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This work aims to observationally anchor the R-layer outer edge in disc galaxies and derive the hierarchical index.

June 23, 20260 citationsOpen Access

R-layer Mode Theory (RLMT) XLI-A: Observational Determination of the Disc Edge and the Hierarchical Index

Key Points

This work aims to observationally anchor the R-layer outer edge in disc galaxies and derive the hierarchical index.
Utilized large-scale spectroscopic and astrometric surveys including Gaia, APOGEE, and LAMOST.
Identified the observed edge of the Milky Way’s star-forming disc at RSF ≃ 12 kpc.
Derived a closed-form expression for the hierarchical index from the curvature condition of the R-layer tension field.
Identified the hierarchical index α ≃ 3 consistent with the observed range of Type II disc breaks (R/Rd ≃ 2.5–3.5).
Demonstrated agreement between α and the U-shaped age profile of disc galaxies.
Established a direct observational bridge between the R-layer hierarchy and the outer structure of disc galaxies.

Abstract

This volume provides an observational anchoring of the R-layer outer edge in disc galaxies. Using recent large-scale spectroscopic and astrometric surveys (Gaia, APOGEE, LAMOST), we identify the observed edge of the Milky Way’s star-forming disc at “RSF ≃ 12 kpc” with the theoretical R-layer outer radius Rx. The corresponding hierarchical index “α := R/Rd ≃ 3” emerges naturally from the R-layer tension-field profile and is fully consistent with the observed universality of Type II disc breaks (R/Rd ≃ 2.5–3.5). We derive a closed-form expression for the hierarchical index α(v) from the curvature condition of the R-layer tension field, show that α ≃ 3 arises for a typical hierarchical index v ≃ 1, and demonstrate agreement with the U-shaped age profile and the drift/re-projection structure of the oII series. This volume establishes a direct observational bridge between the R-layer hierarchy and the outer structure of disc galaxies.

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