Structure Formation

From measured temperature fluctuations of the cosmic microwave background, we know that the observable universe started from almost homogeneous and isotropic initial conditions. According to the standard model of cosmology, around 80% of all matter appears to be cold dark matter with small velocity dispersion and vanishing non-gravitational interaction. Only the remaining fifth exists in the form of known particles as described by the standard model of particle physics. While constraints on dark matter become more and more precise, its particle nature is largely known. Finding the particle or particles constituting dark matter is at the core of modern cosmology research.

Structure formation tells us how this homogeneous, initial state evolved into a state that hosts large-scale filaments (the cosmic web), galaxies, stars, planets and other structures. The present paradigm is that small initial over-densities of dark matter underwent gravitational collapse forming the cosmic web of one-dimensional filaments connecting halos which merge to increasingly massive structures. In their potential wells, baryons can accumulate, clump together and eventually form stars. The UV emission from these stars and supernova explosions at the end of their life cycle in turn have a strong impact on their environment even on super-galactic scales.

These highly non-linear dynamics require dedicated numerical simulations on high performance computing clusters. The goal is to identify and correctly model the dominant processes of structure formation and to discriminate between different dark matter candidates.
Fuzzy dark matter (FDM) effectively models ultra-light bosons with negligible non-gravitational interactions e.g. axion-like particles generically arising in string theories. Its temporal evolution is governed by the Schroedinger equation with (self-)gravitational potential. Analogous to quantum mechanics, this results in wave like features at the corresponding de Broglie scale even though FDM is a classical field. While indistinguishable from cold dark matter (CDM) on larger scales, FDM with masses around 10^-22 eV strongly deviates from CDM within halos, where velocity dispersion results in fluctuating interference patterns with granular structure. The central granule is found to form an oscillating but stable galactic core which is the solitonic ground state solution of the Schroedinger-Poisson system.

Our group extends pre-existing cosmological codes to incorporate FDM dynamics employing various numerical schemes including finite difference, pseudo-spectral, particle based and semi-analytic algorithms. Large simulations are then run on high performance computing clusters like the HLRN.

With these simulations we were able to define important parameters for the outcome of binary solitonic core mergers. Employing them, we semi-analytically arrived at the same core to halo mass relation that was previously found in cosmological FDM simulations. We investigated tidal dispution of solitonic cores in a simplified host halo potential. A comparison with Milky Way satellites resulted in a lower bound on the FDM mass.
If the Peccei-Quinn symmetry is broken after inflation, large axion isocurvature perturbations can collapse very early and form small, gravitationally bound structures called axion miniclusters (MCs).

To gain insight into the characteristics of the MCs, we study their formation and evolution using a variety of methods including large cosmological N-body simulations and a combination of linear and semi-analytical formulae. Using initial conditions from the largest available early-universe simulations of the axion field, we start at an initial redshift of z=10^6 and follow the gravitational collapse of axion dark matter isocurvature perturbations into axion MCs.

Our simulations provide the first quantitative results of the mass distribution of axion MCs, the amount of axions bound in these MCs, and their radial density profiles up to redshift z=100. Our work is an essential step to predict the properties and the distribution of MCs at the present time with
extensive implications for both direct and indirect detection of axion dark matter.