The correlation between interstellar turbulent speed and local star formation rate surface density, ΣSFR, is studied using CO observations in the PHANGS survey. The local velocity dispersion of molecular gas, σ, increases with ΣSFR, but the virial parameter, α vir, is about constant, suggesting the molecular gas remains self-gravitating. The correlation arises because σ depends on the molecular surface density, Σmol, and object cloud mass, M mol, with the usual molecular cloud correlations, while ΣSFR increases with both of these quantities because of a nearly constant star formation efficiency for CO. Pressure fluctuations with ΔΣSFR are also examined. Azimuthal variations of molecular pressure, ΔP mol, have a weaker correlation with ΔΣSFR than expected from the power-law correlation between the total quantities, suggesting slightly enhanced star formation rate (SFR) efficiency per molecule in spiral arms. Dynamical equilibrium pressure and SFR correlate well for the whole sample, as PDE∝ΣSFR1.3 , which is steeper than in other studies. The azimuthal fluctuations, ΔP DE(ΔΣSFR), follow the total correlation P DE(ΣSFR) closely, hinting that some of this correlation may be a precursor to star formation, rather than a reaction. Galactic dynamical processes correlate linearly such that ΣSFR∝(ΣgasR)1.0±0.3 for total gas surface density Σgas and galactic dynamical rates, R, equal to κ, A, or Ω, representing epicyclic frequency, shear rate A, and orbit rate Ω. These results suggest important roles for both feedback and galactic dynamics.
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