Constraining Self-Interacting Dark Matter with the Milky Way's dwarf spheroidals

TL;DR

The paper investigates whether a constant SIDM cross section can reconcile the inner densities of Milky Way dwarfs with a Milky Way–sized halo under cluster constraints. Using high-resolution cosmological simulations of the Aq-A halo with CDM and multiple SIDM implementations, it shows that $\sigma_T/m = 0.1$ cm$^2$ g$^{-1}$ fails to create the needed $\,{\rm kpc}$-scale cores, while $\sigma_T/m \approx 1$ cm$^2$ g$^{-1}$ produces ~1 kpc cores and better matches Fornax/Sculptor mass profiles; velocity-dependent SIDM further resolves the Too-Big-To-Fail problem. However, halo-shape constraints from clusters disfavor very large cross sections, leaving only a narrow window for a velocity-independent SIDM to stand as an alternative to CDM. The study also notes that the overall dwarf subhalo abundance remains similar to CDM, suggesting baryonic physics or alternative interaction channels may be needed for a definitive SIDM solution. Overall, the results tightly constrain the viable SIDM parameter space and highlight the ongoing tension between dwarf-scale benefits and cluster-scale constraints.

Abstract

Self-Interacting Dark Matter is an attractive alternative to the Cold Dark Matter paradigm only if it is able to substantially reduce the central densities of dwarf-size haloes while keeping the densities and shapes of cluster-size haloes within current constraints. Given the seemingly stringent nature of the latter, it was thought for nearly a decade that SIDM would be viable only if the cross section for self-scattering was strongly velocity-dependent. However, it has recently been suggested that a constant cross section per unit mass of sigma_T/m~0.1cm^2/g is sufficient to accomplish the desired effect. We explicitly investigate this claim using high resolution cosmological simulations of a Milky-Way size halo and find that, similarly to the Cold Dark Matter case, such cross section produces a population of massive subhaloes that is inconsistent with the kinematics of the classical dwarf spheroidals, in particular with the inferred slopes of the mass profiles of Fornax and Sculptor. This problem is resolved if sigma_T/m~1cm^2/g at the dwarf spheroidal scales. Since this value is likely inconsistent with the halo shapes of several clusters, our results leave only a small window open for a velocity-independent Self-Interacting Dark Matter model to work as a distinct alternative to Cold Dark Matter.

Figures (4)

• Figure 1: Dependence of the momentum-transfer weighted cross-section per unit mass on the relative velocity for the different SIDM models considered here. The constant cross section cases with ${\sigma_T/m\!\geq\!1\,{\rm cm}^2\,{\rm g}^{-1}}$ are likely ruled out by halo shapes based on X-ray and lensing observations of clusters Peter2012. The models with a velocity-dependent cross-section are tuned to satisfy all current astrophysical constraints and have been shown to be consistent with the kinematics of MW dSphs (VZL).
• Figure 2: The circular velocity profiles at $z = 0$ encompassing the $1^{\rm st}$ and $3^{\rm rd}$ quartiles of the distribution of the 15 subhaloes with the largest values of $V_{\rm max}(z=0)$. The symbols with error bars are estimates of the circular velocity within the half-light radii for 9 MW dSphs Walker2009Wolf2010. Clearly, the most massive CDM subhaloes are inconsistent with the kinematics of the MW dSphs. SIDM can alleviate this problem only for a constant scattering cross-section ${\sigma_T/m\!\gtrsim\! 1\,{\rm cm}^2\,{\rm g}^{-1}}$ (SIDM10 and SIDM1) or if it has a velocity dependence (vdSIDMa and vdSIDMb). Current constraints from clusters put an upper limit to the constant cross section case close to ${\sigma_T/m\!\sim\!0.1\,{\rm cm}^2\,{\rm g}^{-1}}$ (SIDM0.1). This value is too low to solve the too big to fail problem. The observational data in the bottom right can be fitted by lower mass subhaloes, not shown here since they are affected by the limited resolution of our simulations.
• Figure 3: Density profile of the 15 subhaloes with the largest $V_{\rm max}(z=0)$ values within CDM and different SIDM models (see Fig. \ref{['fig:cross_section']}). We show the median and $1^{\rm st}$ and $3^{\rm rd}$ quartiles of the subhalo distribution for each case. The velocity-dependent SIDM cases produce cores of approximately $600\,{\rm pc}$. Of the constant cross section SIDM models we explored, the one that is currently allowed by cluster constraints, SIDM0.1 (${\sigma_T/m\!=\!0.1\,{\rm cm}^2\,{\rm g}^{-1}}$), only deviates slightly from CDM; the associated core sizes are less than $300\,{\rm pc}$.
• Figure 4: Subhalo mass function for a MW-size halo within CDM and different elastic SIDM models. The only model that leads to a difference relative to CDM has a constant cross section of ${\sigma_T/m\!=\!10\,{\rm cm}^2\,{\rm g}^{-1}}$, which is clearly ruled out by cluster observations.