Abstract
The current standard model of the Universe primarily consists of three components: baryons, dark matter and dark energy. Dark energy is the mysterious component of the Universe causing the current accelerated expansion as measured by supernovae sources. Baryons and dark matter are the two matter components, one luminous and hence observable, and one only detectable through its effect on gravity from its mass. To understand the unknown and more dominant component (dark matter) we must therefore restrict ourselves to direct measurements of baryons (typically in the form of galaxies) and indirect or simulated measurements of dark matter. It is therefore vitally important that we understand the link between galaxies and dark matter and can create models of this that can quickly be compared to observation.In this thesis I create a minimally parametrised empirical model linking galaxy and halo masses to produce clusters (and smaller structures) and to study the expected Stellar-Halo Mass Relation (SHMR). This is referred to as the Davidson model. I do this through connecting the most well described elements of each component: dark matter theory (measured from N-body simulations) and galaxy observations. The primary method for connecting these objects is through an empirical technique called SubHalo Abundance Matching (SHAM) where we assume that galaxy mass monotonically scales with halo mass. This technique encodes the fundamentals of structure formation as more massive halos typically contain more massive galaxies due to their larger gravitational potential. The Davidson model also encodes galaxy evolution through the parametrisation of a model proposed in Peng et al. (2010) and furthered in Peng et al. (2012). This is the quenching fraction which sets the expected quenched fraction of galaxies for a given halo mass. This ensures that the mass distribution of halos assigned star-forming (blue) or quenched (red) galaxies matches the expected abundance of galaxies.
I parametrise the quenching function as a modified error function with the following parameters: Mµ is the mean of the function, where half the halos should receive quenched galaxies (when starting at 0); σ is the standard deviation, controlling the width of the transition region between dominant blue and red masses; b is the starting value of the function at low mass, the baseline quenched fraction associated with satellite galaxies. Physically, Mµ and σ control ‘mass quenching’ which occurs in central and satellite galaxies and b controls ‘environment quenching’ only seen in satellites. These differing effects were derived in Peng et al. (2012).
By comparing my model to other literature SHMRs, I use simulation based inference techniques to constrain the parameters of the model. Testing two different galaxy mass functions, I find that the best fit for galaxies in the Weigel et al. (2016) model is log Mµ = 11.94+0.02, σ = 0.49+0.04 and b = 0.31+0.01. For the Birrer et al. (2014) galaxies we find best fit values of log −0.04−0.01
Mµ = 11.93+0.01, σ = 0.53+0.04 and b = 0.51+0.05. These produce models which are reasonably −0.01−0.04−0.04 close to the literature for central galaxies, however the satellite normalisation is significantly different and hence the b values are not particularly well constrained.
To test the applicability and potential versatility of the Davidson model, I test it in two different edge-case scenarios. To test the clusters produced by the best fit model, I compare them to a set of various observed cluster data sets which includes various scaling relations such as SHMR and quenched fraction etc. The model compares fairly to the SHMRs (as we might expect) but tends to not match any data from significantly distant redshifts. This is expected as the model does not currently have any redshift dependence other than in the halo mass function. The Davidson model also tends to match mass relations, again as we might expect from a SHMR calibrated model. My model also typically does poorly against data measuring the number of satellites or substructures, likely because the Davidson model does not contain a full forward model of instrumental limitations. These comparisons give a clear indication of limitations and future improvements currently present in the model.
At the low mass end, I test a wave dark matter model, which suppresses small scale structure, against the previous literature SHMR models. I again run the simulation based inference to constrain m22 (mass of the dark matter particle in units of 10−22eV) and the mass quenching parameters, once with only m22 and once with all parameters. I find that all tested parametrisations prefer significantly non-ΛCDM values. For the Birrer galaxies, I find the single fit as m22 = 2.16±0.94 and the full fit as [m22, log Mµ, σ] = [2.09±1.22, 11.85±0.05, 0.63±0.16]. For the Weigel galaxies, I find similar, with the single fit producing m22 = 1.03±0.26 and the full fit [m22, log Mµ, σ] = [0.98±0.17, 12.12±0.18, 0.77±0.20]. However, the lack of literature model values at the critical low mass values, plus the significant degeneracy between the parameters, implies that the parameters are simply the ones that minimise the distance between the model and literature and are not necessarily physically meaningful.
| Date of Award | 22 Oct 2025 |
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| Original language | English |
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| Supervisor | David Bacon (Supervisor), Adam Amara (Supervisor) & Kazuya Koyama (Supervisor) |