Cored galaxies in cuspy dark matter halos

TL;DR

This work addresses whether cored stellar distributions in dwarf galaxies necessitate cored dark matter halos, and whether photometric data can decisively reveal the inner DM structure. It introduces a rigorous spherical framework that classifies 3D stellar densities by central slopes $b_0$ and $\\gamma_0$, connects them to 2D projections via Abel projection, and employs the Eddington inversion to test DF positivity under cuspy halos. The key finding is that weak 3D cores can reside in cuspy DM halos while strong 3D cores cannot, but projection effects make 2D cores common even for cusped halos, limiting the diagnostic power of photometry alone; analyses of UFDs and Fornax corroborate this ambiguity. The study emphasizes the necessity of incorporating velocity information, anisotropy, and more general geometries to robustly distinguish cusp vs core DM halos in dwarf galaxies, with implications for interpreting small-scale structure in the CDM paradigm.

Abstract

We investigate constraints on the inner stellar density profile from photometric data of dwarf spheroidal and ultra-faint dwarf galaxies. Our aim is to clarify under what conditions cored stellar profiles require dark matter halos that are also cored, deviating from the cuspy profiles expected for cold dark matter halos. We consider a variety of spherically symmetric stellar profiles, which we classify as "strong" or "weak" cores and cusps according to the behavior of the slope ($b_0$) and logarithmic slope ($γ_0$) at their centers. We explore which profiles lead to unphysical negative distribution functions when embedded in a cuspy halo, treating isotropic and anisotropic kinematics separately. We find that weakly-cored stellar profiles in 3D (i.e., $b_0 \neq 0$, $γ_0=0$) can be consistent with cuspy dark matter profiles, but strong 3D cores ($b_0=γ_0=0$) are not. However, both weak and strong 3D cores yield nearly indistinguishable inner profiles in projection, which implies that ruling out a dark matter cusp from photometric data alone is highly challenging. As an example, we study the profiles of ultra-faint dwarf galaxies and find that they are consistent with both weak and strong 3D cores. This is not just a result of the limited numbers of stars in these systems, since we reach the same conclusion even for Fornax, one of the most luminous and best-studied dwarf spheroidal companions of the Milky Way. We conclude that, based on current data and analysis techniques, cored surface density profiles in nearby dwarf galaxies cannot be taken as strong evidence against the presence of cuspy dark matter halos.

Figures (9)

• Figure 1: Schematic overview of the proposed classification: strong cores (), weak cores (), weak cusps () and strong cusps () labeled by their asymptotic behavior at the center. The left panels show the three-dimensional (volumetric) density profiles, together with the corresponding log-slope $\gamma$ (upper right) and parameter $b$ (lower right). The right panels present the analogous projected (surface–density) quantities. Within this framework, strong and weak cores both appear as strong cores in projection, weak cusps resemble weak cores, and strong cusps remain clearly cuspy.
• Figure 2: Stellar surface density $\Sigma_\star$, 3D density $\rho_\star$, line-of-sight velocity dispersion $\sigma_\mathrm{los}$ and DF, obtained for various stellar profiles embedded into a DM halo based on the Hernquist potential with total mass $M_{h}=10^9M_{\odot}$ and scale radius $r_s=1$kpc. For the stellar tracers we use $\Sigma_0=3\times10^7M_{\odot}\text{kpc}^{-2}$, $R_{1/2}=0.1$kpc and assume an isotropic velocity distribution. Curves plotted with solid lines () or dot-dashed lines ( . ) correspond to weak or strong core profiles in 3D, respectively.
• Figure 3: Fits to the surface brightness profile of Horologium I with weak () and strong ( . ) core profiles. See Appendix \ref{['sec:dwarfs_data']} for details.
• Figure 4: Fornax surface density profile by elliptical radius after background subtraction fitted with different weak () and strong ( . ) core profiles, index parameter and reduced $\chi^2$ is shown in the plot, the rest of the parameters can be found in Appendix \ref{['sec:fornaxfit']}.
• Figure 5: Surface density profile (left), isotropic DF (middle) and $d^2\rho/d\Psi^2$ (right) of a Double-Exponential stellar profile as defined in Eq. \ref{['eq:dexp']}. Sharp transition parameter between the inner and outer slope result in a marked decrease of $d^2\rho/d\Psi^2$, which may drive the DF to negative values.