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

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 BulletCluster. 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 theoryto the dark matter model and in this thesis, the results of MOND are compared to results from the paper ofParaficz et al which have studied the Bullet Cluster with the dark matter model [15]. In MOND, the Newtoniangravity 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 andshould 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 standardinterpolation function, the Verlinde interpolation function and the Angus interpolation function.First the Newtonian gravitational potential ΦN is introduced which can be calculated for a certain massdistribution ρ using the Poisson equation. Also the acceleration field can be obtained from ΦN . It couldbe seen that in the model used in this thesis for the Bullet Cluster, the strength of the acceleration field ais mostly below a0, but not much. Similarly the MOND potential ΦM can also be calculated for ρ with theMOND equations, which are different equations for each interpolation function. The MOND equations arenon-linear and can not be solved analytically in most cases. Thus a numerical iterative method is introducedto solve the MOND equations and to obtain ΦM . After obtaining ΦM for each interpolation function, the acceleration field f can also be calculated. We found that ΦM is steeper than ΦN 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 usedin this thesis.By substituting ΦM 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 gravitylaw. 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 apparentmatter distribution can be compared to the image of the Bullet Cluster. For both apparent dark matter andapparent 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 numberof galaxies or increasing the mass of the galaxies, dark matter distributions that spatially coincide with thegalaxies can be obtainedApplied Physic