The Non-universal Pseudo Phase-Space Density Profiles of Symphony Host Halos

TL;DR

The paper demonstrates that the pseudo phase-space density $Q(r)$ in CDM halos is not a universal power law; its slope depends on the halo’s dynamical state and formation history, as quantified by the Jeans-deviation parameter $\delta_J$. Using the Symphony simulations, the authors show that deviations from Jeans equilibrium correlate with steeper $Q_r$ slopes, and that inner regions tend toward a quasi-universal $\chi\approx-2.0$ while outer regions retain halo-to-halo variation. The results align closely with one-dimensional fluid-collapse predictions (Nadler 2017), indicating that halo mass assembly history, rather than 3D structure or environment, primarily governs the PPSD shape. These findings imply that PPSD encodes assembly history and that secondary properties like concentration and accretion rate reflect this underlying dynamical state, with implications for interpreting observations and modeling halo structure across cosmic time.

Abstract

Cosmological N-body simulations have long suggested that the pseudo phase-space density (PPSD), $ρ/σ^3$, of cold dark matter halos follows the universal relation $ρ/σ^3 \propto r^χ$, with $χ\approx -1.875$, as predicted by spherical secondary-infall similarity solutions. This power law appears to hold despite the fact that neither the density $ρ(r)$ nor velocity dispersion $σ(r)$ follow universal power law relations individually, even at fixed mass. We analyze 246 host halos from the Symphony suite of high-resolution cosmological zoom-in simulations, to consistently measure PPSD profiles across host masses from $10^{11}$ to $10^{15} M_\odot$. We find that the PPSD systematically deviates from a power law, and that halos with larger deviations from Jeans equilibrium systematically develop steeper average PPSD slopes. This result suggests that the PPSD is not universal; instead, it is linked to a halo's degree of dynamical equilibrium, which is ultimately set by halo formation history. As a result, we show that secondary halo properties such as concentration and accretion rate inherit significant correlations with the PPSD slope. Moreover, our hosts' PPSD profiles are remarkably consistent with predictions from 1D self-similar fluid collapse models, indicating that three-dimensional structure, velocity anisotropy, and cosmological environment all play negligible roles in shaping the PPSD. These findings imply that the PPSD does not follow a universal power law, but is instead determined by halo mass assembly history alone.

Figures (17)

• Figure 1: Projected radial pseudo phase-space density (PPSD) maps of representative host halos at $z=0$ from the LMC, Milky-Way, Group, and Cluster suites in our simulations, shown across columns. The top row shows relaxed systems close to Jeans equilibrium, while the bottom row shows disturbed systems far from Jeans equilibrium in the corresponding suites. The departure from equilibrium is quantified by the Jeans deviation parameter $\delta_J$ (See Section \ref{['sec:jeans_dev']} for details). For each host, the best-fit average radial PPSD slope, $\chi_{\rm fit}$, is also indicated in the corresponding panel. Each visualization is a slice of thickness $0.2R_{\rm vir}$ extending out to the virial radius.
• Figure 2: Density (left) and radial velocity dispersion (right) profiles of host halos in Symphony suites. Solid lines show suite averages, with radii scaled by $R_{\text{vir}}$, densities scaled by $\rho_m$ (the mean matter density at $z=0$), and velocity dispersions scaled by $v_{\text{vir}}$ (the host virial velocity). Densities are multiplied by $(r/R_{\text{vir}})^2$, to enhance the dynamic range. Dashed lines in the left panel show the best-fit Einasto density profiles, while dashed lines in the right panel are obtained by solving the Jeans equation for the corresponding Einasto models using the measured velocity anisotropy profiles. Shaded regions indicate the 68% halo-to-halo scatter within each suite. The dotted vertical line marks the most conservative convergence radius across suites, below which measurements may not be converged.
• Figure 3: Left panel: Velocity anisotropy profiles of host halos in the Symphony suites at $z=0$. The dotted vertical line marks the most conservative convergence radius across all suites, below which measurements may not be converged. Right panel: Mean density slope--velocity anisotropy relation (Equation \ref{['eq:linear_beta_gamma']}) for host halos in Symphony suites at $z=0$. The dotted line shows the linear relation proposed by 2006NewA...11..333H. The dot–dashed curves depict the model of 2011MNRAS.415.3895L, given by Equation \ref{['eq:beta_gamma']}, assuming that $\gamma(r)$ follows an Einasto profile. Blue, green, and red dot–dashed lines correspond to $\alpha = 0.230$, $0.178$, and $0.132$, respectively.
• Figure 4: Left panel: Mean radial PPSD $\rho/\sigma_{\mathrm{rad}}^3$ profiles of Symphony host halos, normalized by $\rho_m/V_{\rm vir}^3$, as a function of radius in units of $R_{\rm vir}$ for each suite. Shaded regions denote the 68% halo-to-halo scatter. The dashed line represents the 1985ApJS...58...39B spherical secondary-infall similarity solution, $\rho/\sigma^3 \propto r^{-1.875}$. The dotted vertical line marks the most conservative convergence radius across suites. Right panel: Same as the left panel, but shown as a function of enclosed mass normalized by the host virial mass $M_{\rm vir}$.
• Figure 5: Mean logarithmic slope of PPSD profiles of host halos in Symphony suites at $z=0$. The dashed line marks the universal relation $Q_r \propto r^{-1.875}$. The dotted vertical line marks the most conservative convergence radius across the suites.