Speaker
Description
We present an analytical model that embeds the cusp–core transition into the c–M relation of dark matter halos. The model accounts for deviations from scaling relations in galaxies, where central surface densities fall below c–M predictions. In contrast, UFDs retain high central densities consistent with CDM. Assuming supernova (SN) feedback drives the transition, the model predicts it operates within a characteristic halo mass range of 108–1011 M⊙, defining a critical stellar mass and a “forbidden region” where core formation is ineffective. The framework is validated by analysis using SPARC and UFD data. These data confirm that most galaxies lie outside this region and can undergo the transition, while groups, clusters, and UFDs remain trapped within it. The observed diversity in low-mass density profiles likely arises from variations in star formation efficiency and the coupling efficiency between SN feedback and the dark matter potential. By calibrating the coupling efficiency to observed central densities, we find that ~1% of supernova feedback energy is enough to drive the cusp–core transition in SPARC galaxies.
