The X-ray emission by hot gas at the centers of clusters of galaxies is
commonly modeled assuming the existence of steady-state, inhomogeneous cooling
flows. We derive the metallicity profiles of the intracluster medium expected
from such models. The inflowing gas is chemically enriched by type Ia
supernovae and stellar mass loss in the outer parts of the central galaxy,
which may give rise to a substantial metallicity gradient. The amplitude of the
expected metallicity enhancement towards the cluster center is proportional to
the ratio of the central galaxy luminosity to the mass inflow rate. The
metallicity of the hotter phases is expected to be higher than that of the
colder, denser phases. The metallicity profile expected for the Centaurus
cluster is in good agreement with the metallicity gradient recently inferred
from ASCA measurements (Fukazawa et al. 1994). However, current data do not
rule out alternative models where cooling is balanced by some heat source. The
metallicity gradient does not need to be present in all clusters, depending on
the recent merging history of the gas around the central cluster galaxy, and on
the ratio of the stellar mass in the central galaxy to the gas mass in the
cooling flow.Comment: uuencoded postscript, 8 pages of text + 2 figures, accepted by The
Astrophysical Journal (Letters