[Paper Review] Presence of a Fundamental Acceleration Scale in Galaxy Clusters

D. Edmonds, Djordje Minić+1 more|arXiv (Cornell University)|Sep 27, 2020

Astronomy and Astrophysical Research3 references4 citations

TL;DR

This paper identifies a universal acceleration scale of approximately $10^{-10}\,\text{m/s}^2$ in the baryonic Faber-Jackson relation across galaxy clusters, elliptical galaxies, and globular clusters, suggesting a fundamental role in structure formation independent of dark matter or modified gravity models. The scale emerges naturally from data without theoretical bias, implying a deep connection to dark matter physics beyond the $\Lambda$CDM paradigm.

ABSTRACT

An acceleration scale of order $10^{-10}\mathrm{m/s^2}$ is implicit in the baryonic Tully-Fisher and baryonic Faber-Jackson relations, independently of any theoretical preference or bias. We show that the existence of this scale in the baryonic Faber-Jackson relation is most apparent when data from pressure supported systems of vastly different scales including globular clusters, elliptical galaxies, and galaxy clusters are analyzed together. This suggests the relevance of the acceleration scale $10^{-10}\mathrm{m/s^2}$ to structure formation processes at many different length scales and could be pointing to a heretofore unknown property of dark matter.

Motivation & Objective

• To investigate whether the baryonic Faber-Jackson relation extends to galaxy clusters, thereby testing the universality of a fundamental acceleration scale.
• To determine if the acceleration scale $a_0 \approx 10^{-10}\,\text{m/s}^2$, previously observed in spiral galaxies via the baryonic Tully-Fisher relation, also governs pressure-supported systems.
• To assess whether this scale is an emergent property of structure formation across multiple scales, independent of theoretical assumptions or dark matter models.
• To explore the implications of this scale for dark matter physics, particularly in light of its apparent universality across vastly different astrophysical systems.

Proposed method

• Analysis of velocity dispersion and baryonic mass data from galaxy clusters, elliptical galaxies, and globular clusters to test the baryonic Faber-Jackson relation.
• Fitting the relation $M_{\text{bar}} \propto \sigma^n$ across systems spanning 5–6 decades in mass, with $n \approx 4$ yielding a consistent acceleration scale.
• Calculation of the effective acceleration $a_\varnothing = \sigma^4 / (G M_{\text{bar}})$ to extract the universal scale $a_0$ from the data, without invoking MOND or modified gravity.
• Comparison of best-fit relations across subsets of data (clusters alone, clusters + ellipticals, all three systems) to assess consistency and universality of the scale.
• Use of error bars and statistical fitting to quantify the significance of the observed correlation and the robustness of the acceleration scale.
• Evaluation of the theoretical implications of $a_0$ as a potential fundamental constant in structure formation, independent of $\Lambda$CDM or alternative gravity models.

Experimental results

Research questions

• RQ1 Does the baryonic Faber-Jackson relation, which holds for elliptical galaxies, extend to galaxy clusters when considering baryonic mass and velocity dispersion?
• RQ2 Is the acceleration scale $a_0 \approx 10^{-10}\,\text{m/s}^2$, observed in rotationally supported systems via the baryonic Tully-Fisher relation, also present in pressure-supported systems like galaxy clusters?
• RQ3 Can the observed universality of this acceleration scale across globular clusters, elliptical galaxies, and galaxy clusters be explained by standard $\Lambda$CDM cosmology, or does it imply new physics?
• RQ4 What does the presence of a single acceleration scale across such diverse systems imply about the nature of dark matter or the dynamics of structure formation?
• RQ5 Is the acceleration scale $a_0$ a fundamental constant of nature, or does it emerge from deeper physical principles yet to be understood?

Key findings

• The baryonic Faber-Jackson relation holds across galaxy clusters, elliptical galaxies, and globular clusters when baryonic mass and velocity dispersion are used, with a power-law index $n \approx 4$.
• The effective acceleration $a_\varnothing = \sigma^4 / (G M_{\text{bar}})$ yields a consistent value of $a_0 \approx 10^{-10}\,\text{m/s}^2$ across all three systems, indicating a universal scale.
• The best-fit relation to the combined data set (clusters, ellipticals, globular clusters) shows a single power-law with $n \approx 4$, confirming the universality of the acceleration scale.
• The acceleration scale $a_0$ is extracted directly from data without assuming MOND or modified gravity, indicating it is a robust empirical feature of the baryonic Faber-Jackson relation.
• The consistency of $a_0$ across systems spanning 5–6 decades in mass suggests a fundamental role in structure formation processes at all scales.
• The observed scale is not explained by current $\Lambda$CDM simulations, implying a potential gap in understanding dark matter or gravity at large scales.