  The disks of spiral galaxies are commonly thought to be truncated: the radial
surface brightness profile steepens sharply beyond a certain radius (3--5
inner-disk scale lengths). Here we present the radial brightness profiles of a
number of barred S0--Sb galaxies with the opposite behavior: their outer
profiles are distinctly shallower in slope than the main disk profile. We term
these "anti-truncations"; they are found in at least 25% of a larger sample of
barred S0--Sb galaxies. There are two distinct types of anti-truncations. About
one-third show a fairly gradual transition and outer isophotes which are
progressively rounder than the main disk isophotes, suggestive of a disk
embedded within a more spheroidal outer zone -- either the outer extent of the
bulge or a separate stellar halo. But the majority of the profiles have rather
sharp surface-brightness transitions to the shallower, outer exponential
profile and, crucially, outer isophotes which are not significantly rounder
than the main disk; in the Sab--Sb galaxies, the outer isophotes include
visible spiral arms. This suggests that the outer light is still part of the
disk. A subset of these profiles are in galaxies with asymmetric outer
isophotes (lopsided or one-armed spirals), suggesting that interactions may be
responsible for at least some of the disklike anti-truncations.
