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Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves

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Internal ID: CGI-RSR-000029
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: June 2026
Original Creation Date: April 20, 2026
Revised Document Date: June 10, 2026
Status: Public
Domains: Physics
Sub-Domain: Cosmology
Research Topics: Cosmology, Galactic Dynamics, Flux Scaling Model

Abstract


We show that a conserved outward flux in a class of field systems naturally produces an effective mass density scaling as \(\rho(r) \sim r^{-2}\), leading to flat galactic rotation curves. The result follows directly from Noether energy flux conservation in the exterior region of a localized configuration. Under general conditions, this provides a simple dynamical mechanism for the observed scaling of galactic rotation profiles, without requiring additional particle components or modifications to gravitational dynamics.

Available Document

DOI: 10.5281/zenodo.20618642

Citation:
Petersen, B. L. (2026). Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves. Zenodo. https://doi.org/10.5281/zenodo.20618642

Source Code and Supporting Materials

N/A.

Summary and Notes

Core result:
The paper establishes the following chain:

conserved outward flux -> rho(r) ~ r^-2 -> M(r) ~ r -> v(r) approximately constant.

Under general conditions, inverse-square density profiles and flat galactic rotation curves arise as direct consequences of flux conservation in three-dimensional space.

Scope:
This paper focuses on the dynamical origin of inverse-square density scaling and its connection to galactic rotation curves.

It does not attempt to provide a complete cosmological model, dark matter theory, structure formation theory, gravitational lensing analysis, or detailed comparison with observational survey data. Its purpose is to isolate and analyze the scaling mechanism itself.

Relation to subsequent work:
This paper forms the first part of a three-paper sequence investigating inverse-square density scaling and its observational consequences.

Subsequent papers examine gravitational lensing behavior associated with the resulting density profile, and coherence-driven structure formation as a possible source of the conserved exterior flux.

Relation to Coherence Geometry:
Although motivated in part by broader Coherence Geometry investigations, the derivation presented here is formulated using standard field-theoretic concepts and does not require the Coherence Geometry framework for its interpretation.

The result is intended to stand independently as a dynamical scaling argument based on conserved outward flux.

Related Work

Petersen, B. L. (2026). Inverse-Square Density Profiles and Gravitational Lensing from Conserved Flux. Zenodo.
https://doi.org/10.5281/zenodo.20618733

Petersen, B. L. (2026). Constraint-Driven Formation of Coherence Structures and Their Inverse-Square Exterior Flux. Zenodo.
https://doi.org/10.5281/zenodo.20618890

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