  Context: The environmental conditions for asympotic giant branch (AGB) stars
to reach the carbon-rich (C-rich) phase are important to understand the
evolutionary process of AGB stars. The difference between the spatial
distributions of C-rich and oxygen-rich (O-rich) AGB stars is essential for the
study of the Galactic structure and the chemical evolution of the interstellar
medium (ISM). Aims: We quantitatively investigate the spatial distributions of
C-rich and O-rich AGB stars in our Galaxy. We discuss the difference between
them and its origin. Methods: We classify a large number of AGB stars newly
detected by the AKARI id-infrared all-sky survey. In the color-color diagrams,
we define their occupation zones based on the locations of known objects. We
then obtain the spatial distributions of C-rich and O-rich AGB stars, assuming
that they have the same luminosity for a given mass-loss rate. Results: We find
that O-rich AGB stars are concentrated toward the Galactic center and that the
density decreases with Galactocentric distance, whereas C-rich AGB stars show a
relatively uniform distribution within about 8kpc of Sun. Conclusion: Our
result confirms the trends reported in previous studies and extends them to a
Galactic scale. We discuss the relations between our result, the Galactic
metallicity gradient, and the chemical evolution of the ISM in our Galaxy.
