  The inner and outer shapes and orientations of core-Sersic galaxies may hold
important clues to their formation and evolution. We have therefore measured
the central and outer ellipticities and position angles for a sample of 24
core-Sersic galaxies using archival HST images and data. By selecting galaxies
with core-Sersic break radii R_b---a measure of the size of their partially
depleted core---that are > 0".2, we find that the ellipticities and position
angles are quite robust against HST seeing. For the bulk of the galaxies, there
is a good agreement between the ellipticities and position angles at the break
radii and the average outer ellipticities and position angles determined over
R_e/2 < R < R_e, where R_e is the spheroids' effective half light radius.
However there are some interesting differences. We find a median "inner"
ellipticity at R_b of e_med = 0.13 +- 0.01, rounder than the median ellipticity
of the "outer" regions e_med = 0.20 +- 0.01, which is thought to reflect the
influence of the central supermassive black hole at small radii. In addition,
for the first time we find a trend, albeit weak (2 sigma significance), such
that galaxies with larger (stellar deficit)-to- (supermassive black hole) mass
ratios---thought to be a measure of the number of major dry merger
events---tend to have rounder inner and outer isophotes, suggesting a
connection between the galaxy shapes and their merger histories. We show that
this finding is not simply reflecting the well known result that more luminous
galaxies are rounder, but it is no doubt related.
