The stellar population and luminosity function in M31 bulge and Inner Disk Fields

We report infrared photometry and stellar identifications for stars in five fields in the M31 bulge located from 2 to 11 arcmin from the nucleus. These fields have been chosen such that the bulge/disk star ratio predicted from Kent's (1989) small bulge model varies from 7:1 to 1:5, allowing a study of near pure disk and near pure bulge stellar populations. We reject the hypothesis of Davies et al. (1991) that luminous stars found within 500 pc of the nucleus are due to a contaminating disk population. We find that the bulge contains stars in excess of M(sub bol) = -5 mag and that the bulge luminosity function has a distinct shape different from the disk fields. We find many stars redder than (J-K) = 2 mag, and suggest that these stars may be the counterparts of the IRAS-selected Galactic bulge Miras studied by Whitelock et at. (1991). The number of bright stars (M(sub bol) is less than -5 mag) falls off more rapidly than the r band surface brightness. By building model fields out of a bulge luminosity function and artificial stars, we are able to show that the change in the luminosity function toward the center cannot be explained simply by the mismeasurement of overcrowded star images. However, these tests also raise the possibility that the asymptotic giant branch (AGB) tip may be approximately equal to 1 mag fainter than actually measured in our most crowded field, reaching only M(sub bol) = -5. We compare observed counts of AGB stars with those predicted from theoretical lifetimes using a technique of general interest for this problem, the Fuel Consumption Theorem of Renzini & Buzzoni (1986) Spectral Evolution of Galaxies (Reidel, Dordrecht). Our methodology is generally applicable to the study of other resolved extragalactic stellar populations. The number of observed stars per magnitude up to a luminosity of M(bol) = -5.5 mag is consistent with AGB evolution of the whole population of the innermost bulge field with the standard lifetime on the AGB of 1.3 Myr/mag. We advance the possibility that the bulge of M31 may be younger than the oldest Galactic globular clusters. We note that M33 has recently been found to have an r(exp 1/4)-law spheroid consisting of intermediate-age stars; bulges can form later than the old halo population.