Late-Type Stars in M31. I.: A Photometric Study of AGB Stars and Metallicity Gradients.

We have imaged five 7\arcmin \x 7\arcmin\ fields in M31 spanning galactocentric radii from 4 to 32 kpc along the SW-major axis. The fields were observed through two broad-band (\V\ and \I) and two narrow-band (\CN\ and \TiO) filters. The broad-band data were used to construct \IvsVI
color-magnitude diagrams (CMDs) and, in some of our fields, we found significant numbers of stars in the Cepheid instability strip. A distance modulus for the Cepheids in the middle field was found that agreed well with other values in the literature values. The width of the giant branch (GB) in the \IvsVI\ CMD of all 5 fields was investigated, and we show that in four of the fields a likely explanation for the GB width is a combination of {\it both} metallicity and mass variations. Using the broad-band data, the asymptotic giant branch (AGB) luminosity functions (LFs) were measured in the five fields, and we show that differences exist between these LFs. We speculate on how the different star forming histories in the fields may lead to the observed AGB LFs and GB widths. Using the narrow-band data along with the broad-band data we separated the AGB stars into carbon-rich © and oxygen-rich (M) types. The carbon stars LFs were used to obtain an estimate for the distance modulus of M31 which agrees with the value derived from Cepheids. The ratio of C- to M-stars (C/M) is believed to be an indicator of gaseous chemical abundance at the time of formation of these stars. We show that the C/M ratio increases smoothly with galactocentric distance, suggesting an inverse correlation with metallicity. This is the first demonstration of this effect within a single extragalactic system. We find that differences in the width of the GB and the AGB LFs do not significantly affect the C/M ratio. We consider the effect of the increasing C/M ratio on the ISM in M31, and cite evidence in favor of a model where the grain composition in M31 is a function of galactocentric distance.