Testing the isothermal Jeans model for self-interacting dark matter halos in the collapse phase

Abstract

We benchmark the semi-analytical isothermal Jeans model against a high-resolution isolated N-body simulation that follows a self-interacting dark matter (SIDM) halo into deep core collapse. The model accurately reproduces the density evolution through much of the collapse phase, although it does not capture the sharp rise in central velocity dispersion during collapse. When applied to strong gravitational lensing observables, such as the projected mass and logarithmic density slope of SIDM halos, the Jeans model tracks the simulated evolution more closely than the parametric approach in the deep collapse regime. Our results demonstrate that the isothermal Jeans model provides a reliable and computationally efficient description of SIDM halo evolution.

Figures (6)

• Figure 1: Evolutionary tracks of the projected logarithmic density slope ($\gamma_{\rm 2D}$) and enclosed mass ($M_{\rm 2D}$) calculated at various projected radii ($R_{\rm 2D}$). Solid and dashed lines represent the results from the reference $N$-body simulation and the isothermal Jeans model, respectively. The dots mark the starting point of each track ($t=0$), corresponding to the initial NFW profile. The black dashed box represents the $3\sigma$ observational uncertainty from Minor2021, shown for scale only.
• Figure 2: Comparison of the temporal evolution of the central density and the radial structure. Left: Central density $\rho_0$ as a function of time $t$ for the isolated reference simulation (grey points, showing all available simulation snapshots), the rescaled cosmological Pippin simulation (red circles), and the isothermal Jeans model (orange curve). The dashed segment of the orange curve indicates a regime where isothermal solutions do not exist and is constructed using extrapolated values of $\rho_0$. The grey vertical lines indicate the merger time $t_{\rm merge}$ and the collapse time $t_{\rm coll}$ within the Jeans framework, while the colored horizontal bars mark the epochs at which density profiles are shown in the right panel. Right: Spherically averaged density profiles at the selected time. Dots show the reference simulation results, where only radial bins with particle numbers exceeding 200 are included. Curves show the corresponding isothermal Jeans profiles. Dashed segment correspond to profile constructed using extrapolated $\rho_0$ and $\nu_0$. Colors indicate the snapshot times as labeled in the legend and the grey curve denotes the initial CDM NFW halo.
• Figure 3: Radial profiles of the one-dimensional velocity dispersion, $\sigma_{\rm v}(r)$, for the SIDM halo at selected times. Dots show the spherically averaged results of the reference simulation, where only radial bins with particle numbers exceeding 200 are included. Curves represent the corresponding isothermal Jeans model results. Dashed segment indicates profile computed using extrapolated values of $\rho_0$ and $\nu_0$ in the absence of isothermal solutions. Colors indicate the snapshot times as labeled in the legend and the grey curve denotes the initial CDM NFW halo.
• Figure 4: Same as Fig. \ref{['Figure1']}, but comparing the results from the isolated $N$-body simulation with the parametric SIDM model based on the gravothermal fluid solution from Hou2025.
• Figure B1: Comparison of the temporal evolution of the central velocity dispersion. Grey points show $\nu_0$ measured directly from the reference $N$-body simulation. Blue points show the same simulation results after rescaling the time coordinate by matching the central density $\rho_0$ to the corresponding isothermal solution. The orange curve shows the prediction of the isothermal Jeans model. The grey vertical lines indicate the merger time $t_{\rm merge}$ and the collapse time $t_{\rm coll}$ within the Jeans framework.