Limits on Collisional Dark Matter from Elliptical Galaxies in Clusters

TL;DR

This work analyzes how self-interacting dark matter (SIDM) in galaxy clusters impacts galactic halos via heat conduction, potentially evaporating halos and altering stellar kinematics. It develops a diffusion-based framework to treat SIDM in both fluid and scattering regimes, applying it to NGC 4869 in the Coma cluster to derive evaporation timescales that depend on the cross-section $\sigma_p/m_p$ and velocity dependencies. The authors find that for velocity-independent SIDM, halos would evaporate on a Hubble timescale within a broad cross-section range $\lesssim$ $\sigma_p/m_p \lesssim 10^4\,\mathrm{cm^2\,g^{-1}}$, conflicting with the observed fundamental plane unless dark matter fractions are small; allowing $\sigma_p/m_p = 0.1\,\mathrm{cm^2\,g^{-1}}$ and introducing a temperature dependence imposes strong bounds on the slope $\delta$, and dwarf galaxies further tighten the allowed parameter space. Overall, the combination of FP constraints and dwarf-galaxy data disfavors the SIDM cross-sections that would most effectively reduce central cusps, though very small cross-sections may remain astrophysically relevant, such as for black-hole growth.

Abstract

The dynamical evolution of galaxies in clusters is modified if dark matter is self-interacting. Heat conduction from the hot cluster halo leads to evaporation of the relatively cooler galactic halos. The stellar distribution would adiabatically expand as it readjusts to the loss of dark matter, reducing the velocity dispersion and increasing the half-light radius. If the dark matter content within that radius was f_dm = 25-50% of the total, as indicated by current observations, the ellipticals in clusters would be offset from the fundamental plane relation beyond the observational scatter. The requirement that their halos survive for a Hubble time appears to exclude just that range of the dark matter cross-section, 0.3 < sigma/m < 10^4 cm^2/g, thought to be optimal for reducing central halo cusps, unless f_dm < 15%. If the cross-section is allowed to vary with the relative velocity of dark matter particles, sigma \propto v^{-2 delta}, a new problem of evaporation of dark matter arises in the dwarf galaxies with low velocity dispersion. The halos of large galaxies in clusters and dwarf galaxies in the Local Group can both survive only if delta < 1.1 or delta > 1.8. In either case the problem of central density cusps remains.

Figures (4)

• Figure 1: Evolution of the density profile of NGC 4869 in the fluid regime. The galaxy halo is initially a Hernquist model with the concentration $c = 7$, the cluster is similar to an isothermal sphere. The origin of the coordinate system is placed at the galactic center which does not coincide with the cluster center. Dashed vertical line marks the initial tidal radius of the galaxy halo. The outputs are at the times indicated, in units of $t_0 = 6.5\times 10^4\, (\sigma_p/m_p)$ yr. As time progresses the galactic density falls continuously and approaches the ambient cluster profile.
• Figure 2: Evolution of the temperature profile of NGC 4869 in the fluid regime. The temperature is converted to the velocity units, independent of the particle mass $m_p$.
• Figure 3: Fundamental plane relation for the elliptical galaxies (solid line) and its scatter (dots). The half-light mass-to-light ratio $M_e/L_e$ is in solar units. If NGC 4869 loses its dark matter halo, it would deviate from the plane either upward (if the core velocity dispersion stays constant as the effective radius expands) or downward (if $\sigma_c \propto R_e^{-1}$). The length of solid arrows is calculated using $f_{dm}=0.25$, a minimum dark matter fraction within $R_e$, while dashed arrows are for best-fitting model, $f_{dm}=0.5$.
• Figure 4: Evaporation time of the dark matter halos of elliptical galaxies in clusters in the fluid ($\tau_t > 1$) and scattering ($\tau_t < 1$) regimes. The lines broke into dashes in the marginal range, for the optical depth at the tidal radius $1/3 < \tau_t < 3$. The arrows indicate the range of the cross-section excluded by the requirement that the halos survive for $10^{10}$ yr.