An empirical measurement of the Halo Mass Function from the combination of GAMA DR4, SDSS DR12, and REFLEX II data

We construct the halo mass function (HMF) from the GAMA galaxy group catalogue over the mass range 10^12.7M_sol to 10^15.5M_sol, and find good agreement with the expectation from LambdaCDM. In comparison to previous studies, this result extends the mass range over which the HMF has now been measured over by an order of magnitude. We combine the GAMA DR4 HMF with similar data from the SDSS DR12 and REFLEX II surveys, and fit a four-parameter Murray-Robotham-Power (MRP) function, valid at z~0.1, yielding: a density normalisation of: log10 (phi Mpc^3)=-3.96[+0.55,-0.82], a high mass turn-over of: log10(M/M_sol)=14.13[+0.43,-0.40], a low mass power law slope of: alpha=-1.68[+0.21,-0.24] , and a high mass softening parameter of: beta= 0.63[+0.25,-0.11]. If we fold in the constraint on Omega_M from Planck 2018 Cosmology, we are able to reduce these uncertainties further, but this relies on the assumption that the power-law trend can be extrapolated from 10^12.7M_sol to zero mass. Throughout, we highlight the effort needed to improve on our HMF measurement: improved halo mass estimates that do not rely on calibration to simulations; reduced halo mass uncertainties needed to mitigate the strong Eddington Bias that arises from the steepness of the HMF low mass slope; and deeper wider area spectroscopic surveys. To our halo mass limit of 10^12.7 M_sol, we are directly resolving (`seeing') 41+/-5 per cent of the total mass density, i.e. Omega_[M>12.7]=0.128+/-0.016, opening the door for the direct construction of 3D dark matter mass maps at Mpc resolution.