Thesis topics 2024

Context: Cosmic rays are highly energetic, charged particles that propagate through our Galaxy and are believed to be accelerated in supernova remnants. The spatial dimensions and activity times of the accelerators are much smaller than the propagation lengths and times of the cosmic rays. Thus, supernova remnants are well-described as point sources that inject a burst-like spectrum at a specific point in space and time, which contradicts the often-assumed smooth source density throughout the Galaxy in simplified models.

Goals: To gain a better understanding of the distribution of cosmic rays in our Galaxy, we model the multitude of cosmic ray sources in a Monte Carlo simulation. This problem is well-suited to parallel programming on GPUs as contributions from millions of sources must be calculated in as little time as possible to make a Monte Carlo approach feasible. We will compare the results and performance of GPU and non-GPU based implementations and consider new use cases of this technique.

Requirements: An interest in astrophysics, Monte Carlo simulations, and the parallel programming paradigm on GPUs; coding skills in Python or C++.

Context: The local dark matter density is a vital ingredient for predicting the signal in laboratory detectors and potentially helpful for understanding the nature of dark matter particles. With more and more data available about stellar populations within a couple hundred parsecs, we have better means than ever to constrain our mass model of the local galactic disc – and therefore also of the local dark matter density.

Goals: We will solve a version of the Poisson-Jeans system of equations connecting the kinetic properties of stellar populations and the gravitational potential, thereby learning the dark matter contribution in the local galactic disc. We will use novel Bayesian inference techniques to quantify uncertainties along the way, eventually obtaining estimates for the vertical distribution of various components of the galactic disc.

Requirements: An interest in galactic astrophysics and numerical techniques; ideally some familiarity with Python

Context: Cosmic rays are high-energy, charged particles that pervade the Galaxy and the Universe. Their transport is mostly diffusive, but under certain conditions, cosmic rays can influence the medium that they diffuse in through the so-called streaming instability. This makes their transport inherently non-linear, which is causing difficulties for the numerical techniques used in conventional cosmic-ray simulations.

Goals: We will explore the use of a different numerical technique, that is stochastic differential equations (SDEs). SDEs are mathematically equivalent to diffusion equations, but have proven more robust than conventional techniques in some applications. We will compare the results from both techniques in the presence of the streaming instability and will apply them to a topucal problem in galactic cosmic rays.

Requirements: An interest in differential equations and their numerical solutions; coding skills in python or C++.

Context: The solar system is embedded in the so-called local bubble, an underdense region a few hundred lightyears in size, carved out by supernova explosions several million years ago. Today we have exquisite information on the times and positions of these supernovae and can therefore model the evolution of gas density, velocity, temperature and magnetic fields. The structure of the magnetic field might hold the key to the surprisingly small flux of cosmic rays measured on Earth.

Goals: We will simulate the transport of cosmic rays by solving their equations of motions in the magnetic field of the local bubble, making use of and modifying existing codes. This can be done very efficiently by running in parallel on GPUs. We will quantify the distribution of cosmic rays from the supernova remnants that created the local bubble, but also from sources outside, thus trying to explain the suppression of cosmic rays at Earth.

Requirements: An interest in astrophysics and numerical techniques; ideally some familiarity with C++