Simple Dark Matter Models Don't Work

Even dark matter particle model proponents concede that a simple collisionless dark matter model that has no non-gravitational interactions doesn't work. The authors of a new preprint call this problem "the galaxy diversity problem."

To get even a tolerable fits to the data from a decent sized sample of ordinary galaxies from the SPARC catalog, with a dark matter particle model, one needs either self-interacting dark matter that creates a new fifth force between dark matter particles, or some sort of fifth force feedback beyond gravitational interactions between ordinary baryonic matter and dark matter.

Galactic rotation curves exhibit a diverse range of inner slopes. Observational data indicates that explaining this diversity may require a mechanism that correlates a galaxy's surface brightness with the central-most region of its dark matter halo. 

In this work, we compare several concrete models that capture the relevant physics required to explain the galaxy diversity problem. We focus specifically on a Self-Interacting Dark Matter (SIDM) model with an isothermal core and two Cold Dark Matter (CDM) models with/without baryonic feedback. Using rotation curves from 90 galaxies in the Spitzer Photometry and Accurate Rotation Curves (SPARC) catalog, we perform a comprehensive model comparison that addresses issues of statistical methodology from prior works. The best-fit halo models that we recover are consistent with the Planck concentration-mass relation as well as standard abundance matching relations. 

We find that both the SIDM and feedback-affected CDM models are better than a CDM model with no feedback in explaining the rotation curves of low and high surface brightness galaxies in the sample. However, when compared to each other, there is no strong statistical preference for either the SIDM or the feedback-affected CDM halo model as the source of galaxy diversity in the SPARC catalog.

Aidan Zentner, Siddharth Dandavate, Oren Slone, Mariangela Lisanti, "A Critical Assessment of Solutions to the Galaxy Diversity Problem" arXiv:2202.00012 (January 31, 2022).

As the body text of the introduction explains (citations omitted):

Galactic rotation curves have historically served as a powerful tool for understanding the distribution of dark and visible matter in the Universe. With recent catalogs of rotation curves that span a wide range of galaxy masses, we now have the unique opportunity to test the consistency of dark matter (DM) models across a broad population of galaxies. One important observation that must be accounted for by any DM model is the diversity of galactic rotation curves and their apparent correlation with the baryonic properties of a galaxy. In this work, we use the Spitzer Photometry & Accurate Rotation Curves (SPARC) catalog to critically assess the preference for models of collisionless Cold DM (CDM) with and without feedback, and for self-interacting DM (SIDM). 

The diversity problem is the simple observation that the rotation curves of spiral galaxies exhibit a diverse range of inner slopes. Specifically, high surface brightness galaxies typically have more steeply rising rotation curves than do their low surface brightness counterparts, even if both have similar halo masses. This behavior cannot easily be explained if halo formation is self-similar, for example if the halo is modeled using the standard Navarro-Frenk-White (NFW) profile. Within the CDM framework, two galaxies with similar halo masses will have comparable total stellar mass and concentration. If no feedback mechanism is invoked, this sets the properties of the DM profile, typically modeled as an NFW profile, such as its scale radius and overall normalization. The inner slope of the halo density is insensitive to baryons and is fixed at a constant value. In this scenario, therefore, the halo model has little flexibility to account for correlations with the surface brightness of the galaxy. 

One way to address galaxy diversity within the CDM framework is to use baryonic feedback to inject energy into the halo and redistribute DM to form larger cores near the halo’s center. For example, repetitive star bursts have been demonstrated to effectively produce cores in the brightest dwarf galaxies. For less massive dwarfs, such feedback is not strong enough to efficiently remove a galaxy’s inner-most mass. For larger systems, the galaxies are so massive that feedback is insufficiently powerful to create coring and profiles similar to NFW are preserved. Baryonic feedback processes therefore link the properties of a galaxy’s DM density profile to its baryonic content, as needed to explain the galaxy diversity, and provide improved fits to rotation curve data. 

An alternate approach to address the galaxy diversity problem is to change the properties of the DM model itself. A well-known example is that of SIDM. If DM can self interact, heat transfer in the central regions of the halo is efficient, creating an isothermal region within the density profile. This central, isothermal profile is exponentially dependent on the baryonic potential of the galaxy. While a DM-dominated system will form a core, a baryon-dominated system will retain a more cuspy center, similar to that of an NFW profile. Thus, in the SIDM framework, the size of the core naturally correlates with the baryonic surface brightness of the galaxy, allowing for a mechanism that can account for galaxy diversity. Since the time-scale for forming the isothermal core is shorter than the time-scale for baryonic feedback, this mechanism is mostly insensitive to the details of feedback processes.

Another preprint released today also favors certain SIDM models (with a fairly strong self-interaction) over plain vanilla CDM models and SIDM models with a weaker self-interaction, in galaxy clusters. 

The introduction to this second paper also discusses at length the quantitative observational bounds on the self-interaction cross-section (basically the strength of the interaction) from the literature in this kind of model. 

This study suggests that prior literature limited this to 0.1 to 1.0 cm^2/gram, with values under 0.4 disfavored, and they find a range of 0.5-1.0 cm^2/gram could fit the data (in accord with this Power Point presentation). It would operate at distances consistent with a Yukawa force mediator boson with a mass of 1-100 MeV.

This is about 10^14 times stronger than the interaction strength of particles that interact only via the weak force with a Z boson carrier boson (which is 10^25 times stronger than gravity), and is in the same general ballpark of strength as the electromagnetic force and strong force (which is about 100 times stronger than the electromagnetic force).