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Revisiting the missing mass problem in MOND for nearby galaxy clusters

Dong Zhang1,*, Akram Hasani Zonoozi1,2, and Pavel Kroupa1,3,†

  • *Contact author: zhang_dong_96@163.com
  • †Contact author: pkroupa@uni-bonn.de
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Phys. Rev. D 113, 043027 – Published 17 February, 2026

DOI: https://doi.org/10.1103/mp3f-q5dc

Abstract

In the framework of Milgromian dynamics (MOND), galaxy clusters have been thought to have about a factor of two less baryonic mass than gravitational mass. One hypothesized source of this missing mass is undetected baryons. Extensive observations and studies indicate that the baryon content of galaxy clusters is primarily composed of the intracluster medium (ICM). In this work we reevaluate the overall stellar mass in galaxy clusters taking into account recent work on the galaxy-wide stellar initial mass function of stars (gwIMF) needed to synthesise the metals observed in galaxies. Given their supersolar metallicities and short formation timescales, massive elliptical galaxies are inferred to have formed with highly top-heavy gwIMFs, which in turn leave behind a substantial mass in stellar remnants. The dependency of the gwIMF on the properties and evolution of a galaxy is well encapsulated by the integrated galaxy-wide initial mass function (IGIMF) theory, developed independently of MOND. We utilize observational data at redshifts z<0.1 from the Wide-field Nearby Galaxy-cluster Survey (WINGS) and the Two Micron All Sky Survey (2MASS). Masses of galaxies and intracluster light (ICL) are calculated for 46 galaxy clusters using the IGIMF theory. The resulting masses in stars and in remnants are combined with previously derived ICM masses to estimate the total baryonic masses of the clusters. These baryonic masses are then compared to the MOND dynamical masses of the clusters, which are derived from hydrostatic equilibrium of the ICM based on earlier studies. As a complement, we include a comparison with several weak/strong lensing masses in the MOND framework. Our results show that the stellar masses of galaxies and the ICL increase substantially when applying the galaxy-wide mass-to-light ratios derived from the IGIMF theory. This leads to a significant rise in the estimated baryonic masses of galaxy clusters. In the sample of 46 galaxy clusters, the baryonic component on average accounts for 52−3+4% of the MOND dynamical mass when considering only the ICM contribution. The baryonic mass in stars, remnants and the ICM accounts for at least 88−4−1+5+2% of the MOND dynamical mass. The contribution by stellar remnants that arises from nucleosynthesis constraints thus significantly alleviates the missing mass problem in MOND. Finally, we briefly discuss the compatibility of the IGIMF framework with the radial acceleration relation (RAR), and studies of MOND weak/strong lensing and related issues. A more comprehensive investigation will require future work that combines the IGIMF with self-consistent, spatially resolved formation, evolution, and resulting mass distribution models of galaxies.

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Phys. Rev. D 113, 043027– Published 17 February, 2026
  • Received 1 October 2025
  • Accepted 22 January 2026
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