Speaker
Description
Scaling relations between dark matter halos provide profound insights into dark matter properties, revealing empirical correlations across cosmic structures. Many studies suggest that the mass surface density of dark matter halos remains remarkably constant over a wide range of total masses (Burkert 1995; Spano et al. 2008; Donato et al. 2009; Salucci et al. 2012; Kormendy & Freeman 2016; Salucci et al. 2019). While the physical origins of this phenomenon remain uncertain, Kaneda et al. (2024) recently identified the radius of maximum circular velocity, $R_\mathrm{max}$, as a key parameter. At this radius, the surface density $\Sigma_{R_\mathrm{max}}$ aligns well with both observational data and CDM model predictions across a broad mass spectrum (see also Ogiya et al. 2014).
In low-mass galaxies, however, the $R_\mathrm{max}(M_{200})$ relation in the CDM model exhibits a significant discrepancy with observational results. Observations indicate that the virial mass of $10^{11} M_\odot$ serves as a critical boundary, below which $R_\mathrm{max}$ becomes larger than theoretical predictions. Assuming this discrepancy shares the same physical origin as the cusp-core problem, where models predict a cusp-like profile but observations show a core-like distribution, we developed an analytical model in which supernova feedback drives the transition from the NFW profile (Navarro et al. 1996) to the Burkert profile (Burkert 1995) and applied it to the $R_\mathrm{max}(M_{200})$ relation. Our results show that this cusp-to-core transition is effective for dark matter halo masses below $10^{11} M_\odot$, corresponding to a critical stellar mass, $M_\mathrm{∗, crit}$, which defines a "forbidden region" where systems with stellar masses beyond $M_\mathrm{∗, crit}$ cannot form cores through supernova feedback alone. Most individual galaxies lie outside this forbidden region, allowing the cusp-core transition, while galaxy groups, clusters, and extremely low-mass systems such as ultra-faint galaxies remain within it, making the transition physically impossible. The diversity in low-mass galaxy density profiles likely arises from variations in star formation efficiency, which influence supernova feedback strength and modulate the intensity and timing of baryonic mass ejection.
The radius $R_\mathrm{max}$ is related to the classical virial radius and mass as $R_\mathrm{max} = x\ r_{200}/c(M_{200})$, where $x$ is a coefficient set by the mass distribution function (e.g., 2.16 for the NFW profile and 3.24 for the Burkert profile), and $c$ is the concentration parameter as a function of the virial mass. During the cusp-core transition, significant mass ejection shifts $R_\mathrm{max}$ outward, altering $c$ and potentially expanding the outer boundary of the dark matter halo. We examine how halo boundaries respond to this transition, combining theoretical models with observational data to elucidate the complex interplay between baryonic feedback processes and dark matter dynamics.
