Testing the Radial Acceleration Relation with SPARC: A Maximum-Likelihood Estimation of the MOND Acceleration Scale a 0

This project presents a comprehensive analysis of the radial acceleration relation (RAR) using galaxy rotation curve data from the SPARC database. The primary goal is to estimate the MOND acceleration scale on a per-galaxy basis and evaluate its universality across different galactic systems. We implement a Bayesian-inspired fitting procedure to infer for each galaxy individually, using a likelihood defined in logarithmic space to ensure numerical stability and robustness across several orders of magnitude. The analysis incorporates physical constraints, parameter priors, and careful treatment of observational uncertainties. To quantify the statistical reliability of the inferred parameters, uncertainty estimates are obtained via resampling techniques (bootstrap) and/or Markov Chain Monte Carlo (MCMC) sampling. This allows for the construction of a distribution of values across the galaxy sample. A key objective of this work is to decompose the observed scatter in into: measurement uncertainty, and intrinsic (physical) scatter. This is achieved through variance decomposition: \sigma_{\text{obs}}^2 = \sigma_{\text{intrinsic}}^2 + \sigma_{\text{err}}^2 Furthermore, we investigate possible correlations between and galaxy properties such as stellar mass and structural parameters. The presence (or absence) of statistically significant correlations provides insight into whether is a universal constant or an emergent parameter dependent on galaxy characteristics. The results have direct implications for the validity of Modified Newtonian Dynamics (MOND) and its interpretation as either a fundamental modification of gravity or an effective phenomenological d escription.