The Physical Origin of the Mass-Size Relation and Its Scatter of Disk Galaxies

Utilizing a kinematic decomposition of simulated galaxies, we focus on galaxies with tiny kinematically inferred stellar halos, indicative of weak external influences. We investigate the intricate interplay between internal (natural) and external (nurture) processes in shaping the scaling relationships of specific angular momentum ($j_\star$), stellar mass ($M_\star$), and size of disk galaxies within the IllustrisTNG simulation. The correlation among mass, size, and angular momentum of galaxies is examined by comparing simulations with observations and the theoretical predictions of the exponential hypothesis. Galaxies with tiny stellar halos exhibit a large scatter in the $j_\star$-$M_\star$ relation, which suggests that it is inherently present in their initial conditions. The analysis reveals that the disks of these galaxies adhere to the exponential hypothesis, resulting in a tight fiducial $j_\star$-$M_\star$-scale length (size) relation that is qualitatively consistent with observations. The inherent scatter in $j_\star$ provides a robust explanation for the mass-size relation and its substantial variability. Notably, galaxies that are moderately influenced by external processes closely adhere to a scaling relation akin to that of galaxies with tiny stellar halos. This result underscores the dominant role of internal processes in shaping the overall $j_\star$-$M_\star$ and mass-size relation, with external effects playing a relatively minor role in disk galaxies. Furthermore, the correlation between galaxy size and the virial radius of the dark matter halo exists but fails to provide strong evidence of the connection between galaxies and their parent dark matter halos.