Only a handful of observations truly constrain the nature of dark matter, which is why dozens
of different physical models are still viable. Several of the most popular alternatives predict
that dark matter halos slowly “thermalize” over time, gradually changing shape and expanding
until they form a central region of nearly constant density -- a core. This transformation would
not occur if the dark matter particles were completely collision-less, as assumed in the
standard model. Therefore, the presence or absence of such a core provides a powerful
way to distinguish between the standard picture and these more complex physical models.
Our work shows that the appearance of cores in the "stellar" distribution is fully
consistent with any model in which the dark matter halo slowly expands into a core.

Astronomers are discovering many faint galaxies whose stars are spread out so thinly that the
galaxies barely appear brighter than the night sky. Some of them do not even show a clear center,
which is surprising -- gravity usually gathers stars together. These ghostly galaxies are more than
cosmic curiosities -- they may offer a rare window through which to glimpse the true nature
of dark matter. The explanation within the standard dark matter model is that young stars
can blow gas out of small galaxies, reducing the gravitational pull and spreading the stars
outward. But this cannot work in the faintest galaxies, where there are not enough
exploding stars to drive such powerful effects.

In this work, we show that if dark matter gradually expands and forms a core, the stars within
the galaxy naturally drift outward along with it, producing the large, diffuse stellar
distributions that telescopes observe. Because dark matter dominates the gravity, even subtle
changes in its structure over billions of years can pull the stars along. Using simplified
analytical models, we demonstrate that this slow, steady evolution can reproduce the soft,
extended shapes seen in many of these faint galaxies. And since the process occurs so gradually,
the stars adjust smoothly, with the final structures determined primarily by the initial and
final configurations of the dark matter.

The key result of our work is illustrated schematically in Fig. 1 -- extended stellar cores arise
naturally in dark matter models where internal processes gradually thermalize the dark matter
distribution over cosmic time.