Letter to the Editor

The baryonic Faber-Jackson relation and fundamental plane of galaxy groups, elliptical galaxies, and dwarf galaxies

¹ Department of Physics, National Central University, Taoyuan 320317, Taiwan
² Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro Gwangjin-gu, Seoul 05006, Republic of Korea
³ INAF – Arcetri Astrophysical Observatory, Viale Enrico Fermi 5, 50125 Florence, Italy
⁴ Leibniz-Institute for Astrophysics, An der Sternwarte 16, 14482 Potsdam, Germany
⁵ Department of Astronomy, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
⁶ Globe Institute–Center for Star and Planet Formation, University of Copenhagen, Øster Voldgade 5-7 Copenhagen 1350, Denmark
⁷ Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
⁸ Department of Economics, National Central University, Taoyuan 320317, Taiwan
⁹ Department of Biomedical Sciences and Engineering, National Central University, Taoyuan 320317, Taiwan
¹⁰ Institute of Astronomy, National Central University, Taoyuan 320317, Taiwan
¹¹ Department of Physics and Center for Complex Systems, National Central University, Taoyuan 320317, Taiwan

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Received: 18 February 2026
Accepted: 11 May 2026

Abstract

The baryonic Faber-Jackson relation (BFJR) links the baryonic mass of pressure-supported systems to their mean velocity dispersion. For elliptical galaxies, the BFJR is thought to be a projection of the fundamental plane (FP), which includes the stellar half-mass radius as a third variable. We studied the BFJR and FP across eight orders of magnitude in baryonic mass, encompassing galaxy groups, ellipticals, dwarf ellipticals, and dwarf spheroidals. We compiled and homogenized data for 1400 pressure-supported systems and measured their mean internal baryonic acceleration, ⟨g_bar⟩. We find that the properties of the BFJR and FP systematically depend on the internal acceleration of the sampled systems, with a transition around the acceleration scale a₀ ≃ 1.2 × 10⁻¹⁰ m s⁻². For low-acceleration systems with ⟨g_bar⟩< 0.6 a₀ (dwarf galaxies and galaxy groups), the BFJR takes the form log₁₀(M_bar/M_⊙) = (4.19 ± 0.10) log₁₀(σ_los/km s⁻¹) + (2.55_−0.16^+0.16. The FP expected from the Newtonian virial theorem is followed by high-acceleration systems (massive ellipticals with ⟨g_bar⟩≳6 a₀), whereas low-acceleration systems deviate from the FP at both low masses (dwarf galaxies) and high masses (galaxy groups). Our results generally agree with the expectations of modified Newtonian dynamics (MOND): high-acceleration systems follow the Newtonian virial theorem in which a radial variable explicitly appears (the FP), while low-acceleration systems follow the MOND virial theorem in which the radial dependence disappears (the BFJR). On average, the MOND external field effect seems to play a secondary role in dwarf galaxies in galaxy groups and clusters.