Swirls of FIRE: Spatially Resolved Gas Velocity Dispersions and Star Formation Rates in FIRE-2 Disk Environments

We study the spatially resolved (sub-kpc) gas velocity dispersion ($\sigma$)--star formation rate (SFR) relation in the FIRE-2 (Feedback in Realistic Environments) cosmological simulations. We specifically focus on Milky Way mass disk galaxies at late times. In agreement with observations, we find a relatively flat relationship, with $\sigma \approx 15-30$ km/s in neutral gas across 3 dex in SFRs. We show that higher dense gas fractions (ratios of dense gas to neutral gas) and SFRs are correlated at constant $\sigma$. Similarly, lower gas fractions (ratios of gas to stellar mass) are correlated with higher $\sigma$ at constant SFR. The limits of the $\sigma$-$\Sigma_{\rm SFR}$ relation correspond to the onset of strong outflows. We see evidence of "on-off" cycles of star formation in the simulations, corresponding to feedback injection timescales of 10-100 Myr, where SFRs oscillate about equilibrium SFR predictions. Finally, SFRs and velocity dispersions in the simulations agree well with feedback-regulated and marginally stable gas disk (Toomre's $Q =1$) model predictions, and the data effectively rule out models assuming that gas turns into stars at (low) constant efficiency (i.e., ${\rm 1\%}$ per free-fall time). And although the simulation data do not entirely exclude gas accretion/gravitationally powered turbulence as a driver of $\sigma$, it appears to be strongly subdominant to stellar feedback in the simulated galaxy disks.