The pseudo-evolution of halo mass
  A dark matter halo is commonly defined as a spherical overdensity of matter
with respect to a reference density, such as the critical density or the mean
matter density of the Universe. Such definitions can lead to a spurious
pseudo-evolution of halo mass simply due to redshift evolution of the reference
density, even if its physical density profile remains constant over time. We
estimate the amount of such pseudo-evolution of mass between z=1 to 0 for halos
identified in a large N-body simulation, and show that it accounts for almost
the entire mass evolution of the majority of halos with M200 of about 1E12
solar masses and can be a significant fraction of the apparent mass growth even
for cluster-sized halos. We estimate the magnitude of the pseudo-evolution
assuming that halo density profiles remain static in physical coordinates, and
show that this simple model predicts the pseudo-evolution of halos identified
in numerical simulations to good accuracy, albeit with significant scatter. We
discuss the impact of pseudo-evolution on the evolution of the halo mass
function and show that the non-evolution of the low-mass end of the halo mass
function is the result of a fortuitous cancellation between pseudo-evolution
and the absorption of small halos into larger hosts. We also show that the
evolution of the low mass end of the concentration-mass relation observed in
simulations is almost entirely due to the pseudo-evolution of mass. Finally, we
discuss the implications of our results for the interpretation of the evolution
of various scaling relations between the observable properties of galaxies and
galaxy clusters and their halo masses.
