R e, or not R e: Developing R 5 ≡ R −2 as a scale radius for galaxy sizes, masses, and mass-to-light ratios
- 1Centre for Astrophysics and Supercomputing, Swinburne University of Technology , Hawthorn, VIC 3122 ,
Abstract
The effective half-light radius R_{\text {e}} marks an arbitrary 50 per cent light boundary, and scaling relations involving such effective radii and their associated surface brightnesses, μe, systematically (and undesirably) vary as the percentage changes. Here, the projected radius R5 ≡ R−2, where the logarithmic slope of the surface-brightness and intensity profiles equal 5.00 mag dex−1 and −2, respectively, and where the luminosity per logarithmic radial interval is maximal, is developed as an alternative. It can be measured non-parametrically or with a parametrized fit. For the Sérsic R1/n family, R5=(2n/bn)nR_{\text {e}}, with R5/R_{\text {e}}→ e1/6≈ 1.181 as n → ∞. Reparameterizing the (now bn-free) R1/n model in terms of the observable pair (R5, μ5) removes the non-linear R_{\text {e}}–n coupling, and because the local slope is 5 mag dex−1 at R5, correlated measurement errors in R5 and μ5 better cancel when deriving the inferred total magnitude (∝μ5 − 5log R5). Additionally, an exact single-integral identity is provided to relate any projected light percentage to the percentage within a sphere of the same radius. The scale radius R5 is shown to be connected, through a weakly n-dependent factor, g(n), to the anisotropy-insensitive internal/spatial radius r−3, yielding a refined n-dependent Wolf-type mass estimator M−3 and spatial mass-to-light ratio (Mdyn/L)−3. Specifically, M−3≡ M(<r−3)=3 G−1⟨ σ los2⟩ g(n) R−2, and for n ≳ 2, M−3≈ 4 G−1⟨ σ los2⟩ R−2≈ 4.72 G−1⟨ σ los2⟩R_{\text {e}}. Past half-light substitutions in dynamical mass estimators introduce systematic Sérsic-dependent offsets of 12–18 per cent in enclosed mass and offsets spanning >20 per cent in the mass-to-light ratio within r−3. Dynamical mass estimators appropriate for (dark matter)-free stellar systems are also provided, and all relations are implemented in the companion Python package R5Tools.
Related
- Effect of galaxy mergers on dust masses
- JADES: Dynamical Measurements of Dark Matter Halo Masses at z ≈ 7 Using Galaxy Pairs
- Eight New Ultramassive Black Hole Masses Confirm Best Correlation with Galaxy Core Sizes
- Inferring the Dark from the Observable: Estimating Halo Masses Using Galaxy Properties
- The JWST Ultramassive Galaxy Sample -- II. Supermassive Black Hole Masses for 8 Extreme Early-Type Galaxies via Jeans Anisotropic Modelling of High-Resolution Integral-Field NIRSpec Stellar Kinematics
BibTeX
@article{graham2026developing,
title = {{R e, or not R e: Developing R 5 ≡ R −2 as a scale radius for galaxy sizes, masses, and mass-to-light ratios}},
author = {Alister W Graham},
journal = {Monthly Notices of the Royal Astronomical Society},
year = {2026},
month = oct,
doi = {10.1093/mnras/stag2051},
url = {https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag2051/9004102},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - R e, or not R e: Developing R 5 ≡ R −2 as a scale radius for galaxy sizes, masses, and mass-to-light ratios
AU - Alister W Graham
PY - 2026
DA - 2026/10/28
JO - Monthly Notices of the Royal Astronomical Society
DO - 10.1093/mnras/stag2051
UR - https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag2051/9004102
AB - The effective half-light radius R_{\text {e}} marks an arbitrary 50 per cent light boundary, and scaling relations involving such effective radii and their associated surface brightnesses, μe, systematically (and undesirably) vary as the percentage changes. Here, the projected radius R5 ≡ R−2, where the logarithmic slope of the surface-brightness and intensity profiles equal 5.00 mag dex−1 and −2, respectively, and where the luminosity per logarithmic radial interval is maximal, is developed as an alternative. It can be measured non-parametrically or with a parametrized fit. For the Sérsic R1/n family, R_5=(2n/b_n)^nR_{\text {e}}, with R_5/R_{\text {e}}→ e^1/6≈ 1.181 as n → ∞. Reparameterizing the (now bn-free) R1/n model in terms of the observable pair (R5, μ5) removes the non-linear R_{\text {e}}–n coupling, and because the local slope is 5 mag dex−1 at R5, correlated measurement errors in R5 and μ5 better cancel when deriving the inferred total magnitude (∝μ5 − 5log R5). Additionally, an exact single-integral identity is provided to relate any projected light percentage to the percentage within a sphere of the same radius. The scale radius R5 is shown to be connected, through a weakly n-dependent factor, g(n), to the anisotropy-insensitive internal/spatial radius r−3, yielding a refined n-dependent Wolf-type mass estimator M−3 and spatial mass-to-light ratio (Mdyn/L)−3. Specifically, M_−3≡ M(<r_−3)=3 G^−1⟨ σ _los^2⟩ g(n) R_−2, and for n ≳ 2, M_−3≈ 4 G^−1⟨ σ _los^2⟩ R_−2≈ 4.72 G^−1⟨ σ _los^2⟩R_{\text {e}}. Past half-light substitutions in dynamical mass estimators introduce systematic Sérsic-dependent offsets of 12–18 per cent in enclosed mass and offsets spanning >20 per cent in the mass-to-light ratio within r−3. Dynamical mass estimators appropriate for (dark matter)-free stellar systems are also provided, and all relations are implemented in the companion Python package R5Tools.
SN - 0035-8711
SN - 1365-2966
ER -