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

Abstract: Aims. The main purpose of this work is to provide a 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 and assess their performance in explaining the measured data within the {\Lambda} cold dark matter ({\Lambda}CDM) model. We also study the potential influence of the halo occupation distribution (HOD) parameters in this analysis and discuss two important aspects regarding the HMF parametrization. Methods. We measure the cross-correlation function between a foreground sample of GAMA galaxies with redshifts in the range $0.2<z<0.8$ and a background sample of H-ATLAS galaxies with redshifts in the range $1.2<z<4.0$ and carry out an MCMC algorithm to check this observable against its mathematical prediction within the halo model formalism. Results. If all HMF parameters are assumed to be 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 $p_1$ 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 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.