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March 15, 2026Galaxies0 citationsOpen Access

The MOND Depth Index and Dynamical Maturity Clock: Toward a Universal Classification of Galaxies and Star Clusters

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RERobin EappenPKPavel Kroupa

Key Points

  • To propose a new classification for self-gravitating stellar systems using MOND indices.
  • Introduced MOND depth index, dynamical maturity index, and dynamical collisionality index.
  • Analyzed mass discrepancies in various stellar systems based on acceleration scales and collisionality.
  • Found a clear distinction in mass discrepancies based on dynamical conditions.
  • Demonstrated that dark matter effects only appear in specific dynamical environments.

Abstract

Mass discrepancies in galaxies are empirically known to appear only below a characteristic acceleration scale a0. Here we show that this behaviour is not limited to galaxies: it extends continuously across the full hierarchy of self-gravitating stellar systems, from gas-rich dwarfs and spirals to massive early-type galaxies, and further down to compact stellar clusters. We introduce the— Milgromian dynamics (MOND) depth index DM, together with dynamical maturity index T=tcross/tH, dynamical collisionality index T1=tcross/trelax, with tcross being the crossing time, tH the Hubble time and trelax the median two-body relaxation time, and the MOND acceleration index A=a¯/a0. We uncover a well-defined two-dimensional dividing surface in dynamical space. The ‘dark matter phenomenon’ is found only in systems that are both in the deep-MOND regime (a¯tH), while high-acceleration, collisional systems (a¯>a0, trelax≪tH), including globular clusters and UCDs, show no evidence for a mass discrepancy. This clean dynamical separation defines a new, physically motivated classification scheme for stellar systems, unifying galaxies and clusters under one framework. The observed division emerges naturally within the MOND framework and provides a useful diagnostic for examining how different gravitational paradigms account for the origin of the mass discrepancy.

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Cite This Study

Eappen et al. (2026) studied this question.

synapsesocial.com/papers/69b5ff3b83145bc643d1b7cdhttps://doi.org/10.3390/galaxies14020022
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