The Tidal Torque Theory Revisited: II. Rotational Halo Properties

TL;DR

This work extends the tidal torque theory within the peak model to non-linear protohalos that collapse inside-out, deriving the angular momentum growth and final rotational properties of halos. By splitting protohalos into a central contracted progenitor and an outer fully linear region, the authors obtain a scalable AM growth, leading to a nearly universal $J_c/M_c^{5/3}$ and a lognormal spin distribution with median $\lambda'_{\rm med} \approx 0.035$, consistent with simulations. They obtain detailed inner specific AM profiles $j(r)$ and $j(<M)$ that align with observed halo structure, showing that halos rotate as concentric shells around a fixed AM axis, largely independent of major merger histories. Collectively, the results demonstrate that halo rotation can be fully explained analytically from peak statistics and TTT, with no free parameters, underscoring the robustness of the peak model in predicting CDM halo properties.

Abstract

The peak model of structure formation was built more than fifty years ago with the aim to address the origin of dark matter halo rotation in the tidal torque theory (TTT). Paradoxically, it has allowed one to explain and reproduce all halo properties found in cosmological simulations except their rotation, which remains to be understood. With the present two Papers we remedy this anomaly. In Paper I we derived the angular momentum (AM) of protohalos centered on triaxial peaks of suited scale, taking into account that, to leading order, their density profile is smooth and homogeneous. Here we use that result to derive the AM of these objects, accounting for the fact that their actual density profile is slightly outward decreasing and lumpy so that they do not collapse monolithically at once, but progressively from inside out, undergoing mergers during the process. By monitoring in detail their resulting mass and AM growth, we characterize the spin distribution of final halos and the precise mass and radial distribution of their inner mean specific AM. The results obtained explain and reproduce the rotational properties of simulated halos.

Figures (4)

• Figure 1: Predicted $J_{\rm c}/ M_{\rm c}^{5/3}$ relation as a function of halo virial mass (red solid line). The horizontal black dashed line marks the middle value between the minimum and maximum values in the range from $10^{10}h^{-1}$M$_\odot$ to $10^{14}h^{-1}$M$_\odot$.
• Figure 2: Predicted mean AM growth $J_{\rm p}=J+J_{\rm p}^{\rm lin}$ scaled to the initial value $J_{\rm p}(t_{\rm i})$ at $z_i=50$ of protohalos collapsing into current halos with virial mass $10^{13}$M$_\odot$ in the Planck14 cosmology (thick orange line) compared to the mean and 1-$\sigma$ values of simulated protohalos obtained by Pea02a (black dots and error bars). Also plotted are the predicted contributions to it from the central progenitor halo, $J/J_{\rm p}(t_i)$ (red line), and its surrounding fully linear (and homogeneous) part, $J_{\rm p}^{\rm lin}/J_{\rm p}(t_i)$ (yellow line). For comparison, we plot the linear evolution until $t_{\rm c}$ of the mean scaled AM, $J_{\rm p}^{\rm h}/J_{\rm p}(t_i)$, of globally homogeneous protohalos (blue line). The vertical dotted line marks the time $t/t_{\rm c}=0.5$.
• Figure 3: Left panel: Predicted mass of centered spheres as function of their integrated specific AM scaled to its maximum value, $j_{\rm c}=J_{\rm c}/M_{\rm c}$, at the radius $R_{\rm c}$ of the halo, in current halos of several virial masses (colored lines), compared to the best fit for $M_{\rm c}=10^{13}$M$_\odot$ to the three-parametric function $\mu M_{\rm c} /[1+(j_0/j)^\gamma]^{1/\gamma}$, with $\mu=2.57$, $j_0=0.504$, and $\gamma=0.553$ (black dashed line). Right panel: Same as left panel, but for the local specific AM scaled to its maximum value, $j_{\rm c}=j(R_{\rm c})$, at the radius of the halo, compared to the best fit for $M_{\rm c}=10^{13}$M$_\odot$ to the same analytic function, with $\mu=2.12$, $j_0=0.230$, and $\gamma=0.513$.
• Figure 4: Left panel: Predicted integrated specific AM profile scaled to its maximum value, $j_{\rm c}=J_{\rm c}/M_{\rm c}$, for current halos of several virial masses (solid colored lines). Right panel: Same as left panel, but for the local specific AM profile scaled to the maximum value, $j_{\rm c}=j(R_{\rm c})$, at the radius $R_{\rm c}$ of he halo.