pith. sign in

arxiv: 2606.19454 · v2 · pith:PST5HDSTnew · submitted 2026-06-17 · 🌌 astro-ph.GA · astro-ph.CO

Baryonic mass budgets in the central regions of the Bullet Cluster and their consistency with strong lensing in MOND

Dong Zhang (Bonn) , Hosein Haghi (Bonn , Zanjan) , Elena Asencio (Bonn) , Indranil Banik (Portsmouth) , Akram Hasani Zonoozi (Bonn) , Sangjun Cha (Seoul) , Boseong Young Cho (Seoul)
show 5 more authors
Hyungjin Joo (Seoul) Pavel Kroupa (Bonn Prague) Anastasia Lazutkina (Wuppertal) Eda Gjergo (Nanjing)
This is my paper

Pith reviewed 2026-06-26 20:07 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords Bullet ClusterMONDstrong lensingIGIMFbaryonic massJWST photometryintracluster gasstellar remnants
0
0 comments X

The pith

Baryonic masses from IGIMF models match MOND strong-lensing requirements in the Bullet Cluster cores.

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

The paper re-estimates baryonic masses in three central regions of the Bullet Cluster from recent JWST photometry. It applies the integrated galaxy-wide initial mass function theory, which accounts for more massive stars and their remnants in high-metallicity settings, to produce higher total baryonic masses than standard IMF assumptions allow. These IGIMF-based masses, bounded by constant and enriched metallicity cases, encompass the mass values required by strong-lensing observations when interpreted in MOND. The offset between lensing peaks and X-ray gas has long been cited as evidence for dark matter, so matching the lensing signal with baryons alone would remove that tension inside the cores. The authors note that the physical arrangement of the remnant stars must still be verified to confirm the lensing contribution.

Core claim

Using recent JWST photometry and stellar population synthesis models with constant and self-enriched metallicities as lower and upper limits, the baryonic masses predicted by IGIMF theory for the three BCG-centred cores encompass the MOND strong-lensing mass estimates.

What carries the argument

The integrated galaxy-wide initial mass function (IGIMF) theory, which predicts substantially higher baryonic masses by incorporating a top-heavy IMF for massive stars in high-metallicity, dense environments and the resulting stellar remnants.

If this is right

  • The MOND strong-lensing masses of all three cores lie within the range predicted by the IGIMF models.
  • The baryonic mass budget is consistent with MOND requirements from strong-lensing observations in the core regions.
  • Regardless of MOND validity, less dark matter may be required than previously inferred from the lensing data.
  • High observed metallicities imply a past stellar population dominated by massive stars whose remnants add significant baryonic mass.

Where Pith is reading between the lines

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

  • If remnant distributions can be shown to align with lensing peaks, the scenario would extend to other merging clusters exhibiting similar mass offsets.
  • Future high-resolution imaging of stellar remnant tracers could directly test whether the extra baryonic mass is located where lensing requires it.
  • The same IGIMF adjustment might reduce inferred dark-matter fractions in other high-metallicity galaxy groups and clusters.

Load-bearing premise

The evolved stellar remnants must be spatially distributed and dynamically moving in a way that can produce the observed strong-lensing signal.

What would settle it

Dynamical simulations or direct observations showing that the remnant population cannot concentrate enough to reproduce the measured lensing mass peaks at the BCG locations.

Figures

Figures reproduced from arXiv: 2606.19454 by Akram Hasani Zonoozi (Bonn), Anastasia Lazutkina (Wuppertal), Boseong Young Cho (Seoul), Dong Zhang (Bonn), Eda Gjergo (Nanjing), Elena Asencio (Bonn), Hosein Haghi (Bonn, Hyungjin Joo (Seoul), Indranil Banik (Portsmouth), Pavel Kroupa (Bonn, Prague), Sangjun Cha (Seoul), Zanjan).

Figure 1
Figure 1. Figure 1: FIG. 1. The relation between [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The orange dots show the F090W-band galaxy luminosity [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. 2D projected total baryonic and strong lensing mass distri [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Comparison between the MOND strong lensing masses and [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
read the original abstract

Strong lensing observations of the Bullet Cluster have traditionally been regarded as strong evidence for dark matter and a major challenge to Milgromian dynamics (MOND). The offset between the lensing mass and the X-ray gas centroids implies a substantial amount of unseen mass near the brightest cluster galaxies (BCGs). However, the high metallicities observed in both the intracluster gas and the massive early-type member galaxies suggest a past stellar population dominated by massive stars, whose evolved remnants contribute additional baryonic mass. This effect is naturally incorporated in the integrated galaxy-wide initial mass function (IGIMF) theory, which predicts substantially larger baryonic masses than a canonical IMF. In this work, we re-estimate the baryonic masses of the three BCG-centred core regions of the Bullet Cluster using recent JWST photometry and compare them with MOND strong-lensing masses. We derive IGIMF masses using stellar population synthesis models with constant and (self-) enriched metallicities, representing lower and upper mass limits, respectively. We find that the MOND strong-lensing masses of all three cores lie within the range predicted by the IGIMF models. These results suggest that the baryonic mass budget is consistent with MOND requirements from strong-lensing observations in the core regions of the Bullet Cluster. However, the physical viability of this scenario also depends on the spatial distribution and dynamical behavior of the remnant population, which remain to be established. More generally, regardless of the validity of MOND, the results imply that less dark matter may be required than previously inferred.

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

2 major / 1 minor

Summary. The paper claims that baryonic masses estimated for the three BCG cores in the Bullet Cluster using JWST photometry and IGIMF models (with constant and self-enriched metallicities as lower and upper bounds) encompass the masses inferred from strong lensing under MOND. This is taken to indicate consistency between the baryonic mass budget and MOND lensing requirements, with the caveat that the spatial distribution of stellar remnants must still be shown to reproduce the lensing signal. The work suggests that less dark matter may be required than previously inferred.

Significance. If the mass comparison is robust, this work would demonstrate that IGIMF theory can reconcile baryonic masses with MOND strong-lensing estimates in the Bullet Cluster cores, offering a potential baryonic explanation for what has been seen as a challenge to MOND. The incorporation of recent JWST data and the explicit acknowledgment of the untested distribution assumption are positive features. The result bears on the broader question of dark matter requirements in galaxy clusters.

major comments (2)
  1. [Abstract] Abstract: The statement that the MOND strong-lensing masses of all three cores 'lie within the range predicted by the IGIMF models' is made without accompanying error bars or uncertainty ranges on the lensing masses or the IGIMF bounds. This omission is load-bearing for assessing the robustness of the central consistency claim.
  2. [Abstract] Abstract: The consistency with strong lensing is asserted on the basis of total mass agreement alone. However, strong lensing constrains the projected surface density distribution rather than the integrated mass. The manuscript notes that the spatial distribution and dynamical behavior of the remnant population remain to be established but provides no test (e.g., via ray-tracing) of whether any distribution within the mass range can reproduce the observed lensing features. This is a load-bearing issue for the claim of consistency with strong lensing in MOND.
minor comments (1)
  1. The abstract would benefit from specifying the names or positions of the three BCG cores for improved clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and indicate where revisions will be made to improve clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The statement that the MOND strong-lensing masses of all three cores 'lie within the range predicted by the IGIMF models' is made without accompanying error bars or uncertainty ranges on the lensing masses or the IGIMF bounds. This omission is load-bearing for assessing the robustness of the central consistency claim.

    Authors: We agree that the abstract would benefit from explicit reference to the nature of the ranges. The IGIMF bounds are defined by the constant-metallicity (lower) and self-enriched (upper) cases, while the strong-lensing masses are taken directly from the cited literature values. In the revised version we will amend the abstract to state that the lensing masses lie within the IGIMF-derived bounds, with the detailed values and ranges provided in the main text and tables. revision: yes

  2. Referee: [Abstract] Abstract: The consistency with strong lensing is asserted on the basis of total mass agreement alone. However, strong lensing constrains the projected surface density distribution rather than the integrated mass. The manuscript notes that the spatial distribution and dynamical behavior of the remnant population remain to be established but provides no test (e.g., via ray-tracing) of whether any distribution within the mass range can reproduce the observed lensing features. This is a load-bearing issue for the claim of consistency with strong lensing in MOND.

    Authors: We concur that strong lensing constrains the projected distribution and that total mass agreement alone does not constitute a full reproduction of the lensing signal. The manuscript already states that the spatial distribution and dynamical behavior of the remnants remain to be established and limits its claim to the baryonic mass budget being consistent with the MOND-inferred total masses. A ray-tracing validation lies outside the scope of the present work, which focuses on the mass comparison using JWST photometry and IGIMF models; we will expand the discussion to reiterate this boundary explicitly. revision: partial

Circularity Check

0 steps flagged

No significant circularity; independent mass estimates compared

full rationale

The paper derives baryonic mass estimates for the Bullet Cluster cores from JWST photometry fed into IGIMF stellar-population synthesis models (an external framework) and compares the resulting range to MOND strong-lensing masses taken from prior observational literature. Neither quantity is obtained from the other inside this manuscript; the agreement is presented as an empirical consistency check rather than a derivation that reduces to its own inputs by construction. The paper explicitly flags that spatial distribution of remnants must still be verified, avoiding any claim that the numerical match alone proves the lensing signal. No self-citation load-bearing step, fitted-input prediction, or ansatz smuggling is present in the reported chain. This is the normal non-circular outcome for a comparative study against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of the IGIMF framework to cluster BCGs, the accuracy of the stellar-population synthesis models at high metallicity, and the assumption that the remnant population can be treated as contributing to the lensing mass without further dynamical constraints. No new entities are postulated.

free parameters (1)
  • IGIMF metallicity enrichment parameter
    The paper uses constant and self-enriched metallicities as lower and upper limits; these choices are model inputs that affect the predicted remnant mass.
axioms (2)
  • domain assumption IGIMF theory correctly predicts a higher fraction of massive stars and therefore more remnants in dense, high-metallicity environments
    Invoked to justify the larger baryonic masses relative to a canonical IMF.
  • domain assumption Strong-lensing mass estimates under MOND are reliable once the baryonic distribution is known
    The comparison assumes the MOND lensing calculation itself is not in question.

pith-pipeline@v0.9.1-grok · 5909 in / 1530 out tokens · 17268 ms · 2026-06-26T20:07:28.885043+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

138 extracted references · 1 canonical work pages

  1. [1]

    suggest that 30% of stellar remnants in the Milky Way ac- quire sufficient kinetic energy from natal kicks to escape the Galaxy. However, the relative mass fractions of black holes and neu- tron stars among stellar remnants depend on the shape of the gwIMFs in each galaxy, with the boundary mass between neu- tron stars and black holes depending also on th...

  2. [2]

    The short-to-long axis ratio>0.5

  3. [3]

    A galaxy is classified as an early-type (elliptical) galaxy if at least two of these three criteria are satisfied; otherwise, it is classified as a late-type (spiral) galaxy

    The Sérsic index>2; and 3.m F606W −m F814W >1.2, wherem F606W andm F814W denote the observed apparent magnitudes in the Vega system in the F606W and F814W bands, respectively, withoutK-correction [113]. A galaxy is classified as an early-type (elliptical) galaxy if at least two of these three criteria are satisfied; otherwise, it is classified as a late-t...

  4. [4]

    (21) [40], which is based on the results of Thomaset al.[86] and McDermidet al.[87]

    The SFTs of elliptical galaxies used in this work fol- low the empirical downsizing relation of Eq. (21) [40], which is based on the results of Thomaset al.[86] and McDermidet al.[87]. In reality, however, galaxies may experience longer and more complex SFTs due to en- vironmental processes, internal feedback, or continued gas accretion. Longer SFTs tend ...

  5. [5]

    Although this is supported as a dominant for- mation channel for massive ellipticals, real galaxies may also undergo mergers, tidal interactions, or ex- tended gas infall

    The model further assumes that galaxies evolve as iso- lated systems forming through a pure downsizing se- quence. Although this is supported as a dominant for- mation channel for massive ellipticals, real galaxies may also undergo mergers, tidal interactions, or ex- tended gas infall. These processes generally prolong star formation and modify the pathwa...

  6. [6]

    Moreover, the ICL still remains an active topic of research, with both its definition and observational techniques still un- der development [see, e.g., 120]

    pointed out that the fact that the hot gas is not in dynami- cal equilibrium can lead to overestimations in the X-ray mass. Moreover, the ICL still remains an active topic of research, with both its definition and observational techniques still un- der development [see, e.g., 120]. In our estimation, the ICL luminosity fraction accounts for about 20–30% o...

  7. [7]

    Tucker, P

    W. Tucker, P. Blanco, S. Rappoport, L. David, D. Fabri- cant, E. E. Falco, W. Forman, A. Dressler, and M. Ramella, 1E 0657-56: A Contender for the Hottest Known Cluster of Galaxies, ApJ496, L5 (1998), arXiv:astro-ph/9801120 [astro- ph]

    Pith/arXiv arXiv 1998

  8. [8]

    Clowe, M

    D. Clowe, M. Brada ˇc, A. H. Gonzalez, M. Markevitch, S. W. Randall, C. Jones, and D. Zaritsky, A Direct Empirical Proof of the Existence of Dark Matter, ApJ648, L109 (2006), astro- ph/0608407

    arXiv 2006

  9. [9]

    Efstathiou, W

    G. Efstathiou, W. J. Sutherland, and S. J. Maddox, The cosmo- logical constant and cold dark matter, Nature348, 705 (1990)

    1990

  10. [10]

    J. P. Ostriker and P. J. Steinhardt, The observational case for a low-density Universe with a non-zero cosmological constant, Nature377, 600 (1995)

    1995

  11. [11]

    Milgrom, A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis, ApJ270, 365 (1983)

    M. Milgrom, A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis, ApJ270, 365 (1983)

    1983

  12. [12]

    Bekenstein and M

    J. Bekenstein and M. Milgrom, Does the missing mass prob- lem signal the breakdown of Newtonian gravity?, ApJ286, 7 (1984)

    1984

  13. [13]

    K. G. Begeman, A. H. Broeils, and R. H. Sanders, Extended rotation curves of spiral galaxies - Dark haloes and modified dynamics, MNRAS249, 523 (1991)

    1991

  14. [14]

    Gentile, B

    G. Gentile, B. Famaey, and W. J. G. de Blok, THINGS about MOND, A&A527, A76 (2011), arXiv:1011.4148 [astro- ph.CO]

    Pith/arXiv arXiv 2011

  15. [15]

    S. S. McGaugh, F. Lelli, and J. M. Schombert, Radial Accel- eration Relation in Rotationally Supported Galaxies, Physical Review Letters117, 201101 (2016), arXiv:1609.05917 [astro- ph.GA]

    Pith/arXiv arXiv 2016

  16. [16]

    Famaey and S

    B. Famaey and S. S. McGaugh, Modified Newtonian Dynam- ics (MOND): Observational Phenomenology and Relativis- tic Extensions, Living Reviews in Relativity15, 10 (2012), arXiv:1112.3960

    Pith/arXiv arXiv 2012

  17. [17]

    Banik and H

    I. Banik and H. Zhao, From Galactic Bars to the Hubble Ten- sion: Weighing Up the Astrophysical Evidence for Milgro- mian Gravity, Symmetry14, 1331 (2022), arXiv:2110.06936 [astro-ph.CO]

    arXiv 2022

  18. [18]

    Kroupa, E

    P. Kroupa, E. Gjergo, E. Asencio, M. Haslbauer, J. Pflamm- Altenburg, N. Wittenburg, N. Samaras, I. Thies, and W. Oehm, The many tensions with dark-matter based models and impli- cations on the nature of the Universe, inSchool and Work- shops on Elementary Particle Physics and Gravity(2023) p. 231, arXiv:2309.11552 [astro-ph.CO]

    arXiv 2023

  19. [19]

    L. S. The and S. D. M. White, Modified Newtonian Dymanics and the Coma Cluster, AJ95, 1642 (1988)

    1988

  20. [20]

    Gerbal, F

    D. Gerbal, F. Durret, M. Lachieze-Rey, and G. Lima-Neto, Analysis of X-ray galaxy clusters in the framework of modi- fied Newtonian dynamics., A&A262, 395 (1992)

    1992

  21. [21]

    R. H. Sanders, The Virial Discrepancy in Clusters of Galaxies in the Context of Modified Newtonian Dynamics, ApJ512, L23 (1999), arXiv:astro-ph/9807023 [astro-ph]

    Pith/arXiv arXiv 1999

  22. [22]

    R. H. Sanders, Clusters of galaxies with modified Newtonian dynamics, MNRAS342, 901 (2003), astro-ph/0212293

    Pith/arXiv arXiv 2003

  23. [23]

    Pointecouteau and J

    E. Pointecouteau and J. Silk, New constraints on modified Newtonian dynamics from galaxy clusters, MNRAS364, 654 (2005), arXiv:astro-ph/0505017 [astro-ph]

    Pith/arXiv arXiv 2005

  24. [24]

    Natarajan and H

    P. Natarajan and H. Zhao, MOND plus classical neutrinos are not enough for cluster lensing, MNRAS389, 250 (2008), arXiv:0806.3080 [astro-ph]

    Pith/arXiv arXiv 2008

  25. [25]

    G. W. Angus, Dwarf spheroidals in MOND, MNRAS387, 1481 (2008), arXiv:0804.3812 [astro-ph]

    Pith/arXiv arXiv 2008

  26. [26]

    Ettori, V

    S. Ettori, V . Ghirardini, D. Eckert, E. Pointecouteau, F. Gastaldello, M. Sereno, M. Gaspari, S. Ghizzardi, M. Ron- carelli, and M. Rossetti, Hydrostatic mass profiles in X-COP galaxy clusters, A&A621, A39 (2019), arXiv:1805.00035 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  27. [27]

    Famaey, L

    B. Famaey, L. Pizzuti, and I. D. Saltas, Nature of the miss- ing mass of galaxy clusters in MOND: The view from gravitational lensing, Phys. Rev. D111, 123042 (2025), arXiv:2410.02612 [astro-ph.CO]

    arXiv 2025

  28. [28]

    Kelleher and F

    R. Kelleher and F. Lelli, Galaxy clusters in Milgromian dy- namics: Missing matter, hydrostatic bias, and the external field effect, A&A688, A78 (2024), arXiv:2405.08557 [astro- ph.CO]

    arXiv 2024

  29. [29]

    G. W. Angus, Is an 11eV sterile neutrino consistent with clus- ters, the cosmic microwave background and modified Newto- nian dynamics?, MNRAS394, 527 (2009), arXiv:0805.4014

    Pith/arXiv arXiv 2009

  30. [30]

    H. Katz, S. McGaugh, P. Teuben, and G. W. Angus, Galaxy Cluster Bulk Flows and Collision Velocities in QUMOND, 13 ApJ772, 10 (2013), arXiv:1305.3651 [astro-ph.CO]

    Pith/arXiv arXiv 2013

  31. [31]

    Wittenburg, P

    N. Wittenburg, P. Kroupa, I. Banik, G. Candlish, and N. Sama- ras, Hydrodynamical structure formation in Milgromian cos- mology, MNRAS523, 453 (2023), arXiv:2305.05696 [astro- ph.CO]

    arXiv 2023

  32. [32]

    Samaras, S

    N. Samaras, S. Grandis, and P. Kroupa, On the initial condi- tions of theνHDM cosmological model, MNRAS541, 784 (2025), arXiv:2506.19196 [astro-ph.CO]

    arXiv 2025

  33. [33]

    Russell, I

    A. Russell, I. Banik, O. Cray, and H. Zhao, How does a MOND cosmology fare on Gpc scales? - Collisionless N-body simulations ofνHDM, Mon. Not. R. Astron. Soc. 10.1093/mn- ras/stag399 (2026), arXiv:2602.21975 [astro-ph.CO]

    work page doi:10.1093/mn- 2026

  34. [34]

    G. W. Angus, B. Famaey, and A. Diaferio, Equilibrium config- urations of 11 eV sterile neutrinos in MONDian galaxy clus- ters, MNRAS402, 395 (2010), arXiv:0906.3322

    Pith/arXiv arXiv 2010

  35. [35]

    Haslbauer, I

    M. Haslbauer, I. Banik, and P. Kroupa, The KBC void and Hubble tension contradictΛCDM on a Gpc scale - Milgro- mian dynamics as a possible solution, MNRAS499, 2845 (2020), arXiv:2009.11292 [astro-ph.CO]

    arXiv 2020

  36. [36]

    Haslbauer, I

    M. Haslbauer, I. Banik, P. Kroupa, H. Zhao, and E. Asencio, The Magellanic Clouds Are Very Rare in the IllustrisTNG Simulations, Universe10, 385 (2024), arXiv:2409.17259 [astro-ph.GA]

    arXiv 2024

  37. [37]

    Hernandez and P

    X. Hernandez and P. Kroupa, Dynamical Friction Constraints on the Dark Matter Hypothesis Across Astronomical Scales, Universe11, 367 (2025), arXiv:2511.03776 [astro-ph.GA]

    arXiv 2025

  38. [38]

    Kroupa, J

    P. Kroupa, J. Pflamm-Altenburg, S. Mazurenko, W. Wu, I. Thies, V . Jadhav, and T. Jerabkova, Open Star Clusters and Their Asymmetrical Tidal Tails, Astrophys. J.970, 94 (2024), arXiv:2405.09609 [astro-ph.GA]

    arXiv 2024

  39. [39]

    Asencio, I

    E. Asencio, I. Banik, S. Mieske, A. Venhola, P. Kroupa, and H. Zhao, The distribution and morphologies of Fornax Cluster dwarf galaxies suggest they lack dark matter, MNRAS515, 2981 (2022), arXiv:2208.02265 [astro-ph.GA]

    arXiv 2022

  40. [40]

    Pflamm-Altenburg, Asymmetry in the tidal tails of open star clusters from direct N-body integrations in Milgrom-law dynamics, A&A693, A127 (2025), arXiv:2411.13675 [astro- ph.GA]

    J. Pflamm-Altenburg, Asymmetry in the tidal tails of open star clusters from direct N-body integrations in Milgrom-law dynamics, A&A693, A127 (2025), arXiv:2411.13675 [astro- ph.GA]

    arXiv 2025

  41. [41]

    Markevitch, A

    M. Markevitch, A. H. Gonzalez, L. David, A. Vikhlinin, S. Murray, W. Forman, C. Jones, and W. Tucker, A Text- book Example of a Bow Shock in the Merging Galaxy Clus- ter 1E 0657-56, ApJ567, L27 (2002), arXiv:astro-ph/0110468 [astro-ph]

    Pith/arXiv arXiv 2002

  42. [42]

    A. E. Blackwell, J. N. Bregman, and S. L. Snowden, The Missing Metal Problem in Galaxy Clusters: Characteriz- ing the Early Enrichment Population, ApJ927, 104 (2022), arXiv:2105.04638 [astro-ph.GA]

    arXiv 2022

  43. [43]

    Kroupa and C

    P. Kroupa and C. Weidner, Galactic-Field Initial Mass Func- tions of Massive Stars, ApJ598, 1076 (2003), arXiv:astro- ph/0308356 [astro-ph]

    arXiv 2003

  44. [44]

    Kroupa, On the variation of the initial mass function, MN- RAS322, 231 (2001), astro-ph/0009005

    P. Kroupa, On the variation of the initial mass function, MN- RAS322, 231 (2001), astro-ph/0009005

    Pith/arXiv arXiv 2001

  45. [45]

    Je ˇrábková, A

    T. Je ˇrábková, A. Hasani Zonoozi, P. Kroupa, G. Beccari, Z. Yan, A. Vazdekis, and Z. Y . Zhang, Impact of metallic- ity and star formation rate on the time-dependent, galaxy- wide stellar initial mass function, A&A620, A39 (2018), arXiv:1809.04603 [astro-ph.GA]

    Pith/arXiv arXiv 2018

  46. [46]

    Z. Yan, T. Je ˇrábková, and P. Kroupa, Downsizing revised: Star formation timescales for elliptical galaxies with an environment-dependent IMF and a number of SNIa, A&A 655, A19 (2021), arXiv:2107.03388 [astro-ph.GA]

    arXiv 2021

  47. [47]

    A. H. Zonoozi, H. Haghi, and P. Kroupa, Stellar population synthesis models with a physically varying IMF, MNRAS 537, 2782 (2025), arXiv:2502.03529 [astro-ph.GA]

    arXiv 2025

  48. [48]

    Kroupa, E

    P. Kroupa, E. Gjergo, T. Jerabkova, and Z. Yan, The initial mass function of stars, inEncyclopedia of Astrophysics, Vol- ume 2, V ol. 2 (2026) pp. 173–210, arXiv:2410.07311 [astro- ph.GA]

    arXiv 2026

  49. [49]

    Loewenstein, Perspectives on Intracluster Enrichment and the Stellar Initial Mass Function in Elliptical Galaxies, ApJ 773, 52 (2013), arXiv:1301.3200 [astro-ph.CO]

    M. Loewenstein, Perspectives on Intracluster Enrichment and the Stellar Initial Mass Function in Elliptical Galaxies, ApJ 773, 52 (2013), arXiv:1301.3200 [astro-ph.CO]

    Pith/arXiv arXiv 2013

  50. [50]

    Kraljic and S

    D. Kraljic and S. Sarkar, How rare is the Bullet Cluster (in a ΛCDM universe)?, JCAP4, 050, arXiv:1412.7719

    Pith/arXiv arXiv

  51. [51]

    Asencio, I

    E. Asencio, I. Banik, and P. Kroupa, A massive blow for ΛCDM - the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology, MNRAS500, 5249 (2021)

    2021

  52. [52]

    S. Cha, B. Y . Cho, H. Joo, W. Lee, K. HyeongHan, Z. P. Scofield, K. Finner, and M. J. Jee, A High-Caliber View of the Bullet Cluster through JWST Strong and Weak Lensing Analyses, ApJL987, L15 (2025), arXiv:2503.21870 [astro- ph.GA]

    arXiv 2025

  53. [53]

    Paraficz, J

    D. Paraficz, J. P. Kneib, J. Richard, A. Morandi, M. Limousin, E. Jullo, and J. Martinez, The Bullet cluster at its best: weigh- ing stars, gas, and dark matter, A&A594, A121 (2016), arXiv:1209.0384 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  54. [54]

    Richard, A

    J. Richard, A. Claeyssens, D. Lagattuta, L. Guaita, F. E. Bauer, R. Pello, D. Carton, R. Bacon, G. Soucail, G. P. Lyon, J.-P. Kneib, G. Mahler, B. Clément, W. Mercier, A. Variu, A. Tamone, H. Ebeling, K. B. Schmidt, T. Nanayakkara, M. Maseda, P. M. Weilbacher, N. Bouché, R. J. Bouwens, L. Wisotzki, G. de la Vieuville, J. Martinez, and V . Patrício, An atl...

    arXiv 2021

  55. [55]

    Einstein, Die Feldgleichungen der Gravitation, Sitzungs- berichte der Königlich Preußischen Akademie der Wis- senschaften (Berlin)6, 844 (1915)

    A. Einstein, Die Feldgleichungen der Gravitation, Sitzungs- berichte der Königlich Preußischen Akademie der Wis- senschaften (Berlin)6, 844 (1915)

    1915

  56. [56]

    J. D. Bekenstein, Relativistic gravitation theory for the mod- ified Newtonian dynamics paradigm, Physical Review D70, 083509 (2004), astro-ph/0403694

    Pith/arXiv arXiv 2004

  57. [57]

    Virgo & LIGO Collaborations, GW170817: Observa- tion of Gravitational Waves from a Binary Neutron Star Inspiral, Physical Review Letters119, 161101 (2017), arXiv:1710.05832 [gr-qc]

    Pith/arXiv arXiv 2017

  58. [58]

    Skordis and T

    C. Skordis and T. Zło ´snik, Gravitational alternatives to dark matter with tensor mode speed equaling the speed of light, Physical Review D100, 104013 (2019), arXiv:1905.09465 [gr-qc]

    arXiv 2019

  59. [59]

    G. W. Angus, H. Y . Shan, H. S. Zhao, and B. Famaey, On the Proof of Dark Matter, the Law of Gravity, and the Mass of Neutrinos, ApJ654, L13 (2007), astro-ph/0609125

    Pith/arXiv arXiv 2007

  60. [60]

    Bernal, S

    T. Bernal, S. Capozziello, J. C. Hidalgo, and S. Mendoza, Re- covering MOND from extended metric theories of gravity, Eu- ropean Physical Journal C71, 1794 (2011), arXiv:1108.5588 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  61. [61]

    Skordis and T

    C. Skordis and T. Zło´snik, New Relativistic Theory for Mod- ified Newtonian Dynamics, Physical Review Letters127, 161302 (2021), arXiv:2007.00082 [astro-ph.CO]

    arXiv 2021

  62. [62]

    Monjo, Galaxy rotation curve in hyperconical universes: a natural relativistic MOND, Classical and Quantum Gravity40, 235002 (2023), arXiv:2410.05477 [gr-qc]

    R. Monjo, Galaxy rotation curve in hyperconical universes: a natural relativistic MOND, Classical and Quantum Gravity40, 235002 (2023), arXiv:2410.05477 [gr-qc]

    arXiv 2023

  63. [63]

    R. Monjo, Hydrostatic Equilibrium Constraints in X-COP Galaxy Clusters: Testing Hyperconical Modified Grav- ity in Hot-gas-dominated Regions, ApJ981, 195 (2025), arXiv:2408.08102 [astro-ph.CO]

    arXiv 2025

  64. [64]

    Monjo and I

    R. Monjo and I. Banik, Distinct Acceleration Relations of Galaxies and Galaxy Clusters from Hyperconical Modi- 14 fied Gravity, ApJ992, 35 (2025), arXiv:2405.10019 [astro- ph.CO]

    arXiv 2025

  65. [65]

    H. C. Plummer, On the problem of distribution in globular star clusters, MNRAS71, 460 (1911)

    1911

  66. [66]

    Ferreras, M

    I. Ferreras, M. Sakellariadou, and M. F. Yusaf, Necessity of Dark Matter in Modified Newtonian Dynamics within Galactic Scales, Physical Review Letters100, 031302 (2008), arXiv:0709.3189 [astro-ph]

    Pith/arXiv arXiv 2008

  67. [67]

    Ferreras, N

    I. Ferreras, N. E. Mavromatos, M. Sakellariadou, and M. F. Yusaf, Confronting MOND and TeVeS with strong gravita- tional lensing over galactic scales: An extended survey, Phys- ical Review D86, 083507 (2012), arXiv:1205.4880 [astro- ph.CO]

    Pith/arXiv arXiv 2012

  68. [68]

    Chang, M.-H

    Z. Chang, M.-H. Li, X. Li, H.-N. Lin, and S. Wang, Finslerian MOND versus the strong gravitational lensing of the early- type galaxies, European Physical Journal C73, 2550 (2013), arXiv:1309.1343 [astro-ph.GA]

    Pith/arXiv arXiv 2013

  69. [69]

    Famaey and J

    B. Famaey and J. Binney, Modified Newtonian dynamics in the Milky Way, MNRAS363, 603 (2005), astro-ph/0506723

    Pith/arXiv arXiv 2005

  70. [70]

    Banik, C

    I. Banik, C. Pittordis, W. Sutherland, B. Famaey, R. Ibata, S. Mieske, and H. Zhao, Strong constraints on the gravitational law from Gaia DR3 wide binaries, MNRAS527, 4573 (2024), arXiv:2311.03436 [astro-ph.SR]

    arXiv 2024

  71. [71]

    A. Hees, W. M. Folkner, R. A. Jacobson, and R. S. Park, Con- straints on modified Newtonian dynamics theories from radio tracking data of the Cassini spacecraft, Physical Review D89, 102002 (2014), arXiv:1402.6950 [gr-qc]

    Pith/arXiv arXiv 2014

  72. [72]

    A. Hees, B. Famaey, G. W. Angus, and G. Gentile, Combined Solar system and rotation curve constraints on MOND, MN- RAS455, 449 (2016), arXiv:1510.01369

    Pith/arXiv arXiv 2016

  73. [73]

    Desmond, A

    H. Desmond, A. Hees, and B. Famaey, On the tension between the radial acceleration relation and Solar system quadrupole in modified gravity MOND, MNRAS530, 1781 (2024), arXiv:2401.04796 [astro-ph.GA]

    arXiv 2024

  74. [74]

    V okrouhlický, D

    D. V okrouhlický, D. Nesvorný, and S. Tremaine, Testing MOND on Small Bodies in the Remote Solar System, ApJ 968, 47 (2024), arXiv:2403.09555 [astro-ph.CO]

    arXiv 2024

  75. [75]

    Kroupa, The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems, Science295, 82 (2002), arXiv:astro-ph/0201098 [astro-ph]

    P. Kroupa, The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems, Science295, 82 (2002), arXiv:astro-ph/0201098 [astro-ph]

    Pith/arXiv arXiv 2002

  76. [76]

    Gjergo, Z.-Y

    E. Gjergo, Z.-Y . Zhang, P. Kroupa, A. Sorokin, Z. Yan, Z. Guo, T. Jerabkova, A. H. Zonoozi, and H. Haghi, Massive Star For- mation at Supersolar Metallicities: Constraints on the Initial Mass Function, Research in Astronomy and Astrophysics26, 025003 (2026), arXiv:2509.20440 [astro-ph.GA]

    arXiv 2026

  77. [77]

    Haslbauer, Z

    M. Haslbauer, Z. Yan, T. Jerabkova, E. Gjergo, P. Kroupa, and A. Hasani Zonoozi, The effect of the environment- dependent stellar initial mass function on the photometric properties of star-forming galaxies, A&A689, A221 (2024), arXiv:2405.05313 [astro-ph.GA]

    arXiv 2024

  78. [78]

    A. H. Zonoozi, H. Haghi, P. Kroupa, S. Yousefizadeh, Z. Yan, T. Jerabkova, and E. Gjergo, The effect of the environment-dependent stellar initial mass function on the baryonic Tully–Fisher relation, MNRAS542, 1864 (2025), arXiv:2507.12521 [astro-ph.GA]

    arXiv 2025

  79. [79]

    Zhang, A

    D. Zhang, A. H. Zonoozi, and P. Kroupa, Revisiting the miss- ing mass problem in MOND for nearby galaxy clusters, Phys. Rev. D113, 043027 (2026), arXiv:2602.06082 [astro-ph.CO]

    arXiv 2026

  80. [80]

    Z. Yan, T. Jerabkova, and P. Kroupa, Chemical evolution of ultra-faint dwarf galaxies in the self-consistently calcu- lated integrated galactic IMF theory, A&A637, A68 (2020), arXiv:2003.11029 [astro-ph.GA]

    arXiv 2020

Showing first 80 references.