Empirical models for dark matter halos. II. Inner profile slopes, dynamical profiles, and ρ/σ3

Alister W. Graham*, David Merritt, Ben Moore, Jürg Diemand, Balša Terzić

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    144 Citations (Scopus)


    We have recently shown that both the Prugniel-Simien model and Sérsic's function (hereafter referred to as the Einasto model when applied to internal density profiles) describe simulated dark matter halos better than a Navarro-Frenk-White-like model with an equal number of parameters. Here we provide analytical expressions for the logarithmic slopes of these models and compare them with data from real galaxies. Depending on the Einasto parameters of the dark matter halo, one can expect an extrapolated inner (0.01-1 kpc) logarithmic profile slope ranging from approximately -0.2 to approximately -1.5, with a typical value at 0.1 kpc around -0.7. Application of this (better fitting) model therefore alleviates some of the past disagreement with observations on this issue. In addition, we provide useful expressions for the concentration and assorted scale radii: rs, r-2, r e, Re, rvir, and rmax, the radius where the circular velocity profile has its maximum value. We also present the circular velocity profiles and the radial behavior of ρ(r)/σ(r) 3 for both the Einasto and Prugniel-Simien models, where σ(r) is the velocity dispersion associated with the density profile ρ(r). We find this representation of the phase-space density profile to be well approximated by a power law with a slope slightly shallower than -2 near r = r-2.

    Original languageEnglish
    Pages (from-to)2701-2710
    Number of pages10
    JournalAstronomical Journal
    Issue number6
    Publication statusPublished - Dec 2006


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