Stellar cores live long and prosper in cuspy dark matter halos

TL;DR

This study challenges the claim that stellar cores in ultra-faint dwarfs rule out cuspy dark matter halos by demonstrating that cored stellar systems can remain stable for many Hubble times when initialized in equilibrium with a cuspy host potential. It employs an external fixed NFW halo and a DF-based Plummer stellar component, enabling long, high-resolution simulations with solar-mass stars and no halo live-particle effects. A hierarchical Bayesian analysis shows that the inner-density slope parameter $\gamma$ is not constrained to be positive and remains highly degenerate with other profile parameters, even for modest stellar samples, underscoring the difficulty of inferring the true inner potential from UFDs. Consequently, the presence of stellar cores in UFDs provides no robust evidence against cuspy CDM halos, and careful modeling with long-term, equilibrium-consistent simulations is essential for interpreting core-like stellar configurations.

Abstract

The existence of cuspy or cored centers of dark matter halos is a crucial discriminant between different dark matter models. It has recently been claimed based on dynamical arguments that perfectly cored stellar systems cannot survive inside cuspy dark matter halos, which would make the observation of stellar cores in ultra-faint dwarf galaxies, where dark matter cores cannot form through baryonic processes, a direct falsification of the cold dark matter paradigm. Here, we use idealized simulations to show explicitly that cored stellar systems like those observed in dwarf galaxies can be stable within cuspy dark matter halos over at least several Hubble times. We also demonstrate that observations of ultra-faint dwarf galaxies cannot distinguish mildly positive, flat, or negative inner density slopes, further precluding the dynamical inference of the gravitational potential from the stellar configuration.

Figures (5)

• Figure 1: Evolution of the stellar density $\rho_*$ and the velocity anisotropy $\beta_\mathrm{ani}$ in simulations, as a function of radius $r$. Left column: One realization of the fiducial system for selected times. Right column: Seven simulations, where $M_\mathrm{ext}$ is varied from $M_\mathrm{IC}$, at $t=50\,\mathrm{Gyr}$. Top row: Binned $\rho_*$ from simulation data. The zoomed-in region shows $\rho_*$ for the inner region within $r=0.075\,\mathrm{kpc}$. The dotted line shows $r_\mathrm{S, P}=0.2\,\mathrm{kpc}$, and the dashed line shows the analytic Plummer profile $\rho_\mathrm{P}$. Middle row: The ratio of $\rho_*$ to $\rho_\mathrm{P}$, with the dashed line showing $\rho_* / \rho_\mathrm{P} = 1$. Bottom row: Binned $\beta_\mathrm{ani}$ from simulation data, with the dashed line showing $\beta_\mathrm{ani} = 0$. The triangles show the time-average of $\beta_\mathrm{ani}$ within (on the left) and outside (on the right) $r_\mathrm{S, P}$ for each mass ratio.
• Figure 2: Similar to the middle-left panel of \ref{['fig:evolution']}, but for 10 realizations of the fiducial system, at times $t=0\,\mathrm{Gyr}$ (left) and $t=50\,\mathrm{Gyr}$ (right). The orange line shows the average ratio of all 10 runs.
• Figure 3: The ratio of the Lagrangian radii $r_{35}$ in simulations to that of the Plummer profile $r_{35, \mathrm{P}}$, as a function of time $t$ for eight different mass ratios $M_\mathrm{ext} / M_\mathrm{IC}$. The lighter fluctuating lines show the evolution at each output, while the darker horizontal lines corresponds to the time-averaged value across the whole simulation. The $t$-axis is divided into two ranges separated by the black dotted line: the left side shows the evolution within the first 1 $\mathrm{Gyr}$ and the right side within the remaining 99 $\mathrm{Gyr}$.
• Figure 4: Results of the stellar density fitting. Top-left panel: The distribution of $\gamma$ for selected times (same as in the left column of \ref{['fig:evolution']}) for the hierarchical fit. The orange lines show the median of the fit at each time, and the dotted line shows $\gamma=0$. Top-right panel: The PDF of $\gamma$ at $t=0\,\mathrm{Gyr}$. The orange line shows the hierarchical fit, and the remaining lines the non-hierarchical fits for the 10 fiducial simulations. Bottom panels: Correlation of $\gamma$ with the parameters $\alpha$, $\beta$, $r_\mathrm{S}$, and $\rho_\mathrm{S}$, respectively. The contours show their 68% and 95% confidence intervals, and the dashed crossing lines show the true parameters of the underlying Plummer distribution.
• Figure 5: Directed acyclic graph showing the model parameters in the fit to the density profile. Single-line circle nodes represent fit parameters, double-line circles represent measured quantities (the data), and diamond nodes represent deterministic quantities. Parameters outside the inner rectangle do not depend on the measured radius.