Testing the Suitability of Modified Gravity Theories for Spherical Self-gravitating Systems (2025)
ABSTRACT: The study of galactic dynamics has traditionally invoked dark matter to reconcile theoretical models with observations such as the flatness of galactic rotation curves. Modified Newtonian Dynamics (MOND), first proposed by Milgrom in 1983, offers an alternative by modifying gravity in the low-acceleration regime, eliminating the need for dark matter. This thesis develops and tests a numerical framework for solving the MOND field equations, focusing on the AQUAL and QMOND formulations. A spherically symmetric Hernquist profile was adopted as the mass model, appropriate for systems ranging from galaxies to globular clusters. The gravitational potential was obtained by numerically solving Poisson’s equation under both Dirichlet and Neumann boundary conditions. The code was validated against the analytical Newtonian Hernquist solution, demonstrating high accuracy and stability. Once validated, the framework was extended to MOND. An iterative solver for AQUAL was implemented, initialized with QMOND-based estimates and refined until convergence. From the resulting potentials, dynamical observables—including circular velocity, escape velocity, and radial velocity dispersion—were derived. The results reproduce the characteristic MONDian signatures: flattened rotation curves, higher escape velocities, and enhanced dispersions in the outskirts of stellar systems. AQUAL provides greater accuracy, while QMOND offers a computationally faster alternative, making it suitable for broad parameter-space exploration. Since the model depends only on the total mass and scale radius, it can be applied to diverse astrophysical systems, including galaxies, dwarf spheroidals, and globular clusters. Although this work remains theoretical, the framework establishes a foundation for confronting MOND with observational data. Future applications include direct comparisons with kinematic measurements from Gaia DR3 for systems such as the Fornax dwarf galaxy and Omega Centauri, which will provide stringent tests of MOND’s validity as an alternative to dark matter.