Kiloparsec-scale star formation law in M81 and M101 based on AKARI far-infrared observations

Aims. We assess the relationships between the surface densities of the gas and star formation rate (SFR) within spiral arms of the nearby late-type spiral galaxies M81 and M101. By analyzing these relationships locally, we empirically derive a kiloparsec scale Kennicutt-Schmidt Law (Sigma(SFR) proportional to Sigma(N)(gas)). Methods. Both M81 and M101 were observed with the Far-Infrared Surveyor (FIS) aboard AKARI in four far-infrared bands at 65, 90, 140, and 160 mu m. Results. The spectral energy distributions of the whole galaxies show the presence of the cold dust component (T-C similar to 20 K) in addition to the warm dust component (T-W similar to 60 K). We deconvolved the cold and warm dust emission components spatially by making the best use of the multi-band photometric capability of the FIS. The cold and warm dust components show power-law correlations in various regions, which can be converted into the gas mass and the SFR, respectively. We find a power-law correlation between the gas and SFR surface densities with significant differences in the power-law index N between giant HII regions (N = 1.0 +/- 0.5) and spiral arms (N = 2.2 +/- 0.2) in M101. The power-law index for spiral arms in M81 is similar (N = 1.9 +/- 0.4) to that of spiral arms in M101. Conclusions. The power-law index is not always constant within a galaxy. The difference can be attributed to the difference in the star formation processes on a kiloparsec scale. N similar or equal to 2 seen in the spiral arms in M81 and M101 supports the scenario of star formation triggered by cloud-cloud collisions enhanced by a spiral density wave, while N similar or equal to 1 derived in giant HII regions in M101 suggests the star formation induced by the Parker instability triggered by high-velocity Hi gas infall. The present method can be applied to a large galaxy sample for which the AKARI All Sky Survey provides the same 4 far-infrared band data.