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 And Mass Assembly) galaxy group catalogue over the mass range of 10(12.7)-10(15.5) M-circle dot, and find good agreement with the expectation from Lambda cold dark matter. 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 data release (DR) 4 HMF with similar data from the Sloan Digital Sky Survey (SDSS) DR12 and REFLEX II (ROSAT-ESO Flux Limited X-ray Galaxy Cluster Survey) surveys, and fit a four-parameter Murray-Robotham-Power function, valid at (z) over tilde approximate to 0.1, yielding a density normalization of log(10) (phi* Mpc(3)) = -3.96(-0.82)(+0.55), a high mass turnover of log(10) (M* M-circle dot(-1)) = 14.13(-0.40)(+0.43), a low-mass power-law slope of alpha = -1.68(-0.24)(+0.21), and a high-mass softening parameter of beta = 0.63(-0.11)(+0.25). If we fold in the constraint on Omega(M) from the 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(12.7)( )M(circle dot) 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-circle dot, we are directly resolving ('seeing') 41 +/- 5 percent of the total mass density, i.e. Omega(M,>)(12)(.7) = 0.128 +/- 0.016, opening the door for the direct construction of three-dimensional dark matter mass maps at Mpc resolution.