  Long dynamical timescales in the outskirts of galaxies preserve the
information content of their accretion histories, for example in the form of
stellar population gradients. We present a detailed analysis of the stellar
halo properties of a statistically representative sample of early-type galaxies
from the Illustris simulation and show that stellar population gradients at
large radii can indeed be used to infer basic properties of galactic accretion
histories. We measure metallicity, age, and surface-brightness profiles in
quiescent Illustris galaxies ranging from $\mathrm{M}_\star = 10^{10} - 2\times
10^{12}\;\mathrm{M}_\odot$ and show that they are in reasonable agreement with
observations. At fixed mass, galaxies that accreted little of their stellar
halo material tend to have steeper metallicity and surface-brightness profiles
between 2 - 4 effective radii (R$_e$) than those with larger accreted
fractions. Profiles of metallicity and surface-brightness in the stellar halo
typically flatten from z = 1 to the present. This suggests that the accretion
of stars into the stellar halo tends to flatten metallicity and
surface-brightness profiles, a picture which is supported by the tight
correlation between the two gradients in the stellar halo. We find no
statistical evidence of additional information content related to accretion
histories in stellar halo metallicity profiles beyond what is contained in
surface-brightness profiles. Age gradients in the stellar halo do not appear to
be sensitive to galactic accretion histories, and none of the stellar
population gradients studied are strongly correlated with the mean merger
mass-ratio. Future observations that reach large radii outside galaxies will
have the best potential to constrain galactic accretion histories.
