Concentration to mass relation describes how a parameter of a
dark matter density profile changes with the
mass of the halo.
Usually the
concentration parameter (denoted
,
, etc) implies the ratio of the
halo radius (
or
) to the characteristic radius (
) of the
Navarro-Frenk-White density distribution. Both observations
(See e.g. a ScienceWISE collection of bookmarked paper here) and
numerical simulations of structure formation show that the more massive halos are less concentrated.
In the
Lambda CDM concentration to mass relation follows a power law trend:
where the index
(see e.g.
[2]). In
warm or
mixed (cold plus warm) dark matter models numerical simulations show that the relation between concentration and mass flattens at low mass end (even for halo masses
above free streaming scale) (see e.g.
[5] and
[6])
The concentration-to-mass relation depends non-trivially on the redshift (see e.g. Bullock et al.
[1] (2001), Maccio et al. (2008)
[2]) and cosmological parameters
[2, 7].
References:- [1]^ J. S. Bullock, T. S. Kolatt, Y. Sigad, R. S. Somerville, A. V. Kravtsov, A. A. Klypin, J. R. Primack and A. Dekel, ``Profiles of dark haloes. Evolution, scatter, and environment,'' Mon. Not. Roy. Astron. Soc. 321 (2001) 559 [astro-ph/9908159].
- [2]^abc A. V. Maccio', A. A. Dutton and F. C. v. d. Bosch, ``Concentration, Spin and Shape of Dark Matter Haloes as a Function of the Cosmological Model: WMAP1, WMAP3 and WMAP5 results,'' arXiv:0805.1926 [astro-ph].
- [3] D. A. Buote, F. Gastaldello, P. J. Humphrey, L. Zappacosta, J. S. Bullock, F. Brighenti and W. G. Mathews, ``The X-Ray Concentration-Virial Mass Relation,'' Astrophys. J. 664 (2007) 123 [astro-ph/0610135].
- [4] R. Mandelbaum, U. Seljak and C. M. Hirata, ``Halo mass - concentration relation from weak lensing,'' JCAP 0808 (2008) 006 [arXiv:0805.2552 [astro-ph]].
- [5]^ V. R. Eke, J. F. Navarro and M. Steinmetz, ``The Power spectrum dependence of dark matter halo concentrations,'' Astrophys. J. 554 (2001) 114 [astro-ph/0012337].
- [6]^ A. V. Maccio', O. Ruchayskiy, A. Boyarsky and J. C. Munoz-Cuartas, ``The inner structure of haloes in Cold+Warm dark matter models,'' arXiv:1202.2858 [astro-ph.CO].
- [7]^ J. C. Munoz-Cuartas, A. V. Maccio, S. Gottlober and A. A. Dutton, ``The Redshift Evolution of LCDM Halo Parameters: Concentration, Spin, and Shape,'' arXiv:1007.0438 [astro-ph.CO].