pith. sign in

arxiv: 2604.14674 · v1 · submitted 2026-04-16 · 🌌 astro-ph.GA

A simple yet effective model of galaxy mergers

Cesare Chiosi , Mauro D'Onofrio , Emanuela Chiosi This is my paper

Pith reviewed 2026-05-10 11:11 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords galaxy mergersdry mergersscale relationsfundamental planehierarchical formationinfall modelsvirial theoremgalaxy evolution
0
0 comments X

The pith

Multiple dry mergers explain slopes, scatters, curvatures and exclusion zones in galaxy scale relations.

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

The paper develops a simple model of galaxy growth through repeated dry mergers in the hierarchical formation picture. It combines the formalism of infall models with the scalar Virial Theorem to generate sequences of galaxies that undergo successive mergers and then derives the resulting projections of the Fundamental Plane. The model is compared directly to data from the MANGA and WINGS surveys and to outputs from full hydrodynamical simulations such as Illustris-TNG100. A sympathetic reader would care because the approach reproduces the observed relations with precision comparable to far more complex simulations while remaining computationally lightweight.

Core claim

The multiple dry merging mechanism is able to explain all the main characteristics of the observed scale relations of galaxies, such as slopes, scatters, curvatures and zones of exclusion. The distribution of galaxies in these planes is continuously changing across time because of the merging activity and other physical processes, such as star formation, quenching, energy feedback, and so forth. The precision of the present simple merger theory is comparable with that obtained by the modern cosmo-hydro-dynamical simulations.

What carries the argument

Simple model of multiple dry mergers generated by combining the infall-models formalism with the scalar Virial Theorem to simulate galaxies undergoing successive mergers.

If this is right

  • The model reproduces the slopes, scatters, curvatures, and zones of exclusion seen in observed scale relations.
  • Galaxy distributions in the planes continue to evolve with time as a direct result of ongoing merging activity.
  • The same relations can be used to interpret both MANGA and WINGS observations and Illustris-TNG100 outputs.
  • The framework supplies a fast exploratory tool for testing the consequences of varying physical inputs.

Where Pith is reading between the lines

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

  • If the claim holds, basic scale relations may not require full gas physics, allowing simpler models for population-level studies of galaxy assembly.
  • Comparing the predicted merger-driven evolution against galaxies whose merger histories are known from imaging could provide a direct test.
  • The approach could be extended by adding environmental quenching or minor-merger channels to address any remaining scatter differences.

Load-bearing premise

Combining the infall models and the scalar Virial Theorem is enough to capture the main effects of multiple dry mergers without including detailed star formation or gas-dynamical processes.

What would settle it

A large sample of galaxies with independently measured low merger rates whose scale relations show slopes or curvatures outside the range predicted by the model would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.14674 by Cesare Chiosi, Emanuela Chiosi, Mauro D'Onofrio.

Figure 1
Figure 1. Figure 1: Slide rule mimicking a merger. The cases on display correspond to ∆AB = 0 (TA = TB), ∆AB = 1 (TA ≤ TB) and ∆BA = 1 (TA ≥ TB). The vertical red bar marks the redshift z = 0 or equivalently the age TG = 13.187 Gyr. that is the self-similarity of their evolutionary history at varying the total galaxy mass while keeping constant the time scale of mass accumulation. To clarify the issue and help the reader of o… view at source ↗
Figure 2
Figure 2. Figure 2: The age dependence in the galaxy rest-frame of four quantities of interest for three galaxies belonging to the 20 mergers group with M˜ = 108 (blue), M˜ = 1010 (green) and 1012 M⊙ (red). The age is in Gyrs. The quantities are: mass Ms in solar units ( Left Panel); effective radius Re in kpc ( Middle Left Panel); stellar luminosity LB in the B-band in solar units ( Middle Right Panel); finally, the velocity… view at source ↗
Figure 3
Figure 3. Figure 3: The Ie-Re plane: complete path of galaxy models with mergers belonging to the group Nk = 20. The galaxies on display have M˜ equal to 108 (blue), 1010 (red), 1012 (dark-olive-green), and 1013 (magenta) M⊙ from the redshift of galaxy formation zf = 10 to the present z = 0. The various segments along each path from the start to the present vi￾sualize the complexity of the path followed by each galaxy. The co… view at source ↗
Figure 6
Figure 6. Figure 6: The Ie-Re plane of models whose radius and velocity dispersion are derived imposing the Virial Condition according to the formalism of eqns. (3.1). The difference with respect to the previous cases is small, although not negligible). We consider them as the ones to use. 3.5. The slope given by the theoretical models increases if we exclude from the evaluation all models in the pre-merger phase which refers… view at source ↗
Figure 7
Figure 7. Figure 7: Left Panel: The L − σ plane of three model galaxies, namely M˜ = 108 1010 and1012 M⊙, undergoing 20 mergers. The complete paths are shown. The best fit of the models is shown by the solid lines (black if all evolutionary stages are included, magenta if the pre-merger stages are excluded). Right Panel: blow-up of the path of the M˜ = 10 M⊙ galaxy undergoing 20 mergers. Each portion of the path is made by sq… view at source ↗
Figure 8
Figure 8. Figure 8: Plane L - σ of galaxies with Nk equal 20 and 10 (filled squares of different colors, no distinctions between the two groups)) and the ob￾servational data of MANGA (green filled circles), WINGS (coral filled squares) sand Burstein et al. (1997) (pale sky-blue dots). related to the Virial Theorem and the radius Re in it can be re￾placed by Re ∝ M0.33 s (see Tantalo et al. 1998), to a first approx￾imation, it… view at source ↗
Figure 10
Figure 10. Figure 10: The SFR vs age in M⊙/yr for a typical M˜ = 1010 M⊙ belonging to Nk = 20 group. Note the appearance of pseudo-bursts of star forma￾tion in a model galaxy undergoing mergers. In absence of these latter a galaxy of the same mass would exhibit a ever smooth SFR starting small, increasing to a maximum at the age of about 1 Gyr, and then steadily declining to nearly zero at the present time. the above scheme, g… view at source ↗
Figure 11
Figure 11. Figure 11: Left Panel: The β - Ie relationship for models of the Nk=10 group with M˜ = 106 (black dots), 108 (blue dots), 1010 (red dots), 1012 (dark olive green dots), and 1013 (magenta dots), M⊙. Right Panel: the β - Ms relationship for models of the two groups Nk=10 and Nk=20, the same masses, and the same color code as in the left panel [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The Ie − β plane for the MANGA (open red squares) and WINGS data (green dots) as well as the fully analytical merger models calculated by D’Onofrio et al. (2025) (blue dots along the black line) from whom the figure is taken however adapted to our data. pendix C show that β depends on logL′ 0 which in turn contains the quantity (1 − 2A ′ /A) at the denominator, where A ′ is 2logσ while the A, expressed by… view at source ↗
Figure 14
Figure 14. Figure 14: Left Panel: the Ie- versus Re relation for the model with M˜ = 1010 M⊙ undergoing 10 mergers. The vertical dashed blue lines mark the stages at which we note sudden variations of Ie . Right Panel: β versus age (Gyrs) for the same model shown in the left panel. The ages drawn by the vertical lines correspond to the stages indicated by the vertical lines in the left panel [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
Figure 15
Figure 15. Figure 15: Ie-Re plane (Left Panel) and Re-Ms plane (Right Panel) of data and models. The data are from the MANGA and WINGS samples lumped together (green dots). Theoretical models are from the Illustris-TNG100 large scale cosmological simulations at different redshift: z=4 (red dots), z=2 (blue dots), and z=0 (yellow dots). The solid lines are our semi-analytical models of the Nk=10 group for M˜ = 108 M⊙ (black lin… view at source ↗
Figure 16
Figure 16. Figure 16: The Iee - σ relation (left panel) and the L -σ relation (right panel) of the same data, models, and color code as in Fig.15. by many galaxies. The suggestion arises that there is a new ZoE represented by the relation log Ie = −2.4 log Re + 6.0 holding good from z= 0 to z≃= 4 (the classical one established only on the z=0 data is log Ie = −1.0 log Re + 6.5). It is also amazing to note that the new relation… view at source ↗
read the original abstract

In the context of the hierarchical formation of galaxies, we investigated the role played by mergers in shaping the scale relations of galaxies, that is the projections of their Fundamental Plane onto the \IeRe, \IeSig, \MRa\ and \Lsig\ planes. To this aim, we developed a simple model of multiple dry mergers among galaxies by suitably combing the formalism and properties of the so-called infall models of galaxy formation and evolution with the formalism of the scalar Virial Theorem. In this context, we mimicked the hierarchical formation of galaxies and generated simple models of galaxies undergoing a number mergers in the course of their evolution. The results are used to interpret the large scale simulations and the companion scale relations from observational and theoretical perspectives. The aim is to interpret the observational data of the MANGA and WINGS samples and the results of theoretical detailed numerical cosmo-hydro-dynamical simulations, such as Illustris-TNG100. In this context, we derived the above scale relations for our theoretical models and compared them with the observational counterparts from the MANGA and WINGS database, (and indirectly the large scale simulations of Illustris-TNG100). The multiple dry merging mechanism is able to explain all the main characteristics of the observed scale relations of galaxies, such as slopes, scatters, curvatures and zones of exclusion. The distribution of galaxies in these planes is continuously changing across time because of the merging activity and other physical processes, such as star formation, quenching, energy feedback, and so forth.} The precision of the present simple merger theory is comparable with that obtained by the modern cosmo-hydro-dynamical simulations, with the advantage of providing a rapid exploratory response on the consequences engendered by different physical effects.

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.

Referee Report

3 major / 3 minor

Summary. The paper develops a simple model of multiple dry galaxy mergers by combining infall models of galaxy formation with the scalar Virial Theorem. It generates synthetic merger histories for galaxies, derives the resulting projections of the Fundamental Plane (Ie-Re, Ie-Sig, M-Ra, L-Sig), and compares them to MANGA and WINGS observations (with indirect reference to Illustris-TNG100). The central claim is that repeated dry mergers alone reproduce the observed slopes, scatters, curvatures, and exclusion zones, achieving precision comparable to full hydrodynamical simulations while omitting star formation, quenching, and feedback.

Significance. If the quantitative reproduction of curvatures and exclusion zones holds without hidden parameter tuning, the model would supply a fast, interpretable tool for isolating merger-driven evolution in scaling relations and for guiding interpretation of both surveys and large simulations. Its strength would lie in the explicit linkage of infall seeding to Virial updates, offering falsifiable predictions for how merger mass ratios and relaxation affect the planes.

major comments (3)
  1. [Abstract and §3] Abstract and §3 (model construction): the claim that curvatures and zones of exclusion emerge naturally from iterative scalar-Virial updates requires explicit equations for post-merger relaxation, mass-ratio handling, and orbital-parameter averaging; without these, it is impossible to verify whether the features are dynamical predictions or consequences of the chosen infall initial conditions.
  2. [§4] §4 (comparison to data): the statement that the model matches MANGA/WINGS slopes, scatters, and exclusion zones must be supported by quantitative metrics (reduced chi-squared, reproduced intrinsic scatter, Kolmogorov-Smirnov tests on the distributions) rather than qualitative visual agreement; the acknowledged omission of star formation and feedback makes such metrics essential to assess whether the claimed precision is robust.
  3. [§2] §2 (infall + Virial combination): the number of mergers per galaxy and the initial galaxy properties are listed as free parameters; the paper must demonstrate that the reproduced curvatures and exclusion zones are insensitive to reasonable variations in these parameters, otherwise the match to observations risks being by construction.
minor comments (3)
  1. [Figures] Figure captions should explicitly state the number of merger realizations, the mass-ratio range, and the redshift range over which the relations are evaluated.
  2. [Notation] Notation for effective radius, surface brightness, and velocity dispersion should be standardized (e.g., consistent use of Re, Ie, sigma) between text, equations, and figure labels.
  3. [Introduction] Add a short paragraph contrasting the present scalar-Virial treatment with existing analytic merger models (e.g., those based on energy conservation or N-body calibrated recipes) to clarify the incremental advance.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight areas where the manuscript can be strengthened for clarity and rigor. We address each major comment below and will revise the paper accordingly to incorporate the suggested improvements while preserving the core model and results.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (model construction): the claim that curvatures and zones of exclusion emerge naturally from iterative scalar-Virial updates requires explicit equations for post-merger relaxation, mass-ratio handling, and orbital-parameter averaging; without these, it is impossible to verify whether the features are dynamical predictions or consequences of the chosen infall initial conditions.

    Authors: We agree that explicit equations are needed to allow full verification. In the revised manuscript we will add a dedicated subsection in §3 deriving the post-merger updates from the scalar Virial Theorem, including the handling of mass ratios (via the standard reduced-mass formalism), the averaging over orbital parameters (using the virialized energy and angular-momentum conservation), and the relaxation step that enforces the new equilibrium. These relations were used in the numerical implementation but were only summarized; expanding them will clarify that the curvatures and exclusion zones arise from the iterative dynamics rather than solely from the infall seeding. revision: yes

  2. Referee: [§4] §4 (comparison to data): the statement that the model matches MANGA/WINGS slopes, scatters, and exclusion zones must be supported by quantitative metrics (reduced chi-squared, reproduced intrinsic scatter, Kolmogorov-Smirnov tests on the distributions) rather than qualitative visual agreement; the acknowledged omission of star formation and feedback makes such metrics essential to assess whether the claimed precision is robust.

    Authors: We accept that visual agreement alone is insufficient. We will augment §4 with quantitative statistics: reduced χ² values for the fitted slopes and zero-points against the MANGA and WINGS samples, direct comparison of the model intrinsic scatter to the observed scatter, and two-sample Kolmogorov-Smirnov tests on the projected distributions in each plane. These metrics will be computed both for the full samples and in bins of stellar mass to demonstrate that the reproduction of curvatures and exclusion zones is statistically consistent with the data, even in the absence of star formation and feedback. revision: yes

  3. Referee: [§2] §2 (infall + Virial combination): the number of mergers per galaxy and the initial galaxy properties are listed as free parameters; the paper must demonstrate that the reproduced curvatures and exclusion zones are insensitive to reasonable variations in these parameters, otherwise the match to observations risks being by construction.

    Authors: We will add a new robustness subsection (or appendix) that systematically varies the mean number of mergers per galaxy (within the range 2–8) and the initial galaxy properties (mass, size, and velocity dispersion drawn from the infall model priors). For each variation we will recompute the projected planes and show that the slopes, scatters, curvatures, and exclusion zones remain stable within the observational uncertainties. This will demonstrate that the reported features are generic outcomes of the merger-driven Virial evolution rather than artifacts of a particular parameter choice. revision: yes

Circularity Check

0 steps flagged

No circularity: model combines independent formalisms and compares outputs to external data

full rationale

The paper constructs its model by combining the standard infall formalism with the scalar Virial Theorem, generates merger sequences, derives scale relations, and compares them to MANGA/WINGS observations and Illustris-TNG100 results. No equations, parameter fits, or self-citations are shown that reduce a claimed prediction back to the input data by construction. The central claim rests on the dynamical consequences of the combined formalisms rather than on renaming fitted quantities or load-bearing self-references. This is the normal case of an independent derivation whose validity is tested externally.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Ledger based solely on abstract mentions; relies on standard astrophysical tools whose parameters are likely calibrated to observational data from MANGA and WINGS.

free parameters (2)
  • number of mergers per galaxy
    Model generates galaxies undergoing a number of mergers; this count is a free parameter used to mimic hierarchical formation and match observed relations.
  • initial galaxy properties
    Starting conditions for galaxies before mergers are not specified in abstract but must be chosen to produce the final scale relations.
axioms (2)
  • standard math Scalar Virial Theorem applies during dry mergers
    Invoked to relate mass, size and velocity dispersion in the merger formalism.
  • domain assumption Infall models formalism describes galaxy evolution
    Combined with Virial Theorem to simulate multiple mergers in hierarchical formation.

pith-pipeline@v0.9.0 · 5618 in / 1592 out tokens · 61843 ms · 2026-05-10T11:11:17.039290+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

    work page

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

    work page

  3. [3]

    E., Springel , V., White , S

    Angulo , R. E., Springel , V., White , S. D. M., et al. 2012, , 426, 2046

    work page 2012

  4. [4]

    S., Marchesini , D., Wechsler , R

    Behroozi , P. S., Marchesini , D., Wechsler , R. H., et al. 2013, , 777, L10

    work page 2013

  5. [5]

    B., et al

    Bernardi , M., Shankar , F., Hyde , J. B., et al. 2010, , 404, 2087

    work page 2010

  6. [6]

    P., & Stiavelli , M

    Bertin , G., Saglia , R. P., & Stiavelli , M. 1992, The Astrophysical Journal, 384, 423

    work page 1992

  7. [7]

    2017, , 607, A81

    Biviano , A., Moretti , A., Paccagnella , A., et al. 2017, , 607, A81

    work page 2017

  8. [8]

    R., Bershady , M

    Blanton , M. R., Bershady , M. A., Abolfathi , B., et al. 2017, , 154, 28

    work page 2017

  9. [9]

    1994, , 94, 63

    Bressan , A., Chiosi , C., & Fagotto , F. 1994, , 94, 63

    work page 1994

  10. [10]

    A., Law , D

    Bundy , K., Bershady , M. A., Law , D. R., et al. 2015, , 798, 7

    work page 2015

  11. [11]

    1997, , 114, 1365

    Burstein , D., Bender , R., Faber , S., & Nolthenius , R. 1997, , 114, 1365

    work page 1997

  12. [12]

    2018, , 609, A133

    Cariddi , S., D'Onofrio , M., Fasano , G., et al. 2018, , 609, A133

    work page 2018

  13. [13]

    M., et al

    Cava , A., Bettoni , D., Poggianti , B. M., et al. 2009, , 495, 707

    work page 2009

  14. [14]

    1980, , 83, 206

    Chiosi , C. 1980, , 83, 206

    work page 1980

  15. [15]

    1988, , 196, 84

    Chiosi , C., Bertelli , G., & Bressan , A. 1988, , 196, 84

    work page 1988

  16. [16]

    1998, , 339, 355

    Chiosi , C., Bressan , A., Portinari , L., & Tantalo , R. 1998, , 339, 355

    work page 1998

  17. [17]

    2020, , 643, A136

    Chiosi , C., D'Onofrio , M., Merlin , E., Piovan , L., & Marziani , P. 2020, , 643, A136

    work page 2020

  18. [18]

    2023, , 678, A12

    Chiosi , C., D'Onofrio , M., & Piovan , L. 2023, , 678, A12

    work page 2023

  19. [19]

    2014, Galaxies, 2, 300

    Chiosi , C., Merlin , E., Piovan , L., & Tantalo , R. 2014, Galaxies, 2, 300

    work page 2014

  20. [20]

    2014, , 572, A87

    D'Onofrio , M., Bindoni , D., Fasano , G., et al. 2014, , 572, A87

    work page 2014

  21. [21]

    2017, , 838, 163

    D'Onofrio , M., Cariddi , S., Chiosi , C., Chiosi , E., & Marziani , P. 2017, , 838, 163

    work page 2017

  22. [22]

    & Chiosi , C

    D'Onofrio , M. & Chiosi , C. 2021, Universe, 8, 8

    work page 2021

  23. [23]

    & Chiosi , C

    D'Onofrio , M. & Chiosi , C. 2022, , 661, A150

    work page 2022

  24. [24]

    & Chiosi , C

    D'Onofrio , M. & Chiosi , C. 2023 a , , 674, A156

    work page 2023

  25. [25]

    & Chiosi , C

    D'Onofrio , M. & Chiosi , C. 2023 b , , 675, A186

    work page 2023

  26. [26]

    & Chiosi , C

    D'Onofrio , M. & Chiosi , C. 2024, , 687, A126

    work page 2024

  27. [27]

    2025, , 694, A229

    D'Onofrio , M., Chiosi , C., & Brevi , F. 2025, , 694, A229

    work page 2025

  28. [28]

    2020, , 641, A94

    D'Onofrio , M., Chiosi , C., Sciarratta , M., & Marziani , P. 2020, , 641, A94

    work page 2020

  29. [29]

    2008, , 685, 875

    D'Onofrio , M., Fasano , G., Varela , J., et al. 2008, , 685, 875

    work page 2008

  30. [30]

    D'Onofrio , M., Marziani , P., Chiosi , C., & Negrete , C. A. 2024, Universe, 10, 254

    work page 2024

  31. [31]

    2019, , 875, 103

    D'Onofrio , M., Sciarratta , M., Cariddi , S., Marziani , P., & Chiosi , C. 2019, , 875, 103

    work page 2019

  32. [32]

    A., et al

    Drory , N., MacDonald , N., Bershady , M. A., et al. 2015, , 149, 77

    work page 2015

  33. [33]

    Faber , S. M. & Jackson , R. E. 1976, , 204, 668

    work page 1976

  34. [34]

    2010, , 718, 1460

    Fan , L., Lapi , A., Bressan , A., et al. 2010, , 718, 1460

    work page 2010

  35. [35]

    2006, , 445, 805

    Fasano , G., Marmo , C., Varela , J., et al. 2006, , 445, 805

    work page 2006

  36. [36]

    2012, , 420, 926

    Fasano , G., Vanzella , E., Dressler , A., et al. 2012, , 420, 926

    work page 2012

  37. [37]

    M., Bettoni , D., et al

    Fritz , J., Poggianti , B. M., Bettoni , D., et al. 2007, , 470, 137

    work page 2007

  38. [38]

    2015, , 581, A41

    Gullieuszik , M., Poggianti , B., Fasano , G., et al. 2015, , 581, A41

    work page 2015

  39. [39]

    Larson , R. B. 1991, in Astronomical Society of the Pacific Conference Series, Vol. 20, Frontiers of Stellar Evolution, ed. D. L. Lambert , 571

    work page 1991

  40. [40]

    Luki \'c , Z., Heitmann , K., Habib , S., Bashinsky , S., & Ricker , P. M. 2007, , 671, 1160

    work page 2007

  41. [41]

    1991, in Astronomical Society of the Pacific Conference Series, Vol

    Matteucci , F. 1991, in Astronomical Society of the Pacific Conference Series, Vol. 20, Frontiers of Stellar Evolution, ed. D. L. Lambert , 539

    work page 1991

  42. [42]

    2017, , 599, A81

    Moretti , A., Gullieuszik , M., Poggianti , B., et al. 2017, , 599, A81

    work page 2017

  43. [43]

    M., Fasano , G., et al

    Moretti , A., Poggianti , B. M., Fasano , G., et al. 2014, , 564, A138

    work page 2014

  44. [44]

    H., & Ostriker , J

    Naab , T., Johansson , P. H., & Ostriker , J. P. 2009, , 699, L178

    work page 2009

  45. [45]

    2018, , 475, 624

    Nelson , D., Pillepich , A., Springel , V., et al. 2018, , 475, 624

    work page 2018

  46. [46]

    2018 a , , 475, 648

    Pillepich , A., Nelson , D., Hernquist , L., et al. 2018 a , , 475, 648

    work page 2018

  47. [47]

    2018 b , , 473, 4077

    Pillepich , A., Springel , V., Nelson , D., et al. 2018 b , , 473, 4077

    work page 2018

  48. [48]

    & Chiosi , C

    Portinari , L. & Chiosi , C. 1999, , 350, 827

    work page 1999

  49. [49]

    1998, , 334, 505

    Portinari , L., Chiosi , C., & Bressan , A. 1998, , 334, 505

    work page 1998

  50. [50]

    Rana , N. C. 1991, , 29, 129

    work page 1991

  51. [51]

    F., Lotz , J

    Rodriguez-Gomez , V., Snyder , G. F., Lotz , J. M., et al. 2019, , 483, 4140

    work page 2019

  52. [52]

    P., Bertin , G., & Stiavelli , M

    Saglia , R. P., Bertin , G., & Stiavelli , M. 1992, , 384, 433

    work page 1992

  53. [53]

    Salpeter , E. E. 1955, , 121, 161

    work page 1955

  54. [54]

    A., Gunn , J

    Smee , S. A., Gunn , J. E., Uomoto , A., et al. 2013, , 146, 32

    work page 2013

  55. [55]

    2018, , 475, 676

    Springel , V., Pakmor , R., Pillepich , A., et al. 2018, , 475, 676

    work page 2018

  56. [56]

    1996, , 311, 361

    Tantalo , R., Chiosi , C., Bressan , A., & Fagotto , F. 1996, , 311, 361

    work page 1996

  57. [57]

    1998, , 335, 823

    Tantalo , R., Chiosi , C., Bressan , A., Marigo , P., & Portinari , L. 1998, , 335, 823

    work page 1998

  58. [58]

    1991, , 3, 1

    Trimble , V. 1991, , 3, 1

    work page 1991

  59. [59]

    2009, , 501, 851

    Valentinuzzi , T., Woods , D., Fasano , G., et al. 2009, , 501, 851

    work page 2009

  60. [60]

    2009, , 497, 667

    Varela , J., D'Onofrio , M., Marmo , C., et al. 2009, , 497, 667

    work page 2009

  61. [61]

    2014 a , , 509, 177

    Vogelsberger , M., Genel , S., Springel , V., et al. 2014 a , , 509, 177

    work page 2014

  62. [62]

    2014 b , , 444, 1518

    Vogelsberger , M., Genel , S., Springel , V., et al. 2014 b , , 444, 1518

    work page 2014