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Abstract:

We present a second-order calculation of relativistic large-scale-structure observables in cosmological perturbation theory, specifically the “cosmic rulers and clock”, which are the building-blocks of any other large-scale-structure observable, including galaxy number counts, on large scales. We calculate the scalar rulers (longitudinal perturbation and magnification) and the cosmic clock to second order, using a fully non-linear covariant definition of the observables. We validate our formulæ on three non-trivial space-time metrics: two of them are null tests on metrics which are obtained by applying a gauge transformation to the background space-time, while the third is the “separate universe” curved background, for which we can also compute the observables exactly. We then illustrate the results by evaluating the second-order observables in a simplified symmetric setup. On large scales, they are suppressed over the linear contributions by ∼10-4, while they become comparable to the linear contributions on mildly non-linear scales. The results of this paper form a significant (and the most complicated) part of the relativistic galaxy number density at second order.

Abstract:

The relationship between the already formed stellar mass in a galaxy and the gas reservoir of neutral atomic hydrogen, is a key element in our understanding of how gas is turned into stars in galaxy haloes. In this paper, we measure the relation based on a stellar-mass selected sample at and the MeerKAT International GHz Tiered Extragalactic Exploration-H i Data Release 1 spectral data. Using a powerful Bayesian stacking technique, for the first time we are also able to measure the underlying bivariate distribution of H i mass and stellar mass of galaxies with M, finding that an asymmetric underlying H i distribution is strongly preferred by our complete samples. We define the concepts of the average of the logarithmic H i mass, , and the logarithmic average of the H i mass, , and find that the difference between and can be as large as 0.5 dex for the preferred asymmetric H i distribution. We observe shallow slopes in the underlying scaling relations, suggesting the presence of an upper H i mass limit beyond which a galaxy can no longer retain further H i gas. From our bivariate distribution we also infer the H i mass function at this redshift and find tentative evidence for a decrease of 2–10 times in the comoving space density of the most H i massive galaxies up to .