  The nature of the Sombrero galaxy (M 104 = NGC 4594) has remained elusive
despite many observational studies at a variety of wavelengths. Here we present
Hubble Space Telescope imaging of two fields at $\sim$16 and 33 kpc along the
minor axis to examine stellar metallicity gradients in the extended spheroid.
We use this imaging, extending more than 2 mag below the tip of the red giant
branch (TRGB), in combination with artificial star tests to forward model
observed color-magnitude diagrams (CMDs), measuring metallicity distribution
functions (MDFs) at different radii along the minor axis. An important and
unexpected result is that the halo of the Sombrero is strikingly metal-rich:
even the outer field, located at $\sim$17 effective radii of the bulge, has a
median metallicity [Z/H]$\sim$-0.15 and the fraction of stars with [Z/H]<-1.0
is negligible. This is unprecedented among massive galaxy halos studied to
date, even among giant ellipticals. We find significant radial metallicity
gradients, characterized by an increase in the fraction of metal-poor stars
with radius and a gradient in median metallicity of $\sim$-0.01 dex/kpc. The
density profile is well fit by power laws with slopes that exhibit a dependence
on metallicity, with flatter slopes for more metal-poor stars. We discuss our
results in the context of recent stellar MDF studies of other nearby galaxies
and potential formation scenarios for the Sombrero galaxy.
