ETHOS - An Effective Theory of Structure Formation: Dark matter physics as a possible explanation of the small-scale CDM problems

TL;DR

ETHOS develops an effective theory for structure formation that couples dark matter to dark radiation and includes velocity-dependent self-interactions, enabling a consistent link between particle physics and cosmological observables. Through N-body simulations of CDM and four ETHOS models in a Milky Way–like halo, the authors show large-scale structure remains CDM-like while small-scale halo counts and inner densities are modified by a combination of primordial power-spectrum damping and DM self-interactions, with a mapping from damping scales to halo-mass cutoffs and kinetic decoupling temperatures. A tuned model, ETHOS-4, demonstrates that MS and TBTF can be alleviated without sacrificing large-scale CDM behavior, though some models over-suppress substructure. The ETHOS framework thus provides a tractable path to constrain dark matter physics using astrophysical data, while highlighting the need to incorporate baryonic processes and Lyman-\alpha constraints in future work.

Abstract

We present the first simulations within an effective theory of structure formation (ETHOS), which includes the effect of interactions between dark matter and dark radiation on the linear initial power spectrum and dark matter self-interactions during non-linear structure formation. We simulate a Milky Way-like halo in four different dark matter models and the cold dark matter case. Our highest resolution simulation has a particle mass of $2.8\times 10^4\,{\rm M}_\odot$ and a softening length of $72.4\,{\rm pc}$. We demonstrate that all alternative models have only a negligible impact on large scale structure formation. On galactic scales, however, the models significantly affect the structure and abundance of subhaloes due to the combined effects of small scale primordial damping in the power spectrum and late time self-interactions. We derive an analytic mapping from the primordial damping scale in the power spectrum to the cutoff scale in the halo mass function and the kinetic decoupling temperature. We demonstrate that certain models within this extended effective framework that can alleviate the too-big-to-fail and missing satellite problems simultaneously, and possibly the core-cusp problem. The primordial power spectrum cutoff of our models naturally creates a diversity in the circular velocity profiles, which is larger than that found for cold dark matter simulations. We show that the parameter space of models can be constrained by contrasting model predictions to astrophysical observations. For example, some models may be challenged by the missing satellite problem if baryonic processes were to be included and even over-solve the too-big-to-fail problem; thus ruling them out.

Figures (13)

• Figure 1: Properties of the effective DM models relevant for structure formation. Left: Linear initial matter power spectra ($\Delta_{\rm linear}(k)^2=k^3 P_{\rm linear}(k)/2\pi^2$) for the different models (CDM and ETHOS models ETHOS-1 to ETHOS-4) as a function of comoving wavenumber $k$. The ETHOS models differ in the strength of the damping and the dark acoustic oscillations at small scales. As a reference, we also include thermal-relic-WDM models, which are close to each model in ETHOS. Right: Velocity dependence of the transfer cross-section per units mass ($\sigma_T/m$) for the different ETHOS models. Models ETHOS-1 to ETHOS-3 have $\sigma_T/m\propto v_{\rm rel}^{-4}$ for large relative velocities. For low velocities the cross sections can be as high as $100\,{\rm cm}^2\,{\rm g}^{-1}$.
• Figure 2: Non-linear dimensionless power spectra, $\Delta(k)^2=k^3 P(k)/(2\pi^2)$, of the parent simulations for the different DM models at the indicated redshifts ($z=10,6,4,2,0$). The dashed gray line denotes the shot-noise limit expected if the simulation particles are a Poisson sampling from a smooth underlying density field. The sampling is significantly sub-Poisson at high redshifts and in low density regions, but approaches the Poisson limit in nonlinear structures. The non-CDM models deviate significantly from CDM at high redshifts, but this difference essentially vanishes towards $z=0$.
• Figure 3: Differential FoF halo mass function (multiplied by FoF mass squared) for the different DM models at $z=0$. Approximating the first DAO feature in the linear power spectrum with a sharp power-law cutoff, we show the resulting analytic estimates for the differential halo mass function of the different DM models (yellow dashed). The lower panel shows the ratios between the different simulation models relative to CDM.
• Figure 4: Central density as a function of halo mass ($M_{\rm 200,crit}$) for all main haloes (i.e. we do not include subhaloes here) for the different DM models. The central (core) density is defined at $8.7\,{\rm kpc}$ (three times the gravitational softening length). The lower panel shows the ratio with respect to the CDM case. ETHOS-1 and ETHOS-2 show decreasing core densities towards smaller halo masses. Interestingly, ETHOS-3 shows a slightly different trend where the core density compared to CDM is most reduced for the most massive haloes in the simulation.
• Figure 5: Stacked density profiles for different halo mass ranges ($M_{\rm 200,crit}$) as indicated in each panel for our different DM models. We show the profiles starting at $2\,{\rm kpc}$ out to the virial radius. One can clearly see that the different non-CDM models affect the profiles in rather different ways depending on the mass scale.