Comparing dark matter and MOND hyphotheses from the distribution function of A, F, early-G stars in the solar neighbourhood

Dark matter is hypothetical matter believed to address the missing mass problem in galaxies. However, alternative theories, such as Modified Newtonian Dynamics (MOND), have been notably successful in explaining the missing mass problem in various astrophysical systems. The vertical distribution function of stars in the solar neighbourhood serves as a proxy to constrain galactic dynamics in accordance to its contents. We employ both the vertical positional and velocity distribution of stars in cylindrical coordinates with a radius of 150 pc and a half-height of 200 pc from the galactic plane. Our tracers consist of main-sequence A, F, and early-G stars from the GAIA, RAVE, APOGEE, GALAH, and LAMOST catalogues. We attempt to solve the missing mass in the solar neighbourhood, interpreting it as either dark matter or MOND. Subsequently, we compare both hypotheses newtonian gravity with dark matter and MOND, using the Bayes factor (BF) to determine which one is more favoured by the data. We found that the inferred dark matter in the solar neighbourhood is in range of \(\sim (0.01\)-\(0.07)\) M\(_{\odot}\) pc\(^{-3}\). We also determine that the MOND hypothesis's acceleration parameter \(a_0\) is \((1.26 \pm 0.13) \times 10^{-10}\) m s\(^{-2}\) for simple interpolating function. The average of bayes factor for all tracers between the two hypotheses is \(\log \textrm{BF}\sim 0.1\), meaning no strong evidence in favour of either the dark matter or MOND hypotheses.