We have studied the relationship between the star formation rate ( SFR ) surface density and gas surface density in the spiral galaxy M51a ( NGC 5194 ) , using multi-wavelength data obtained as part of the Spitzer Infrared Nearby Galaxies Survey ( SINGS ) .
We introduce a new SFR index based on a linear combination of H \alpha emission-line and 24 \mu m continuum luminosities , that provides reliable extinction-corrected ionizing fluxes and SFR densities over a wide range of dust attenuations .
The combination of these extinction-corrected SFR densities with aperture synthesis HI and CO maps has allowed us to probe the form of the spatially-resolved star formation law on scales of 0.5 to 2 kpc .
We find that the resolved SFR vs gas surface density relation is well represented by a Schmidt power law , which is similar in form and dispersion to the disk-averaged Schmidt law .
We observe a comparably strong correlation of the SFR surface density with the molecular gas surface density , but no significant correlation with the surface density of atomic gas .
The best-fitting slope of the Schmidt law varies from N = 1.37 to 1.56 , with zeropoint and slope that change systematically with the spatial sampling scale .
We tentatively attribute these variations to the effects of areal sampling and averaging of a nonlinear intrinsic star formation law .
Our data can also be fitted by an alternative parametrization of the SFR surface density in terms of the ratio of gas surface density to local dynamical time , but with a considerable dispersion .