  We seek the best size estimates of the asteroid (21) Lutetia, the direction
of its spin axis, and its bulk density, assuming its shape is well described by
a smooth featureless triaxial ellipsoid, and to evaluate the deviations from
this assumption. Methods. We derive these quantities from the outlines of the
asteroid in 307 images of its resolved apparent disk obtained with adaptive
optics (AO) at Keck II and VLT, and combine these with recent mass
determinations to estimate a bulk density. Our best triaxial ellipsoid
diameters for Lutetia, based on our AO images alone, are a x b x c = 132 x 101
x 93 km, with uncertainties of 4 x 3 x 13 km including estimated systematics,
with a rotational pole within 5 deg. of ECJ2000 [long,lat] = [45, -7], or
EQJ2000 [RA, DEC] = [44, +9]. The AO model fit itself has internal precisions
of 1 x 1 x 8 km, but it is evident, both from this model derived from limited
viewing aspects and the radius vector model given in a companion paper, that
Lutetia has significant departures from an idealized ellipsoid. In particular,
the long axis may be overestimated from the AO images alone by about 10 km.
Therefore, we combine the best aspects of the radius vector and ellipsoid model
into a hybrid ellipsoid model, as our final result, of 124 +/- 5 x 101 +/- 4 x
93 +/- 13 km that can be used to estimate volumes, sizes, and projected areas.
The adopted pole position is within 5 deg. of [long, lat] = [52, -6] or[RA DEC]
= [52, +12]. Using two separately determined masses and the volume of our
hybrid model, we estimate a density of 3.5 +/- 1.1 or 4.3 +/- 0.8 g cm-3 . From
the density evidence alone, we argue that this favors an enstatite-chondrite
composition, although other compositions are formally allowed at the extremes
(low-porosity CV/CO carbonaceous chondrite or high-porosity metallic). We
discuss this in the context of other evidence.
