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 method derive tabulated observational constraints on the halo mass function (HMF) by studying magnification bias effect high-redshift submillimeter galaxies. Under assumption universality, we parametrize HMF according two traditional models, namely Sheth and Tormen (ST) Tinker fits assess their performance in explaining measured data within {\Lambda} cold dark matter ({\Lambda}CDM) model. We also study potential influence occupation distribution (HOD) parameters analysis discuss important aspects regarding parametrization. Methods. measure cross-correlation between foreground sample GAMA galaxies with redshifts range $0.2<z<0.8$ background H-ATLAS $1.2<z<4.0$ carry out an MCMC algorithm check observable against its mathematical prediction model formalism. Results. If all are assumed be positive, ST fit only seems fully explain measurements forcing mean number satellite increase substantially from prior value. fit, other hand, provides robust description without relevant changes HOD parameters, but some dependence parameters. When normalization condition for dropped allow negative values $p_1$ parameter involved better determined, unlike previous thus deriving most general constraints. While cases agreement uncertainties, last one hints at slightly higher halos intermediate high masses, raising point allowed range.