Tomography-based observational measurements of the halo mass function
  via the submillimeter magnification bias
  Aims. The main goal of this paper is to derive observational constraints on
the halo mass fuction (HMF) by performing a tomographic analysis of the
magnification bias signal on a sample of background submillimeter galaxies. The
results can then be compared with those from a non-tomographic study. Methods.
We measure the cross-correlation function between a sample of foreground GAMA
galaxies with spectroscopic redshifts in the range $0.1 < z < 0.8$ (and divided
up into four bins) and a sample of background submillimeter galaxies from
H-ATLAS with photometric redshifts in the range $1.2 < z < 4.0$. We model the
weak lensing signal within the halo model formalism and carry out a Markov
chain Monte Carlo algorithm to obtain the posterior distribution of all HMF
parameters, which we assume to follow the Sheth and Tormen (ST) three-parameter
and two-parameter fits. Results. While the observational constraints on the HMF
from the non-tomographic analysis are not stringent, there is a remarkable
improvement in terms of uncertainty reduction when tomography is adopted.
Moreover, with respect to the traditional ST triple of values from numerical
simulations, the results from the three-parameter fit predict a higher number
density of halos at masses below $10^{12}M_{\odot}/h$ at 95% credibility. The
two-parameter fit yields even more restricting results, with a larger number
density of halos below $10^{13}M_{\odot}/h$ and a lower one above
$10^{14}M_{\odot}/h$, this time at more than 3$\sigma$ credibility. Our results
are therefore in disagreement with the standard N-body values for the ST fit at
2$\sigma$ and 3$\sigma$, respectively.
