Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ρ/σ3

By Alister W. Graham, D. Merritt, B. Moore, J. Diemand, Balsa Terzic. 2006

148 citations recorded by the source corpus.

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, re, 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.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d3016bf40d67308f9cdcf453c3bc8478dc2a6e97

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantifying the coexistence of massive black holes and dense nuclear star clusters (2009, background): “The associated negative logarithmic slope of the nuclear cluster's internal 3D (i.e. nonprojected ) density profile is 2.0 and 2.7, respectively (Graham et al. 2006, and references therein) which have been biased by bulge stars.”
GHASP: an Hα kinematic survey of spiral and irregular galaxies – V. Dark matter distribution in 36 nearby spiral galaxies (2007, background): “Recent simulations (Graham et al. 2006) have extrapolated inner logarithmic profile slope ranging from -0.2 to -1.5, with a typical value at 0.1 kpc around -0.7.”
The dependence of dark matter profiles on the stellar-to-halo mass ratio: a prediction for cusps versus cores (2013, methodology): “Simulated DM haloes modeled with an Einasto (Einasto 1965) profile have a inner slope of−0.7 (Graham et al. 2006): this value is closer to what observed in real galaxies (Swaters et al. 2003), yet not sufficient to solve the discrepancy (de Blok et al. 2003).”
The Aquarius Project: the subhaloes of galactic haloes (2008, background): “Further evidence for a profile where local slope changes gradually has been presented by Stoehr et al. (2003); Stoehr (2006); Graham et al. (2006).”
Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions (2011, background): “Even though the latest simulations [334] rather point towards Einasto [134] profiles with dlnρ/dlnr ∝ −r(1/n) (with n slightly varying with halo mass, and n ∼ 6 for a Milky Way-sized halo, meaning that the slope is zero only very close to the nucleus [178], and is still ∼ −1 at 200 pc from the cente”
CLASH: JOINT ANALYSIS OF STRONG-LENSING, WEAK-LENSING SHEAR, AND MAGNIFICATION DATA FOR 20 GALAXY CLUSTERS (2015, background): “…NFW) over a wide range of halo masses and radii, with some intrinsic variance associated with the mass accretion histories of individual halos (Jing & Suto 2000; Tasitsiomi et al. 2004; Graham et al. 2006; Navarro et al. 2010; Ludlow et al. 2013; Diemer & Kravtsov 2014; Adhikari et al. 2014).”
Inclination- and dust-corrected galaxy parameters: bulge-to-disc ratios and size–luminosity relations (2008, methodology): “…equations to convert projected densities such as 〈µ〉e into threedimensional densities, are given in Terzić & Graham (2005), Merritt et al. (2006) and Graham et al. (2006a). equation (5) after applying the appropriate stellar mass-toluminosity ratio M/L. Equation (10) has the same functional…”
Empirical Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models (2005, methodology): “In Paper II of this series (Graham et al. 2006a), we explore the Einasto and Prugniel-Simien models in more detail.”
The Core-Cusp Problem (2009, background): “[28] showed that the density distribution presented in Navarro et al.”
GALAXIES IN ΛCDM WITH HALO ABUNDANCE MATCHING: LUMINOSITY–VELOCITY RELATION, BARYONIC MASS–VELOCITY RELATION, VELOCITY FUNCTION, AND CLUSTERING (2010, methodology): “Following the conclusions of Navarro et al. (2004) and Graham et al. (2006), we assume the Einasto profile when extrapolating the inner parts of the largest (Vcirc > 450 km s−1) halos.”
DEPENDENCE OF THE OUTER DENSITY PROFILES OF HALOS ON THEIR MASS ACCRETION RATE (2014, background): “However, they showed that the profiles are more accurately described by the Einasto (1965, 1969) functional form (Navarro et al. 2004; Graham et al. 2006; Merritt et al. 2006; Gao et al. 2008; Stadel et al. 2009; Navarro et al. 2010; Ludlow et al. 2011).”
DARK AND LUMINOUS MATTER IN THINGS DWARF GALAXIES (2010, background): “Rotation curve shape The divergent density profiles (e.g., ∼Rα where α∼−0.8 at 120 pc; Stadel et al. 2009; see also Graham et al. 2006) found in ΛCDM simulations are expected towards the centers of galaxies and thus ought to be observed (see also Navarro et al. 2010).”
THE DENSITY PROFILES OF MASSIVE, RELAXED GALAXY CLUSTERS. II. SEPARATING LUMINOUS AND DARK MATTER IN CLUSTER CORES (2012, unknown): “…simulations following the detailed structure of collisionless CDM halos (e.g., Navarro et al. 1996; Ghigna et al. 2000; Diemand et al. 2005; Graham et al. 2006; Gao et al. 2012b) generically produce a central density cusp with ρDM ∼ r−1, characteristic of the Navarro– Frenk–White (NFW,…”
Two-dimensional kinematics of SLACS lenses – III. Mass structure and dynamics of early-type lens galaxies beyond z ≃ 0.1 (2011, background): “It has been well established by N-body cosmological simulations that dissipationless processes produce inner density di tributions with logarithmic slopesγ′ ≈ 1 (e.g. Navarro et al. 1996) or even shallower (e.g. Graham et al. 2006; Navarro et al. 2010).”
THE SPLASHBACK RADIUS AS A PHYSICAL HALO BOUNDARY AND THE GROWTH OF HALO MASS (2015, background): “…Rsp can be measured from the halo density profile as the radius where the density profile steepens sharply beyond what is expected from the Navarro–Frenk–White density profile (Navarro et al. 1997, hereafter NFW) or the Einasto profile (Einasto 1965; Navarro et al. 2004; Graham et al. 2006).”
Formation of Galaxy Clusters (2012, methodology): “Subsequent simulations (Graham et al. 2006, Merritt et al. 2006, Navarro et al. 2004) showed that the Einasto (1965) profile and other similar models signed to describe deprojection of the Sérsic profile (Merritt et al. 2006) provide a more accurate description of the DM density profiles arising…”
The diversity and similarity of simulated cold dark matter haloes (2008, background): “…of the main halo and of substructure halos, where some recent work has claimed a well-defined central slope of ρ ∝ r−1.2(Diemand et al., 2004, 2005, 2008) whereas others have argued that no compelling evidence for such power-law behaviour is apparent (Navarro et al., 2004; Graham et al., 2006).”
CLASH: WEAK-LENSING SHEAR-AND-MAGNIFICATION ANALYSIS OF 20 GALAXY CLUSTERS (2014, background): “…equilibrium halos (Navarro et al. 1996, hereafter, NFW) over a wide range of halo masses, with some intrinsic variance associated with mass accretion histories of individual halos (Jing & Suto 2000; Merritt et al. 2006; Graham et al. 2006; Navarro et al. 2010; Gao et al. 2012; Ludlow et al. 2013).”
The Milky Way stellar halo out to 40 kpc: squashed, broken but smooth (2011, background): “Forn > 0.5 a good approximation is given bydn = 3n−1/3+0.0079/n (Graham et al. 2006).”