  The near-Earth asteroid population suggests the existence of an inner Main
Belt source of asteroids that belongs to the spectroscopic X-complex and has
moderate albedos. The identification of such a source has been lacking so far.
We argue that the most probable source is one or more collisional asteroid
families that escaped discovery up to now. We apply a novel method to search
for asteroid families in the inner Main Belt population of asteroids belonging
to the X-complex with moderate albedo. Instead of searching for asteroid
clusters in orbital elements space, which could be severely dispersed when
older than some billions of years, our method looks for correlations between
the orbital semimajor axis and the inverse size of asteroids. This correlation
is the signature of members of collisional families, which drifted from a
common centre under the effect of the Yarkovsky thermal effect. We identify two
previously unknown families in the inner Main Belt among the moderate-albedo
X-complex asteroids. One of them, whose lowest numbered asteroid is (161)
Author, is ~3 Gyrs-old, whereas the second one, whose lowest numbered object is
(689) Zita, can be as old as the Solar System. Members of this latter family
have orbital eccentricities and inclinations that spread them over the entire
inner Main Belt, which is an indication that this family could be primordial,
i.e. it formed before the giant planet orbital instability. The vast majority
of moderate-albedo X-complex asteroids of the inner-Main Belt are genetically
related, as they can be included into few asteroid families. Only nine
X-complex asteroids with moderate albedo of the inner Main Belt cannot be
included in asteroid families. We suggest that these bodies formed by direct
accretion of the solids in the protoplanetary disk, and are thus surviving
planetesimals.
