We have conducted interferometric observations with the Combined Array for Research in Millimeter Astronomy ( CARMA ) and an on-the-fly mapping with the 45-m telescope at Nobeyama Radio Observatory ( NRO45 ) in the CO ( J =1–0 ) emission line of the nearby spiral galaxy NGC 3521 .
Using the new combined CARMA + NRO45 data of NGC 3521 , together with similar data for NGC 5194 ( M51a ) and archival SINGS H \alpha , 24 \mu m , THINGS H i and GALEX FUV data for these two galaxies , we investigate the empirical scaling law that connects the surface density of star formation rate ( SFR ) and cold gas ( known as the Schmidt-Kennicutt law or S-K law ) on a spatially-resolved basis , and find a super-linear slope for the S-K law when carefully subtracting the background emissions in the SFR image .
We argue that plausibly deriving SFR maps of nearby galaxies requires the diffuse stellar and dust background emission to be subtracted carefully ( especially in the mid-infrared and to a lesser extent in the FUV ) .
Applying this approach , we perform a pixel-by-pixel analysis on both galaxies and quantitatively show that the controversial results whether the molecular S-K law ( expressed as \Sigma _ { SFR } \propto \Sigma _ { H _ { 2 } } ^ { \gamma _ { H _ { 2 } } } ) is super-linear or basically linear is a result of removing or preserving the local background .
In both galaxies , the power index of the molecular S-K law is super-linear ( \gamma _ { H _ { 2 } } \gtrsim 1.5 ) at the highest available resolution ( \sim 230 pc ) , and decreases monotonically for decreasing resolution .
We also find in both galaxies that the scatter of the molecular S-K law ( \sigma _ { H _ { 2 } } ) monotonically increases as the resolution becomes higher , indicating a trend for which the S-K law breaks down below some scale .
Both \gamma _ { H _ { 2 } } and \sigma _ { H _ { 2 } } are systematically larger in M51a than in NGC 3521 , but when plotted against the de-projected scale ( \delta _ { dp } ) , both quantities become highly consistent for the two galaxies , tentatively suggesting that the sub-kpc molecular S-K law in spiral galaxies depends only on the scale being considered , without varying amongst spiral galaxies .
A logarithmic function \gamma _ { H _ { 2 } } = -1.1 ~ { } \log [ \delta _ { dp } / { kpc } ] +1.4 and a linear relation \sigma _ { H _ { 2 } } = -0.2 ~ { } [ \delta _ { dp } / { kpc } ] +0.7 are obtained through fitting to the M51a data , which describes both galaxies impressively well on sub-kpc scales .
A larger sample of galaxies with better sensitivity , resolution and broader field of view are required to test the general applicability of these relations .