Emergent Galactic Dynamics from the Presence Field: A Zero-Parameter Test of TPOM on 156 SPARC Galaxies V2 Rar

Description

Methods

Description

We present an updated version of the TPOM (Theoretical Presence Operative Model) framework, introducing a minimal phenomenological extension of the Radial Acceleration Relation (RAR) based on observational data from the SPARC galaxy sample.

The RAR provides a tight empirical relation between observed gravitational acceleration and that predicted from baryonic matter. However, residuals are known to exhibit systematic correlations with galaxy structure, suggesting that the relation may not be strictly universal.

In this work, we introduce a weak structural correction through a logarithmic dependence on a baryonic proxy, defined as:

[

\Sigma = \frac{g_{\mathrm{bar}}}{R_d}

]

where R_d is the disk scale length. The resulting model modifies the effective acceleration via a single additional parameter \gamma, while preserving the standard behavior in both high- and low-acceleration regimes.

Applying the model to the SPARC dataset, we find:

- a reduction in total \chi^2 relative to the MOND baseline,

- a decrease in intrinsic scatter,

- and the removal of residual correlations with baryonic structure.

The best-fit value \gamma \approx 0.08 indicates a weak but statistically meaningful structural dependence.

This work should be interpreted as a phenomenological extension of the RAR, rather than a complete theory of gravity. The results suggest that part of the observed dispersion in galaxy dynamics encodes structural information, motivating further investigation within information-theoretic and emergent gravity frameworks.

This version represents an empirical validation step within the broader TPOM program, connecting theoretical constructs to observational constraints at galactic scales.