Matter Distributions of Galaxy Clusters in Modified Newtonian Dynamics

Abstract

Over the past century various different discrepancies in the expected and observed behaviour of galaxies and galaxy clusters were found. Together this is called the missing mass problem and the most well known theory trying to explain these differences states that there is additional undetectable mass in the form of dark matter. Modified Newtonian Dynamics (MOND) is another theory that tries to explain these discrepancies in a different way then by introducing dark matter. Instead the theory changes Newtons law of gravity for low accelerations, smaller than Milgroms constant a0. In this bachelor thesis we look at a discrete model to simulate MOND in galaxy clusters. To simplify calculations we will not be looking at full MOND, which holds for all accelerations but instead we look at the so called deep MOND, which only holds for accelerations much smaller than a0. We use two different versions of the Poisson equation, the standard version for Newtonian dynamics and a modified version for MOND, to compute the gravitational potential fields caused by a mass density distribution. This is done by using the discrete Fourier transform on an discretized region of space. The initial mass density distribution consists of a number  of galaxies ranging between 50 and 1000 per cluster. Each galaxy is modelled as a sphere of constant density. To calculate the potential with MOND we use an iterative process starting from the potential we get using Newtonian dynamics. In this iterative process we made use of the Helmholtz decomposition. From the MOND potential we can compute an apparent mass distribution, which is the mass distribution that would result in the same MOND potential using Newtonian dynamics. This apparent matter distribution we use to predict at what distance of a galaxy most apparent dark matter is located. Lastly we also look at the apparent mass distributions when the galaxy cluster is projected on a 2d plane. All of these calculations were made in Python on a discrete grid of 256 × 256 × 256 points.
When looking at the total amount of apparent mass in concentric spheres around galaxies in our cluster we saw that this increases in three distinct phases. The middle phases, where a linear increase was seen, had a slope in the same order of magnitude as the theoretical value. We found that the average apparent mass density is the highest in the center of galaxies and decreases very quickly at higher distance to the galaxy. When the distance becomes high enough to reach neighbouring galaxies in the same cluster the average apparent mass density stabilizes and becomes almost constant, but still slightly decreases. For the projected mass density a similar pattern was found.