Modified Newtonian Dynamics and the Bullet Cluster

Modified Newtonian Dynamics and the Bullet Cluster: A comparison with the dark matter model

Liu, Darwin (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

Visser, P.M. (mentor)
Eijt, S.W.H. (mentor)

Delft University of Technology

Applied Physics

2022-07-12

The Bullet Cluster is a galaxy cluster, which is often used as evidence for dark matter [10]. In this thesis, Modified Newtonian Dynamics (MOND) is studied for various interpolation functions on a model of the Bullet
Cluster. MOND is a theory proposed by Milgrom which modifies the Newtonian gravity law, such that it explains the flat rotation curves observed in all the galaxies and galaxy clusters [13]. It is an alternative theory
to the dark matter model and in this thesis, the results of MOND are compared to results from the paper of
Paraficz et al which have studied the Bullet Cluster with the dark matter model [15]. In MOND, the Newtonian
gravity law is changed at low accelerations, for a around and below the value of 1.2 · 10^-10  m/s²
, which is introduced as a constant a₀ by Milgrom. Accelerations much smaller than a₀ are in the deep MOND regime and
should satisfy certain conditions. Combining the low acceleration regime (a ≪ a₀) and the Newton regime
(a ≫ a₀), an interpolation function is needed. The following interpolation functions are studied: the standard
interpolation function, the Verlinde interpolation function and the Angus interpolation function.
First the Newtonian gravitational potential Φ_N is introduced which can be calculated for a certain mass
distribution ρ using the Poisson equation. Also the acceleration field can be obtained from ΦN . It could
be seen that in the model used in this thesis for the Bullet Cluster, the strength of the acceleration field a
is mostly below a₀, but not much. Similarly the MOND potential Φ_M can also be calculated for ρ with the
MOND equations, which are different equations for each interpolation function. The MOND equations are
non-linear and can not be solved analytically in most cases. Thus a numerical iterative method is introduced
to solve the MOND equations and to obtain Φ_M . After obtaining Φ_M for each interpolation function, the acceleration field f can also be calculated. We found that Φ_M is steeper than Φ_N for all interpolation functions.
Also the acceleration field f is larger than a, and f is mostly above a₀ in the model of the Bullet Cluster used
in this thesis.
By substituting Φ_M in the Poisson equation, another mass distribution could be obtained: apparent matter. This would be the matter distribution needed to give the acceleration field f using the Newtonian gravity
law. From this matter distribution, the apparent dark matter could be obtained. We can compare this apparent dark matter distribution with the dark matter model found in the paper in Paraficz et al. Also the apparent
matter distribution can be compared to the image of the Bullet Cluster. For both apparent dark matter and
apparent matter, the MOND model is not in agreement with the dark matter model and the observation respectively. In general, the dark matter did not spatially coincide with the galaxies. By increasing the number
of galaxies or increasing the mass of the galaxies, dark matter distributions that spatially coincide with the
galaxies can be obtained

Bullet Cluster
Modified Newtonian Dynamics
Dark Matter

http://resolver.tudelft.nl/uuid:6554a012-3ee4-4d44-8ab7-3ee2a515a20a

Student theses

bachelor thesis

© 2022 Darwin Liu