Dr Harry Desmond

Abstract:

Rotation curves are the key observational manifestation of the dark matter distribution around late-type galaxies. In a halo model context, the precision of constraints on halo parameters is a complex function of properties of the measurements as well as properties of the galaxy itself. Forthcoming surveys will resolve rotation curves to varying degrees of precision, or measure their integrated effect in the HI linewidth. To ascertain the relative significance of the relevant quantities for constraining halo properties, we study the information on halo mass and concentration as quantified by the Kullback–Leibler divergence of the kinematics-informed posterior from the uninformative prior. We calculate this divergence as a function of the different types of spectroscopic observation, properties of the measurement, galaxy properties, and auxiliary observational data on the baryonic components. Using the SPARC (Spitzer Photometry & Accurate Rotation Curves) sample, we find that fits to the full rotation curve exhibit a large variation in information gain between galaxies, ranging from ~1 to ~11 bits. The variation is predominantly caused by the vast differences in the number of data points and the size of velocity uncertainties between the SPARC galaxies. We also study the relative importance of the minimum HI surface density probed and the size of velocity uncertainties on the constraining power on the inner halo density slope, finding the latter to be significantly more important. We spell out the implications of these results for the optimization of galaxy surveys aiming to constrain galaxies’ dark matter distributions, highlighting the need for precise velocity measurements.

Abstract:

When choosing between competing symbolic models for a data set, a human will naturally prefer the “simpler” expression or the one which more closely resembles equations previously seen in a similar context. This suggests a non-uniform prior on functions, which is, however, rarely considered within a symbolic regression (SR) framework. In this paper we develop methods to incorporate detailed prior information on both functions and their parameters into SR. Our prior on the structure of a function is based on a ngram language model, which is sensitive to the arrangement of operators relative to one another in addition to the frequency of occurrence of each operator. We also develop a formalism based on the Fractional Bayes Factor to treat numerical parameter priors in such a way that models may be fairly compared though the Bayesian evidence, and explicitly compare Bayesian, Minimum Description Length and heuristic methods for model selection. We demonstrate the performance of our priors relative to literature standards on benchmarks and a real-world dataset from the field of cosmology.

Abstract:

We set constraints on the dark matter halo mass and concentration of ∼22 000 individual galaxies visible both in H I (from the ALFALFA survey) and optical light (from the Sloan Digital Sky Survey). This is achieved by combining two Bayesian models, one for the H I line width as a function of the stellar and neutral hydrogen mass distributions in a galaxy using kinematic modelling, and the other for the galaxy’s total baryonic mass using the technique of inverse subhalo abundance matching. We hence quantify the constraining power on halo properties of spectroscopic and photometric observations, and assess their consistency. We find good agreement between the two sets of posteriors, although there is a sizeable population of low-line width galaxies that favour significantly smaller dynamical masses than expected from abundance matching (especially for cuspy halo profiles). Abundance matching provides significantly more stringent bounds on halo properties than the H I line width, even with a mass–concentration prior included, although combining the two provides a mean gain of 40 per cent for the sample when fitting an NFW profile. We also use our kinematic posteriors to construct a baryonic mass–halo mass relation, which we find to be near power law, and with a somewhat shallower slope than expected from abundance matching. Our method demonstrates the potential of combining photometric and spectroscopic observations to precisely map out the dark matter distribution at the galaxy scale using upcoming H I surveys such as the SKA.