The slow evolution of dark matter halos from cusp to core naturally produces extended stellar core-like distributions

TL;DR

This study proposes a simple, analytic mechanism by which DM halo expansion from cusp to core can produce extended stellar cores in DM-dominated dwarfs. Using adiabatic invariants in spherical potentials and analyzing circular, isotropic, and radial orbit configurations (via abc-density profiles and Henon’s isochrone), it derives how stellar densities and inner slopes transform during slow DM-driven evolution. The results show that core-like stellar structures form readily for a broad range of initial conditions, with final core radii comparable to DM cores and inner stellar slopes typically below ~0.6; isotropy is preserved at the center while mild radial anisotropy appears outward. The work highlights the role of initial DM and stellar profiles in setting core properties, discusses observational and theoretical constraints, and emphasizes the need for non-spherical, self-gravity-inclusive numerical simulations to test these analytic findings against real galaxies.

Abstract

Motivated by the observation of extended stellar cores in dark matter (DM) dominated dwarf galaxies, this study investigates a simple mechanism by which stellar cores can form as a result of DM halo expansion. Several non-CDM models predict that the DM distribution thermalizes over time, transforming initially cuspy halos into cores. This transformation weakens the gravitational potential, allowing the stellar component to expand and form diffuse, core-like structures. Using analytical models and adiabatic invariants, we examine stellar systems with purely tangential, purely radial, and isotropic orbits evolving under a slowly changing potential. Across a wide range of initial and final conditions, we find that stellar cores form relatively easily, though their properties depend sensitively on these conditions. Orbit types preserve their nature during the DM halo expansion: tangential and radial orbits remain so, while isotropic orbits remain nearly isotropic in the central regions. Systems with circular orbits develop stellar cores when the initial stellar density logarithmic slope lies between -0.5 and -1.2, whereas radial systems do not form cores. Isotropic systems behave similarly to tangential ones, producing cores that are isotropic in the center but develop increasing radial anisotropy outward; the anisotropy parameter "beta" grows from sim 0.07 at the core radius to sim 0.5 at three core radii. The theoretical and observational literature suggests initial DM profiles with steep slopes and stellar distributions that are shallower and isotropic at the center. Given these conditions, the mechanism predicts stellar cores with radii at least 40 % that of the DM core and inner logarithmic slopes shallower than 0.6.

Figures (8)

• Figure 1: Examples of the impact of the DM core formation (from the initial red dashed lines to the final red solid lines) on the formation of a stellar core (the blue solid lines) evolving from an originally concentrated stellar distribution (the dashed blue lines). The vertical dotted lines indicate the radius of the formed cores in DM (red) and stars (blue). The initial stars are assumed to follow circular orbits. For details on the types of profiles represented in the different panels, see Sect. \ref{['sec:example_circular']}. Arbitrary global scale factors affect both densities and radii.
• Figure 2: Summary of the effect of the DM halo expansion on the stellar distribution when the orbits are circular ($\beta=-\infty$). Two parameters are used to characterize the result: the ratio between the stellar and DM cores (top panel) and the final inner slope of the resulting stellar profile (bottom panel). Both are represented versus the initial inner slope of the stellar distribution. The inset next to the top panel describes the initial and final DM profiles, with $a,b,c_{{\rm DM}}$ referring to the parameters defining the $\rho_{abc}$ profiles in Eq. (\ref{['eq:abcprofile']}). The black solid line labelled "Theory" in the bottom panel represents Eq. (\ref{['eq:slopes']}). The vertical dashed lines mark the initial $c_{{\rm DM}}$ and follows the same color code as the upper panel. For further details, see Sect. \ref{['sec:example_circular']}. The region shaded in gray represents the approximate location of an observed stellar core.
• Figure 3: Simulations corresponding to an initially isotropic stellar distribution being hosted in a DM halo set by Henon's isochrone potential. Each figure is split into two panels with the anisotropy parameter on top and the density profiles and core radii at the bottom. The color and line-type code for the densities (bottom panels) is the same as that used in Fig. \ref{['fig:slow_expansion1']} and \ref{['fig:slow_expansion5']}. The inset in the top panel includes the actual value of $\beta$ at the core radius $r_c$ of the final stellar distribution, as well as $r_c/2$, $2\,r_c$, and $3\,r_c$. (a) The DM expands by a factor of 20. The polytropic index $m$ is set to 5, and the cutoff radius of the initial stellar distribution to 1. The cutoff of the final stellar distribution is marked with a vertical green dashed line. (b) Same as (a) except for the initial cutoff, set to 1000. (c) Same as (a) except for the initial cutoff, set to 100, and the polytropic index, set to 2. (d) Same as (a) except for the DM expansion factor, which this time is about 350 ($r_{iso}$ goes from 0.03 to 10). For reference, the four panels include an Osipkov-Merrit (OM) anisotropy distribution (the green solid lines), where $\beta(r)=r^2/(r^2+r_{\rm OM}^2)$. In general, OM does a fair job when the characteristic radius, $r_{\rm OM}$, is tuned to a value much larger than the DM core radius. For further details on the types of line in the density sub-panels, see the caption of Fig. \ref{['fig:slow_expansion1']}.
• Figure 4: Variation of the anisotropy parameter $\beta$ at selected radii of the final stellar profile: at the core radius $r_c$ (the solid lines), within the core radius at $r_c/2$ (the dotted lines) and outside the core at $2\,r_c$ and $3\,r_c$ radii (the dashed and dotted-dashed lines, respectively). Different colors represent different varying parameter as indicated in the inset. The absolute variation, given in the inset, has been normalized so that if $p$ is the varying parameter then the abscissa represents $(p-\min p)/(\max p-\min p)$. The gravitational potential set by DM is an Henon's isochrone with an initial stellar velocity distribution that is isotropic (Sect. \ref{['sec:isochrone']}).
• Figure 5: Ratio between radii characterizing the effect of the expansion of the DM halo on an initially isotropic stellar velocity distribution. It shows final core radius ratio $\star$$r_c$/ DM $r_c$ (the solid lines), the final over initial core ratio of DM (the driving expansion rate, given by the dashed lines), and the final over initial core ratio of the stars (the resulting stellar expansion rate, given by the dotted lines). They are presented versus the variation of the polytropic index (the blue lines), the cutoff radius of the initial stellar distribution (the orange lines), the initial core radius of DM (the green lines), and the initial core radius of DM but assuming circular orbits (Sect. \ref{['sec:spherical']}; the red lines). The gravitational potential is an Henon's isochrone, and the varying parameter has been normalized as explained in the caption of Fig. \ref{['fig:slow_expansion7']}.