Molecular gas, kinematics, and OB star formation in the spiral arms of the southern Milky Way

The rotation curve for the fourth Galactic quadrant within the solar circle is derived from the Columbia University - Universidad de Chile CO (J = 1 -> 0) survey of molecular gas. A new sampling, 4 times denser in longitude than in our previous analysis, is used to compute kinematical parameters that require derivatives with respect to galacto-centric radius, the angular velocity Omega(R), the epicyclic frequency kappa(R), and the parameters A(R) and B(R) describing, respectively, gas shear and vorticity. The face-on surface density of molecular gas is computed from the CO data in galactocentric radial bins for the subcentral vicinity, the same spectral region used to derive the rotation curve, where the twofold ambiguity in kinematical distances is minimum. The rate of massive star formation per unit area is derived for the same radial bins from the luminosity of IRAS pointlike sources with FIR colors of UC H II regions detected in the CS (J = 2 -> 1) line. Massive star formation occurs preferentially in three regions of high molecular gas density, coincident with lines of sight tangent to spiral arms. The molecular gas motion in these arms resembles that of a solid body, characterized by constant angular velocity and by low shear and vorticity. The formation of massive stars in the arms follows the Schmidt law, Sigma(MSFR) proportional to [Sigma(gas)](n), with an index of n = 1.2 +/- 0.2. Our results suggest that the large-scale kinematics, through shear, regulate global star formation in the Galactic disk.