Lowered Nonextensive Stellar Distribution

The structure of globular clusters and elliptical galaxies are described in an unified way through a new class of lowered models inspired on the nonextensive kinetic theory. These power law models are specified by a single parameter q which quantifies to what extent they depart from the class of lowered stellar distributions discussed by Michie and King. For q equal to unity, the Michie-King profiles are recovered. However, for q smaller than unity there is a gradual modification in the shape of the density profiles which depends on the degree of tidal damage imposed on the model, thereby also providing a good fit for globular clusters. It is also shown that a subclass of these models, those with a deeper potential and $q$ slightly less than unity, present a distribution resembling the de Vaucoulers $r^{1/4}$ profile which yields a good description of the structure of elliptical galaxies. This subset of models follows this trend, with a slight departure over nearly 10 orders of magnitudes.

💡 Research Summary

The paper introduces a unified family of “lowered” stellar distribution models derived from non‑extensive (Tsallis) kinetic theory. Traditional lowered models, such as those of Michie and King, describe globular clusters by imposing an energy cut‑off at the tidal radius and are characterized by a central potential depth (Φ₀) and a velocity dispersion (σ). While successful in many cases, these models struggle to capture the gradual flattening of density profiles observed in clusters that have suffered significant tidal stripping, and they do not naturally reproduce the de Vaucouleurs r¹⁄⁴ law that describes the surface‑brightness profiles of elliptical galaxies.

The authors propose a single‑parameter generalization based on the Tsallis q‑exponential distribution. The distribution function is written as

f(E) ∝