The Phase-Space Density Profiles of Cold Dark Matter Halos

By James E. Taylor, J. Navarro. 2001

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We examine the coarse-grained phase-space density profiles of a set of recent, high-resolution simulations of galaxy-sized cold dark matter (CDM) halos. Over two and a half decades in radius the phase-space density closely follows a power law, ρ/σ3 ∝ r-α, with α ≈ 1.875. This behavior closely matches the self-similar solution obtained by Bertschinger for secondary infall of gas onto a point-mass perturber in a uniformly expanding universe. On the other hand, the density profile corresponding to Bertschinger's solution (a power law of slope r2α-6) differs significantly from the density profiles of CDM halos. CDM halo density profiles are clearly not power laws, and they have logarithmic slopes that steepen gradually with radius, roughly as described by Navarro, Frenk, & White (NFW). We show that isotropic, spherically symmetric equilibrium mass distributions with power-law phase-space density profiles form a one-parameter family of structures controlled by the ratio of the local velocity dispersion to the "natural" velocity dispersion at some fiducial radius r0; κ = 4πGρ(r0)r20/σ2(r0). For κ = α = 1.875, one recovers the power-law solution ρ ∝ r2α-6. As κ increases, the density profiles become quite complex but still diverge as r2α-6 near the center. For κ larger than some critical value κcrit(α), solutions become nonphysical, leading to negative densities near the center. The critical solution, κ = κcrit, corresponds to the case where the phase-space density distribution is the narrowest compatible with the power-law phase-space density stratification constraint. Over three decades in radius, the critical solution follows closely an NFW profile, although its logarithmic slope asymptotically approaches -2α/5 = -0.75 (rather than -1) at very small radii. Our results thus suggest that the NFW profile is the result of a hierarchical assembly process that preserves the phase-space stratification of Bertschinger's spherical infall model but "mixes" the system maximally, perhaps as a result of repeated merging, leading to a relatively uniform phase-space density distribution across the system. This finding offers intriguing clues as to the origin of the similarity in the structure of dark matter halos formed in hierarchically clustering universes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bcc8decb190be8081a3c8777902d38a253d7aacf

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Citations in the corpus

The redshift dependence of the structure of massive Λ cold dark matter haloes (2007, background): “Taylor & Navarro (2001), Austin et al (2005) and Dehnen & McLaughlin (2005) investigated a halo model based on the assumption that the phase space density, ρ/σ3, was a simple powerlaw of radius.”
A lower bound on the mass of dark matter particles (2008, background): “[149–154]) essentially investigate the change of PSD from Zeldovich to final stage.”
Numerical simulations of the dark universe: State of the art and the next decade (2012, background): “84, even though neither the density nor the velocity dispersion profiles by themselves are [32, 38–40].”
Cosmological Simulations with Self-Interacting Dark Matter I: Constant Density Cores and Substructure (2012, methodology): “For the density profile in the absence of self-interactions, we assume a NFW profile and to fix the velocity dispersion we use the observed fact that the phase space density is a power-law in radius (Taylor & Navarro 2001).”
The mass profile and accretion history of cold dark matter haloes (2013, background): “…angular momentum (e.g., Williams et al. 2004), or adiabatic invariants (e.g., Avila-Reese et al. 1998; Dalal et al. 2010), or else have argued that entropy generation during virialization might be behind the halo structural similarity (see, e.g., Taylor & Navarro 2001; Pontzen & Governato 2013).”
Tracing the dark matter sheet in phase space (2011, unknown): “In the same figure, we also show the pseudo phase-space density of Taylor & Navarro (2001) which has been found to be a perfect power-law entirely independent of resolution (Navarro et al. 2010).”
Quantifying the heart of darkness with GHALO – a multibillion particle simulation of a galactic halo (2008, background): “There is no compelling theory that can explain universal density and phase-space density profiles (Taylor & Navarro 2001), or correlations such as between the local density profile and the anisotropy parameter (Hansen & Stadel 2006).”
Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ρ/σ3 (2006, background): “They are also in excellent agreement with theoretical expectations based on phase-space arguments which suggest that CDM density profiles should have central cusp slopes equal to 0.75 (Taylor & Navarro 2001, see also Hansen & Stadel 2005 and An & Wyn Evans 2006).”
A Universal Density Profile for Dark and Luminous Matter? (2005, unknown): “With regard to dark halos, Taylor & Navarro (2001) have shown that the dependence of phase-space density on radius is well approximated by a power law whose corresponding inner density profile has the shallowest slope.”
CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z = 0.44 galaxy cluster MACS J1206.2-0847 (2013, background): “It has been argued by Taylor & Navarro (2001) that the NFWlike shape is strictly related to the power-law radial behavior of the pseudo-phase-space density profiles of halos identified in cosmological numerical simulations,Q(r) ≡ ρ/σ3 ∝ r−α with α = −1.875.”
The Core-Cusp Problem (2009, background): “From phasespace density arguments, Taylor and Navarro [21] argue that the density profile should resemble an NFW profile, but converging to an inner slope α = −0.”
Dynamical insight into dark matter haloes (2005, methodology): “This part of the analysis is thus similar to the original work of Taylor & Navarro (2001), and to aspects of Williams et al. (2004) [see also Hansen (2004)].”
Formation of Galaxy Clusters (2012, background): “…betwe n density and velocity dispersion is that for collapsed halos in dissipationless simulations the ratio of density to the cube of the rms velocity dispersion can be accurately described by a power law over at least three decades in radius (Taylor & Navarro 2001):Q(r) ≡ ρ/σ3 ∝ r−α with α ≈ 1.9.”
A dynamical model for the distribution of dark matter and gas in galaxy clusters (2003, unknown): “A few attempts have been done in this direction, both using analytical calculations and numerical simulations (e.g. Sheth et al. 2001; Taylor & Navarro 2001; Hiotelis 2002a,b).”
Cores in warm dark matter haloes: a Catch 22 problem (2012, background): “On the other hand the CDM pseudo phase-space distribution is well fitted by a single power law profile on the whole range, in agreement with previous results (Taylor & Navarro 2001; Schmidt et al 2008).”
Impact of baryon physics on dark matter structures: a detailed simulation study of halo density profiles (2010, background): “…amongst these results has been the existence of power law relationships in the phase-space density of haloes across several decades in radius (Taylor & Navarro 2001) and the halo concentrationmass relation over five decades in mass (Bullock et al. 2001; Neto et al. 2007; Macciò et al. 2008;…”
The diversity and similarity of simulated cold dark matter haloes (2008, methodology): “For example, Taylor & Navarro (2001) used this assumption to show that, for isotropic systems, a power-law pseudo-phasespace density implies an inner density cusp with ρ ∝ r−0.75.”
The Phoenix Project: the dark side of rich galaxy clusters (2012, methodology): “It is well known that PPSD profiles are well approximated by a simple power-law,ρ/σ3 ∝ rχ (Taylor & Navarro 2001), intriguingly similar to the secondary-infall self-similar solutions of Bertschinger (1985), where the exponent,χ = −1.875 (see also Ludlow et al. 2010, and references therein).”