., Armitage-Caplan C., Arnaud M., Ashdown M., Atrio-Barandela F., Aumont J., Aussel H., et al. 2014, , 571, A1

    2014

  56. [64]

    Pontzen A., Governato F., 2012, , 421, 3464

    2012

  57. [65]

    F., Jenkins A., Frenk C

    Power C., Navarro J. F., Jenkins A., Frenk C. S., White S. D. M., Springel V., Stadel J., Quinn T., 2003, , 338, 14

    2003

  58. [66]

    J., Monaghan J

    Price D. J., Monaghan J. J., 2007, , 374, 1347

    2007

  59. [67]

    M., Bower R

    Rosas-Guevara Y. M., Bower R. G., Schaye J., Furlong M., Frenk C. S., Booth C. M., Crain R. A., Dalla Vecchia C., Schaller M., Theuns T., 2015, , 454, 1038

    2015

  60. [68]

    S., Fattahi A., Navarro J

    Sawala T., Frenk C. S., Fattahi A., Navarro J. F., Bower R. G., Crain R. A., Dalla Vecchia C., Furlong M., Helly J. C., Jenkins A., Oman K. A., Schaller M., Schaye J., Theuns T., Trayford J., White S. D. M., 2016, , 457, 1931

    2016

  61. [69]

    B., White S

    Scannapieco C., Tissera P. B., White S. D. M., Springel V., 2008, , 389, 1137

    2008

  62. [70]

    Scannapieco et al 2012, , 423, 1726

    2012

  63. [71]

    G., Theuns T., Crain R

    Schaller M., Dalla Vecchia C., Schaye J., Bower R. G., Theuns T., Crain R. A., Furlong M., McCarthy I. G., 2015, , 454, 2277

    2015

  64. [72]

    S., Bower R

    Schaller M., Frenk C. S., Bower R. G., Theuns T., Jenkins A., Schaye J., Crain R. A., Furlong M., Dalla Vecchia C., McCarthy I. G., 2015, , 451, 1247

    2015

  65. [73]

    Schaye J., 2004, , 609, 667

    2004

  66. [74]

    Schaye J., Dalla Vecchia C., 2008, , 383, 1210

    2008

  67. [75]

    Schaye et al 2015, , 446, 521

    2015

  68. [76]

    A., Debattista V

    Sellwood J. A., Debattista V. P., 2009, , 398, 1279

    2009

  69. [77]

    Sembolini et al 2016, , 459, 2973

    2016

  70. [78]

    J., White S

    Shen S., Mo H. J., White S. D. M., Blanton M. R., Kauffmann G., Voges W., Brinkmann J., Csabai I., 2003, , 343, 978

    2003

  71. [79]

    S., Dav \'e R., 2015, , 53, 51

    Somerville R. S., Dav \'e R., 2015, , 53, 51

    2015

  72. [80]

    Springel V., 2000, , 312, 859

    2000

  73. [81]

    Springel V., 2005, , 364, 1105

    2005

  74. [82]

    Springel V., 2010, , 401, 791

    2010

  75. [83]

    Springel V., Di Matteo T., Hernquist L., 2005, , 361, 776

    2005

  76. [84]

    Springel V., Hernquist L., 2003, , 339, 289

    2003

  77. [85]

    F., Frenk C

    Springel V., Wang J., Vogelsberger M., Ludlow A., Jenkins A., Helmi A., Navarro J. F., Frenk C. S., White S. D. M., 2008, , 391, 1685

    2008

  78. [86]

    Springel V., White S. D. M., Tormen G., Kauffmann G., 2001, , 328, 726

    2001

  79. [87]

    Stadel J., Potter D., Moore B., Diemand J., Madau P., Zemp M., Kuhlen M., Quilis V., 2009, , 398, L21

    2009

  80. [88]

    Stevens A. R. H., Martig M., Croton D. J., Feng Y., 2014, , 445, 239

    2014

  81. [89]

    Stinson G., Seth A., Katz N., Wadsley J., Governato F., Quinn T., 2006, , 373, 1074

    2006

  82. [90]

    J., Brunino R., Mitchell N

    Tasker E. J., Brunino R., Mitchell N. L., Michielsen D., Hopton S., Pearce F. R., Bryan G. L., Theuns T., 2008, , 390, 1267

    2008

  83. [91]

    Teyssier R., 2002, , 385, 337

    2002

  84. [92]

    I., 2013, , 429, 3068

    Teyssier R., Pontzen A., Dubois Y., Read J. I., 2013, , 429, 3068

    2013

  85. [93]

    J., Couchman H

    Thacker R. J., Couchman H. M. P., 2001, , 555, L17

    2001

  86. [94]

    Thi \'e baut J., Pichon C., Sousbie T., Prunet S., Pogosyan D., 2008, , 387, 397

    2008

  87. [95]

    V., Klypin A., Abazajian K

    Tinker J., Kravtsov A. V., Klypin A., Abazajian K. a., 2008, , 688, 709

    2008

  88. [96]

    C., Ogiya G., 2018, , 475, 4066

    van den Bosch F. C., Ogiya G., 2018, , 475, 4066

    2018

  89. [97]

    C., Varoquaux G., 2011, CoRR, abs/1102.1523

    van der Walt S., Colbert S. C., Varoquaux G., 2011, CoRR, abs/1102.1523

    2011 arXiv

  90. [98]

    Vandenbroucke B., De Rijcke S., 2016, Astronomy and Computing, 16, 109

    2016

  91. [99]

    A., Sales L

    Vera-Ciro C. A., Sales L. V., Helmi A., Frenk C. S., Navarro J. F., Springel V., Vogelsberger M., White S. D. M., 2011, , 416, 1377

    2011

  92. [100]

    A., Stinson G

    Wang L., Dutton A. A., Stinson G. S., Macci \`o A. V., Penzo C., Kang X., Keller B. W., Wadsley J., 2015, , 454, 83

    2015

  93. [101]

    R., Hopkins P

    Wetzel A. R., Hopkins P. F., Kim J.-h., Faucher-Gigu \`e re C.-A., Kere s D., Quataert E., 2016, , 827, L23

    2016

  94. [102]

    Wiersma R. P. C., Schaye J., Smith B. D., 2009, , 393, 99

    2009

  95. [103]

    Wiersma R. P. C., Schaye J., Theuns T., Dalla Vecchia C., Tornatore L., 2009, , 399, 574

    2009

  96. [104]

    Yepes G., Kates R., Khokhlov A., Klypin A., 1997, , 284, 235

    1997

Pith tools

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