On Physical Scales of Dark Matter Halos
  It is common practice to describe formal size and mass scales of dark matter
halos as spherical overdensities with respect to an evolving density threshold.
Here, we critically investigate the evolutionary effects of several such
commonly used definitions and compare them to the halo evolution within fixed
physical scales as well as to the evolution of other intrinsic physical
properties of dark matter halos. It is shown that, in general, the traditional
way of characterizing sizes and masses of halos dramatically overpredicts the
degree of evolution in the last 10 Gyr, especially for low-mass halos. This
pseudo-evolution leads to the illusion of growth even though there are no major
changes within fixed physical scales. Such formal size definitions also serve
as proxies for the virialized region of a halo in the literature. In general,
those spherical overdensity scales do not coincide with the virialized region.
A physically more precise nomenclature would be to simply characterize them by
their very definition instead of calling such formal size and mass definitions
'virial'. In general, we find a discrepancy between the evolution of the
underlying physical structure of dark matter halos seen in cosmological
structure formation simulations and pseudo-evolving formal virial quantities.
We question the importance of the role of formal virial quantities currently
ubiquitously used in descriptions, models and relations that involve properties
of dark matter structures. Concepts and relations based on pseudo-evolving
formal virial quantities do not properly reflect the actual evolution of dark
matter halos and lead to an inaccurate picture of the physical evolution of our
universe.
