Self-Interacting Dark Matter Can Explain Diverse Galactic Rotation Curves

The rotation curves of spiral galaxies exhibit a diversity that has been difficult to understand in the cold dark matter (CDM) paradigm. We show that the self-interacting dark matter (SIDM) model provides excellent fits to the rotation curves of a sample of galaxies with asymptotic velocities in the $25–300\mathrm{km}/\mathrm{s}$ range that exemplify the full range of diversity. We assume only the halo concentration-mass relation predicted by the CDM model and a fixed value of the self-interaction cross section. In dark-matter-dominated galaxies, thermalization due to self-interactions creates large cores and reduces dark matter densities. In contrast, thermalization leads to denser and smaller cores in more luminous galaxies and naturally explains the flatness of rotation curves of the highly luminous galaxies at small radii. Our results demonstrate that the impact of the baryons on the SIDM halo profile and the scatter from the assembly history of halos as encoded in the concentration-mass relation can explain the diverse rotation curves of spiral galaxies.

Figure 1

Top: Circular velocity of the SIDM halo and the corresponding CDM halo for $V_{\max }=70\mathrm{km}/\mathrm{s}$ with the $2\sigma$ spread in halo concentration. Bottom: Circular velocity of the SIDM halo with $V_{\max }=120\mathrm{km}/\mathrm{s}$ and median concentration including the impact of a stellar disk of mass $M_d=10^{10}{M}_{\odot }$ for three disk scale lengths $R_d=2$, 3, and 6 kpc. The corresponding SIDM (dashed curves) and CDM (dotted curves) circular velocities without disks are also shown.

Figure 2

The left two panels show the SIDM fits to the rotation curves of NGC 6503 and UGC 128. They asymptote to $V_f\approx 130\mathrm{km}/\mathrm{s}$ in the outer parts, but their inner rotation curves are very different. The right panel shows the SIDM fit to a highly luminous galaxy, NGC 2903. The total fit is displayed in red, and it includes contributions from the SIDM halo (blue solid curve), stars (magenta dashed curve), gas (magenta dot-dashed curve), and bulge (magenta long-dashed curve). The predictions of the corresponding CDM halo (dotted curve) and the SIDM halo neglecting the influence of the baryons (asterisk curve) are also shown.

Figure 3

SIDM fits (red solid curve) to the rotation curves of spiral galaxies UGC 5721, NGC 1560, and UGC 5750, all with $V_f\approx 80\mathrm{km}/\mathrm{s}$ but showing extreme diversity in the inner parts. Line types are the same as in Fig. 2.

Figure 4

The inferred SIDM core density times core radius (“surface density”) for the 30 galaxies we have fit. The “minimal” sample is composed of DM-dominated galaxies for which baryons do not change the SIDM profile significantly. The surface densities of these galaxies scale as $V_{\max }^{0.7}$ (dashed line), which can be traced to the concentration-mass relation. The “intermediate” sample shows progressively increasing effects of the stellar disk on the SIDM halo, while the “maximal” one has the most significant effects, where the baryons dominate the inner regions.