Cosmology

Abstract:

We study the M_HI−M_⋆ relation over the last billion years using the MIGHTEE-H i sample. We first model the upper envelope of the M_HI−M_⋆ relation with a Bayesian technique applied to a total number of 249 H i-selected galaxies, without binning the datasets, while taking account of the intrinsic scatter. We fit the envelope with both linear and non-linear models, and find that the non-linear model is preferred over the linear one with a measured transition stellar mass of log10 (M_⋆M_⊙) = 9.15±0.87, beyond which the slope flattens. This finding supports the view that the lack of H i gas is ultimately responsible for the decreasing star formation rate observed in the massive main-sequence galaxies. For spirals alone, which are biased towards the massive galaxies in our sample, the slope beyond the transition mass is shallower than for the full sample, indicative of distinct gas processes ongoing for the spirals/high-mass galaxies from other types with lower stellar masses. We then create mock catalogues for the MIGHTEE-H i detections and non-detections with two main galaxy populations of late- and early-type galaxies to measure the underlying M_HI−M_⋆ relation. We find that the turnover in this relation persists whether considering the two galaxy populations as a whole or separately. We note that an underlying linear relation could mimic this turnover in the observed scaling relation, but a model with a turnover is strongly preferred. Measurements on the logarithmic average of H i masses against the stellar mass are provided as a benchmark for future studies.

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.