Jeans Model for the Shapes of Self-interacting Dark Matter Halos

TL;DR

The paper addresses the challenge of modeling non-spherical SIDM halos by extending the Jeans formalism beyond spherical symmetry. It introduces two approaches—the nonspherical isothermal Jeans model and the squashed Jeans model—with the latter incorporating a radius-dependent axis ratio that smoothly transitions from the collisionless outer halo to the isothermal inner region as the mean number of scatters $\mathcal{N}$ grows. Validation against Eagle-50 cosmological simulations shows that spherically averaged density profiles can be similar for SIDM and CDM at intermediate masses, but halo shapes carry distinct information, with the squashed model reproducing 2D density and halo-shape trends more faithfully than the non-squashed version. Importantly, incorporating halo shapes improves the ability to infer the SIDM cross section, particularly for $M_{200} \sim 10^{12}-10^{13} M_\odot$, offering a fast, semi-analytic tool to constrain SIDM using lensing and X-ray halo-shape observations alongside full N-body simulations. The framework highlights the joint roles of self-interactions, baryons, and halo assembly history in shaping observable halos and provides a path toward observationally testing SIDM through halo morphology.

Abstract

The Jeans model is a semi-analytical approach to modeling self-interacting dark matter (SIDM) that works remarkably well to reproduce the spherically-averaged halo profiles from observations and simulations of relaxed galaxies and galaxy clusters. However, SIDM halos are not spherically symmetric in general since they respond to nonspherical baryon distributions and retain nonsphericity from their initial collapse. In this work, we generalize the Jeans model to describe SIDM density profiles and halo shapes beyond spherical symmetry. Observational tests via halo shapes are especially important for testing SIDM in massive galaxies, $M_{\rm 200} \sim 10^{12} - 10^{13} \; \Msun$, where SIDM and collisionless dark matter halos can have indistinguishable spherically-averaged profiles but distinct halo shapes. We validate our model by comparing to cosmological simulations with baryons for both SIDM with $\sigmam = 1 \cmg$ and collisionless cold dark matter. Our approach differs from previous work in this direction, taking into account the fact that multiple scatterings are required to impact the shape of the halo, as well as being computationally inexpensive to implement. The nonspherical Jeans model can be used in conjunction with halo shape observations (e.g., from gravitational lensing or X-ray data) to directly constrain dark matter self-interactions.

Figures (17)

• Figure 1: Dark matter 2D density profiles are shown for the nonspherical isothermal Jeans model with $\ell_{\rm max} = 10$ (left) and squashed Jeans model (right) in cylindrical coordinates $(R,z)$. Both panels show an axisymmetric halo with $M_{\rm 200} = 2 \times 10^{12} \,M_\odot$, $c_{\rm 200}=10$, $q_0 = 0.6$, $\alpha=0$, $r_m = 26 \; {\rm kpc}$, and no baryons. Iso-density contours are dashed lines, with light (dark) colors as regions of high (low) density. The squashed model yields a gradual rounding of the halo due to self-interactions, while the isothermal model has an abrupt transition at $r_m$.
• Figure 2: Spherically-averaged density (upper panels) and halo shape (lower panels) profiles for spherical isothermal (solid lines), nonspherical isothermal with $\ell_{\rm max} = 10$ (dashed), and squashed (dot-dashed) Jeans models for SIDM with $\sigma/m \approx 1 \; \textrm{cm}^2/\textrm{g}$, and collisionless CDM (dotted) for a representative $2 \times 10^{12} M_\odot$ halo and other model parameters given in the text. Left side represents the SIDM-only halo with no baryons; right side represents the SIDM halo with a baryonic disk. Orange bands show shape profiles ($20-80\%$) from $N$-body simulations for SIDM halos with $1 \; \textrm{cm}^2/\textrm{g}$ both without baryons (left) Peter:2012jh and with baryons (right) Robertson:2020pxj.
• Figure 3: Simulated SIDM vs CDM halos: Spherically-averaged density profiles (left), azimuthally-averaged iso-density contours (center), and halo shape profiles (right) for five systems from Eagle-50 simulations for $\mathtt{SIDM1}$ (red) and $\mathtt{CDM}$ (blue). For virial mass in the range $M_{\rm 200} \sim 10^{12} - 10^{13} \; M_\odot$, SIDM systems can have similar spherically-averaged density profiles, but different halo shapes.
• Figure 4: CDM halos: Spherically-averaged density profiles (left), halo shape profiles (center), and azimuthally-averaged iso-density contours (right) for two example systems from the Eagle-50 simulation of CDM plus baryons. The points show the measured density and shape profiles for the simulated halos, with the error bars denoting the adopted uncertainties, $\Delta \rho$ and $\Delta q$ in equation \ref{['eq:chi_sq_full']}. The shaded bands show the 10th - 90th percentiles of the model posterior distributions for $\rho(r)$ and $q(r)$ when fitting to this data, adopting a fit with adiabatic contraction (AC) in blue, and without AC in green. The addition of AC improves the match to $\rho(r)$ at small radii. Reduced $\chi^2_{\rm 2D}$ values are shown in (right).
• Figure 5: CDM halos: Example $\mathtt{CDM}$ halos with features not described in our CDM model, i.e., substructure, asymmetries, and steep inner slopes. Panels as in Fig. \ref{['fig:cdm_fits_1']}.