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.
