The Spherical Approximation in MOND
Quantifying Geometric Biases in the Radial Acceleration Relation
M.J. van Dam (TU Delft - Electrical Engineering, Mathematics and Computer Science)
P.M. Visser – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
S.W.H. Eijt – Mentor (TU Delft - Applied Sciences)
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Abstract
The Radial Acceleration Relation (RAR) is one of the most striking empirical regularities in galactic dynamics: the observed centripetal acceleration in galaxies correlates tightly with the acceleration predicted from the baryonic mass distribution alone. Modified Newtonian Dynamics (MOND) naturally explains this relation, while the standard dark matter paradigm requires fine-tuning. However, nearly all observational tests of the RAR adopt a simplifying approximation: the baryonic acceleration at radius r is computed as g_bar = GM(<r)/r², as if the galaxy’s mass distribution were spherically symmetric. Real disk galaxies are highly flattened, and the validity of this approximation has never been directly quantified for the Radial Acceleration Relation.
This thesis addresses two questions: (1) How accurate is the spherical approximation for computing baryonic accelerations in disk galaxies? (2) Does its use bias previous tests of the MOND RAR? Using a numerical AQUAL solver applied to realistic three-dimensional stellar density reconstructions from Spitzer 3.6 μm imaging, we compare the spherical approximation to the true disk gravity for three galaxies spanning a range of morphologies: NGC 2841 (bulge-dominated), NGC 3198 (moderate bulge), and NGC 2976 (bulgeless).
We find that the accuracy of the spherical approximation for computing baryonic acceleration