The pseudo-evolution of halo mass

The masses and sizes of halos are the most important ingredients in our understanding of galaxy formation, and they are critical for the interpretation of numerous observations. The halo boundary is almost universally defined based on the spherical overdensity mass definition, according to which the halo radius encloses a multiple of the critical or matter density of the universe, leading to definitions such as R200c, R200m, and Rvir.

We show that such definitions can lead to a spurious evolution in halo radius and mass that we call “pseudo-evolution”. The reference density decreases with time as the universe expands, leading to a lower overdensity (in physical units) and thus a larger halo radius and mass, even if the density profile of a halo remains static.

While real halo density profiles are not necessarily static, pseudo-evolution can increase halo masses by about a factor of two since z=1. On the other hand, if matter is accreted at radii larger than the spherical overdensity radius in question, that physical accretion can be underestimated by the evolution of the SO mass. As a solution to this problem, we later proposed the splashback radius which does not suffer from pseudo-evolution.

In a follow-up paper, we investigate whether the evolution of cluster scaling relations is affected by pseudo-evolution. We use the relation between mass, M, and velocity dispersion, σ, as a test case. However, we find that the deviation from the M-σ relation due to pseudo-evolution is smaller than 10% for a wide range of mass definitions. The reason for this small impact is a tight relation between the velocity dispersion and mass profiles which holds across a large radial range. We show that such a relation is generically expected for a wide range of density profiles, as long as halos are in approximate Jeans equilibrium.

We consider the implications of these results for other cluster scaling relations, and argue that pseudo-evolution should have very small effects on most scaling relations, except for those which involve the stellar masses of galaxies. In particular, we show that the relation between stellar mass fraction and total mass is affected by pseudo-evolution, and is largely shaped by it for halo masses smaller than 1014 solar masses.


  • Diemer, More & Kravtsov
    The pseudo-evolution of halo mass
    [ads] [arXiv] [2013 ApJ 766, 25]
  • Diemer, Kravtsov & More
    On the evolution of cluster scaling relations
    [ads] [arXiv] [2013 ApJ 779, 159]
  • More, Diemer & Kravtsov
    The splashback radius as a physical halo boundary and the growth of halo mass
    [ads] [arXiv] [2015 ApJ 810, 36]
  • Diemer, More & Kravtsov
    Poster: The pseudo-evolution of halo mass