The physical connection between central stellar surface density and stellar spin in SAMI and MaNGA nearby galaxies

The stellar surface density within the inner 1 kpc ($\Sigma_{1}$) has become a popular tool for understanding the growth of galaxies and its connection with the quenching of star formation. The emerging picture suggests that building a central dense core is a necessary condition for quenching. However, it is not clear whether changes in $\Sigma_{1}$ trace changes in stellar kinematics and the growth of dispersion-dominated bulges. In this paper, we combine imaging from the Sloan Digital Sky Survey with stellar kinematics from the Sydney-AAO Multi-object Integral-field unit (SAMI) and Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) surveys to quantify the correlation between $\Sigma_{1}$ and the proxy for stellar spin parameter within one effective radius ($\lambda_{re}$) for 1599 nearby galaxies. We show that, on the star-forming main sequence and at fixed stellar mass, changes in $\Sigma_{1}$ are mirrored by changes in $\lambda_{re}$. While forming stars, main sequence galaxies remain rotationally-dominated systems, with their $\Sigma_{1}$ increasing but their stellar spin staying either constant or slightly increasing. The picture changes below the main sequence, where $\Sigma_{1}$ and $\lambda_{re}$ are no longer correlated. Passive systems show a narrower range of $\Sigma_{1}$, but a wider range of $\lambda_{re}$ compared to star-forming galaxies. Our results indicate that, from a structural point of view, passive galaxies are a more heterogeneous population than star-forming systems, and may have followed a variety of evolutionary paths. This also suggests that, if dispersion-dominated bulges still grow significantly at $z\sim$0, this generally takes place during, or after, the quenching phase.