  The existence of stellar halos around galaxies is a natural prediction of the
hierarchical nature of the LambdaCDM model. Recent observations of Milky
Way-like galaxies have revealed a wide range in stellar halo mass, including
cases with no statistically significant detection of a stellar halo, as in the
case of M101, NGC3351 and NGC1042. We use the Illustris simulation to
investigate the scatter in stellar halo content and, in particular, to study
the formation of galaxies with the smallest fraction of this diffuse component.
Stellar halos are far from spherical, which diminishes the surface brightness
of the stellar halo for face-on disks. Once accounting for projection effects,
we find that the stellar halo fraction f_SH correlates strongly with galaxy
morphology and star formation rate, but not with environment, in agreement with
observations. Galaxies with the lowest stellar halo fractions are
disk-dominated, star-forming and assemble their dark matter halos on average
earlier than galaxies with similar stellar masses. Accreted satellites are also
lower in stellar mass and have earlier infall times than centrals with high
f_SH. In situ rather than accreted stars dominate the stellar halos of galaxies
with the lowest stellar halo fractions, with a transition radius from in situ
to accretion-dominated r~45 kpc. Our results extrapolated to real galaxies such
as M101 may indicate that these galaxies inhabit old halos which endured
mergers only at higher redshifts and evolved relatively unperturbed in the last
~10 Gyrs.
