The Total Mass of Dark Matter Haloes
  The simple, conventional dark matter halo mass definitions commonly used in
cosmological simulations ("virial" mass, FoF mass, $M_{50,100,200,...}$) only
capture part of the collapsed material and are therefore inconsistent with the
halo mass concept used in analytical treatments of structure formation.
Simulations have demonstrated that typical dark matter particle orbits extend
out to about 90 per cent of their turnaround radius, which results in apocenter
passages outside of the current "virial" radius on the first and also on the
second orbit. Here we describe how the formation history of haloes can be used
to identify those particles which took part in the halo collapse, but are
missed by conventional group-finders because of their remote present location.
These particles are added to the part of the halo already identified by FoF.
The corrected masses of dark haloes are significantly higher (the median mass
increase is 25 per cent) and there is a considerable shift of the halo mass
function towards the Press & Schechter form. We conclude that meaningful
quantitative comparisons between (semi-)analytic predictions of halo properties
(e.g. mass functions, mass accretion rates, merger rates, spatial clustering,
etc.) and simulation results will require using the same halo definition in
both approaches.
