Investigating the equation of hydrostatic equilibrium under the modified Newtonian dynamics

Abstract

This thesis investigates the vertical structure of galactic discs by considering the hydrostatic equilibrium under theModified Newtonian Dynamics (MOND). The observed discrepancies between the galactic rotation curves and the predictions of Newtonian gravity without dark matter inspired me to delve into the investigation of Modified Newtonian Dynamics as an alternative framework. This study examines how MOND influences the vertical distribution of baryonic matter in galactic discs. This thesis derives the classical equation of hydrostatic equilibrium in the Newtonian regime and constructs a modified second-order di↵erential equation for corrections in the deep-MOND regime. The gravitational influence of stars, atomic hydrogen, and molecular hydrogen is considered to construct a self-consistent model for the vertical density distribution. The study further emphasizes scale height as a diagnostic tool for comparing the theoretical predictions with observational data from galaxies. The work presents a numerical analysis and graphical representations of scale height under various assumptions, which highlight the significant deviations introduced by MOND. The findings provide insights into whether MOND can account for the observed vertical structure of galactic discs without invoking dark matter halos. By evaluating the implications of modified dynamics in the vertical structure of galaxies, this thesis contributes to the broader discourse on alternative gravity theories and their observational consequences.