  Context. CM-like asteroids (Ch and Cgh classes) are a major population within
the broader C-complex, encompassing about 10% of the mass of the main asteroid
belt. Their internal structure has been predicted to be homogeneous, based on
their compositional similarity as inferred from spectroscopy (Vernazza et al.,
2016, AJ 152, 154) and numerical modeling of their early thermal evolution
(Bland & Travis, 2017, Sci. Adv. 3, e1602514). Aims. Here we aim to test this
hypothesis by deriving the density of the CM-like asteroid (41) Daphne from
detailed modeling of its shape and the orbit of its small satellite. Methods.
We observed Daphne and its satellite within our imaging survey with the Very
Large Telescope extreme adaptive-optics SPHERE/ZIMPOL camera (ID 199.C-0074, PI
P. Vernazza) and complemented this data set with earlier Keck/NIRC2 and
VLT/NACO observations. We analyzed the dynamics of the satellite with our
Genoid meta-heuristic algorithm. Combining our high-angular resolution images
with optical lightcurves and stellar occultations, we determine the spin
period, orientation, and 3-D shape, using our ADAM shape modeling algorithm.
Results. The satellite orbits Daphne on an equatorial, quasi-circular, prograde
orbit, like the satellites of many other large main-belt asteroids. The shape
model of Daphne reveals several large flat areas that could be large impact
craters. The mass determined from this orbit combined with the volume computed
from the shape model implies a density for Daphne of 1.77+/-0.26 g/cm3 (3
{\sigma}). This density is consistent with a primordial CM-like homogeneous
internal structure with some level of macroporosity (~17%). Conclusions. Based
on our analysis of the density of Daphne and 75 other Ch/Cgh-type asteroids
gathered from the literature, we conclude that the primordial internal
structure of the CM parent bodies was homogeneous.
