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 derive empirically a
kiloparsec scale Kennicutt-Schmidt Law. 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 um. The spectral energy distributions of the whole galaxies
show the presence of the cold dust component (Tc~20 K) in addition to the warm
dust component (Tw~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) and spiral arms (N=2.2) in M101. The power-law index
for spiral arms in M81 is similar (N=1.9) to that of spiral arms in M101.
Conclusions: The power-law index is not always constant within a galaxy. The
difference in the power-law index can be attributed to the difference in the
star formation processes on a kiloparsec scale. N~2 seen in the spiral arms in
M81 and M101 supports the scenario of star formation triggered by cloud-cloud
collisions enhanced by spiral density wave, while N~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.Comment: 12 pages, 8 figures, accepted for publication in A&
