The Milky Way and M31 rotation curves in Yukawa gravity: phenomenology and Bayesian analysis

TL;DR

This study develops a comprehensive framework to analyze galactic rotation curves under Yukawa gravity, assessing the influence of modified gravity parameters and dark matter through Bayesian methods applied to Milky Way and Andromeda data.

Contribution

It introduces a unified analytical and numerical approach to model rotation curves in Yukawa gravity, incorporating all major galactic components and performing Bayesian analysis with real galaxy data.

Findings

Yukawa parameters significantly affect velocity profiles.

Bayesian analysis favors Newtonian gravity for M31 with current data.

High-precision data and informed priors are essential for constraining modified gravity models.

Abstract

Yukawa gravity provides a generalized framework for modeling gravity modification. We investigate the rotation curve profiles of spiral galaxies under Yukawa-like theories governed by the coupling strength $\beta$ and the interaction range $\lambda$. We develop a unified analytical and numerical framework to calculate rotational velocities under Yukawa gravity, which includes contributions from all major galactic components: stellar bulge, disk, dark matter (DM) halo, and central supermassive black hole. The calculations show that $\beta$ and $\lambda$ strongly influence velocity distributions, shifting peaks, creating double-peak structures, or enhancing dark matter dominance in the bulge or disk. To assess observational implications, we perform Bayesian analyses using data from the Milky Way (MW) and Andromeda (M31), which offer complementary characteristics: MW provides precise velocity profiles across multiple scales, while M31 includes broader morphological constraints. We examine four scenarios: Yukawa gravity without dark matter, dark matter with non-trivial coupling, fully modified gravity, and standard Newtonian gravity. Results show that MW models with $\lambda < 1$ kpc yield high Bayes factors but risk overfitting, as dark matter mimics baryonic kinematics, while M31's photometric priors from conjugate observations mitigate this, yielding robust parameter estimates. However, in M31, Bayes factors favor Newtonian gravity, suggesting that current data lack the precision to resolve more complex models. This finding highlights two key needs: (i) realistic, physically or empirically informed priors to avoid biased constraints, and (ii) high-precision data with independent photometry to guard against overfitting. Our framework offers a scalable approach for testing gravity with large galactic rotation curve datasets.