A Scale-Dependent Dimensionality Model of Solar Structure: Modified Lane–Emden Solutions, Neutrino Fluxes, and Helioseismic Constraints

This work develops a modified model of the solar interior where the effective spatial dimension of the core varies smoothly with radius. A scale-dependent dimensional profile is introduced into the Lane–Emden equation, producing small localized changes in hydrostatic structure while keeping the global solar mass and radius unchanged.

Using this approach, the study computes modified polytropic solutions, evaluates changes in solar neutrino production (pp, pep, Be-7, and B-8 channels), and compares the results with modern experimental flux measurements. A full parameter scan identifies a region of solutions that match all major neutrino flux ratios with very good accuracy. The best-fit model achieves a reduced chi-square of about 0.16 and predicts a central temperature shift of only about 0.3 to 0.4 percent relative to the Standard Solar Model.

A simple helioseismic comparison shows that the dimensional modification produces sound-speed deviations of less than 0.2 percent across the solar radius, remaining consistent with observational constraints.

The included Python code provides the modified Lane–Emden solver, neutrino integration routines, solar calibration, helioseismic comparison, and parameter scanning tools. Overall, this project demonstrates that very small, smooth changes in effective dimensionality can influence nuclear reaction rates and neutrino fluxes while preserving the overall structure of the Sun.

Version 2 Update (January 3rd, 2026):

This version clarifies the sign convention used to define the effective dimensional perturbation in the Introduction. The model consistently describes a small dimensional reduction (d_eff < 3) in the dense solar core that relaxes to three dimensions at large radius. This update aligns the introductory definition with the parameterization used throughout the analysis. All results, fits, and conclusions are unchanged.