A direct and robust method to observationally constrain the halo mass function via the submillimeter magnification bias: Proof of concept

Aims. The main purpose of this work is to provide a proof-of-concept method to derive tabulated observational constraints on the halo mass function (HMF) by studying the magnification bias effect on high-redshift submillimeter galaxies. Under the assumption of universality, we parametrize the HMF according to two traditional models, namely the Sheth and Tormen (ST) and Tinker fits, derive posterior distributions for their parameters, and assess their performance in explaining the measured data within the Λ cold dark matter model. We also study the potential influence of the halo occupation distribution (HOD) parameters in this analysis and discuss two aspects regarding the HMF parametrization, namely its normalization and the possibility of allowing negative values for the parameters. Methods. We measure the cross-correlation function between a foreground sample of GAMA galaxies with spectroscopic redshifts in the range 0.2 < z < 0.8 and a background sample of H-ATLAS galaxies with photometric redshifts in the range 1.2 < z < 4.0 and carry out a Markov chain Monte Carlo algorithm in the context of Bayesian inference to check this observable against its mathematical prediction within the halo model formalism, which depends on both the HOD and HMF parameters. Results. Under the assumption that all HMF parameters are positive, the ST fit only seems to fully explain the measurements by forcing the mean number of satellite galaxies in a halo to increase substantially from its prior mean value. The Tinker fit, on the other hand, provides a robust description of the data without relevant changes in the HOD parameters, but with some dependence on the prior range of two of its parameters. When the normalization condition for the HMF is dropped and we allow negative values of the p1 parameter in the ST fit, all the involved parameters are better determined, unlike the previous models, thus deriving the most general HMF constraints. While all the aforementioned cases are in agreement with the traditional fits within the uncertainties, the last one hints at a slightly higher number of halos at intermediate and high masses, raising the important point of the allowed parameter range.