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Dark matter is hypothetical matter believed to address the missing massproblem in galaxies. However, alternative theories, such as Modified NewtonianDynamics (MOND), have been notably successful in explaining the missing massproblem in various astrophysical systems. The vertical distribution function ofstars in the solar neighbourhood serves as a proxy to constrain galacticdynamics in accordance to its contents. We employ both the vertical positionaland velocity distribution of stars in cylindrical coordinates with a radius of150 pc and a half-height of 200 pc from the galactic plane. Our tracers consistof 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 solarneighbourhood, interpreting it as either dark matter or MOND. Subsequently, wecompare both hypotheses newtonian gravity with dark matter and MOND, using theBayes factor (BF) to determine which one is more favoured by the data. We foundthat 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 MONDhypothesis'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 forall tracers between the two hypotheses is $\log \textrm{BF}\sim 0.1$, meaningno strong evidence in favour of either the dark matter or MOND hypotheses.

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