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The mass–concentration–redshift relation of cold and warm dark matter haloes

Ludlow, A.D.; Bose, S.; Angulo, R.E.; Wang, L.; Hellwing, W.A.; Navarro, J.F.; Cole, S.; Frenk, C.S.

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A.D. Ludlow

S. Bose

R.E. Angulo

L. Wang

W.A. Hellwing

J.F. Navarro


We use a suite of cosmological simulations to study the mass–concentration–redshift relation, c(M, z), of dark matter haloes. Our simulations include standard Λ-cold dark matter (CDM) models, and additional runs with truncated power spectra, consistent with a thermal warm dark matter (WDM) scenario. We find that the mass profiles of CDM and WDM haloes are self-similar and well approximated by the Einasto profile. The c(M, z) relation of CDM haloes is monotonic: concentrations decrease with increasing virial mass at fixed redshift, and decrease with increasing redshift at fixed mass. The mass accretion histories (MAHs) of CDM haloes are also scale-free, and can be used to infer concentrations directly. These results do not apply to WDM haloes: their MAHs are not scale-free because of the characteristic scale imposed by the power spectrum suppression. Further, the WDM c(M, z) relation is non-monotonic: concentrations peak at a mass scale dictated by the truncation scale, and decrease at higher and lower masses. We show that the assembly history of a halo can still be used to infer its concentration, provided that the total mass of its progenitors is considered (the ‘collapsed mass history’; CMH), rather than just that of its main ancestor. This exploits the scale-free nature of CMHs to derive a simple scaling that reproduces the mass–concentration–redshift relation of both CDM and WDM haloes over a vast range of halo masses and redshifts. Our model therefore provides a robust account of the mass, redshift, cosmology and power spectrum dependence of dark matter halo concentrations.


Ludlow, A., Bose, S., Angulo, R., Wang, L., Hellwing, W., Navarro, J., …Frenk, C. (2016). The mass–concentration–redshift relation of cold and warm dark matter haloes. Monthly Notices of the Royal Astronomical Society, 460(2), 1214-1232.

Journal Article Type Article
Acceptance Date Apr 29, 2016
Online Publication Date May 3, 2016
Publication Date Aug 1, 2016
Deposit Date May 24, 2016
Publicly Available Date Jun 16, 2016
Journal Monthly Notices of the Royal Astronomical Society
Print ISSN 0035-8711
Electronic ISSN 1365-2966
Publisher Royal Astronomical Society
Peer Reviewed Peer Reviewed
Volume 460
Issue 2
Pages 1214-1232


Published Journal Article (6.8 Mb)

Copyright Statement
This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

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