Dynamics in the Cores of Self-Interacting Dark Matter Halos: Reduced Stalling and Accelerated Core Collapse

TL;DR

This study investigates how self-interactions modify core dynamics in dark matter halos by applying high-resolution idealized N-body simulations across SIDM and CDM models. Using three isotropic halos with distinct inner structures, the authors show that large self-interaction cross sections erase resonant DF features, suppress core stalling and dynamical buoyancy, and prevent the dipole instability, driving perturbers to sink to the center and catalyze rapid core collapse via adiabatic contraction and enhanced heat conduction. The findings imply that SIDM leaves distinctive imprints on the evolution of central massive objects (e.g., SMBHs, nuclear star clusters), offering a pathway to constrain the SIDM cross section through observations of galactic nuclei. The work integrates kinetic theory (LBK torque and DF gradients) with gravothermal-fluid modeling to explain how phase-space diffusion toward an isothermal DF under SIDM alters the balance of torques and the timescales of core evolution, providing a framework for interpreting central dynamics in a universe with self-interacting dark matter.

Abstract

Self-interacting dark matter (SIDM) is an intriguing alternative to the standard cold dark matter (CDM) paradigm, which predicts that dark matter halos typically have large, isothermal cores. Numerical simulations have shown that dynamical friction ceases to operate in cores of (roughly) constant density, a phenomenon known as core stalling. In addition, such cores often are unstable to a dipole instability that gives rise to dynamical buoyancy, causing massive central objects to move outward. Thus far, these manifestations of core dynamics have only been demonstrated in collisionless systems. In this paper, we use idealized N-body simulations to study whether core stalling and dynamical buoyancy operate in SIDM halos. We find that if the self-interactions are sufficiently strong, neither core stalling nor buoyancy are present, and a massive perturber will quickly sink all the way to the center of its host. In doing so, it gravitationally contracts the core, catalyzing a strongly accelerated core collapse. The reason why core dynamics are so different in SIDM halos is that self-interactions drive the halo's distribution function to a featureless exponential, removing any inflections or plateaus that are responsible for the dipole instability and core stalling in the case of CDM. We discuss implications of our finding for constraining the nature of dark matter by using observations of massive objects such as supermassive black holes (SMBHs), globular clusters, and nuclear star clusters in the central regions of galaxies.

Figures (15)

• Figure 1: Initial density and velocity dispersion profiles for the various halos discussed in this paper, as indicated. The gray dashed profiles correspond to the untruncated NFW profile and is shown for comparison. Note that the density profile of the truncated NFW is almost indistinguishable from the untruncated NFW profile inside the virial radius, indicated as the vertical, dotted line.
• Figure 2: Evolution of two SIDM halos ($\sigma_{\rm m} = 25 \>{\rm cm}^2\,{\rm g}^{-1}$) as a function of time, expressed in units of the collision time $t_0$. From left to right the panels show the evolution of the central density, the change in the total energy of the system normalized by the initial energy, and the ratio between the scattering rate in the $N$-body simulation, $\Gamma_{\rm sim}$, and the predicted rate, $\Gamma_{\rm pred}$, based on the instantaneous density and velocity dispersion (equation [\ref{['GammaExp']}]). Top and bottom panels are for the tNFW and ABG[0.1] halos, respectively. The red dashed lines in the left-hand panels are the predictions based on the gravothermal fluid equations (see Appendix \ref{['sec:gravothermal']}). The downward arrow in the top-left panel marks the time of maximum core, which is used as the initial conditions for the cNFW simulations.
• Figure 3: Evolution of the tNFW halo using SIDM with $\sigma_{\rm m} = 25\>{\rm cm}^2\,{\rm g}^{-1}$. Top and bottom panels show the density profile and the 1D velocity dispersion profile, respectively, both normalized to their characteristic values. Different columns correspond to different times, as indicated at the top. In each panel, blue curves show the results from the $N$-body simulation, while the red lines show the predictions based on the gravothermal fluid code. Note the excellent agreement between the two even for $t/t_0=410$, which is well into the core collapse regime (cf. Fig. \ref{['fig:tNFWevol']}). The results at $t/t_0=40$, shown in the second column, serve as the initial conditions for the cNFW halo used in Section \ref{['sec:DFtNFW']}.
• Figure 4: Dynamical friction acting on perturbers of mass $M_{\rm p}=0.01$ (top panels) and $M_{\rm p} = 0.03$ (bottom panels) in the cNFW halo with different levels of self-interactions, as indicated. Left and right-hand panels show the evolution of the distance and velocity of the perturber with respect to the center-of-mass of the host halo. The red dashed lines indicates the predictions based on Chandrasekhar's dynamical friction formula and the initial density profile of the host halo. The horizontal dotted line marks the stalling radius, $r_{\rm stall}$. Radii and velocities are in $N$-body units.
• Figure 5: Enclosed masses as a function of time. The colored lines, ranging from blue to red, indicate the evolution of the enclosed mass fractions at different radii: $r/r_{\rm s} = 0.1, 0.25, 0.5, 1.0, 2.0, 5.0$ and $10.0$. Thicker and thinner lines of the same color correspond to the simulations with and without a perturber, respectively. The thick, green line indicates the mass enclosed by the instantaneous radius of the perturber, which declines as the perturber sinks towards the center. Different columns and rows correspond to different perturber masses and collision cross sections, respectively, as indicated. Note how the perturber affects the mass distribution of the host, and catalyzes core collapse in the case of SIDM. The latter is evident from the fact that when the perturber crosses a particular radius, the enclosed mass within that radius (which is indicated by the thick lines and which does not include the perturber itself) increases rapidly compared to the case without a perturber (thin lines).