  The short-lived radionuclide $^{26}$Al is widely used to determine the
relative ages of chondrite components and timescales of physical and thermal
events that attended the formation of the Solar System. However, an important
assumption for using $^{26}$Al as a chronometer is its homogeneous distribution
in the disk.
  Yet, the oldest components in chondrites, the Ca-Al-rich inclusions (CAIs),
which are usually considered as time anchors for this chronometer, show
evidence of $^{26}$Al/$^{27}$Al variations independent of radioactive decay.
Since their formation epoch may have been contemporaneous with the collapse of
the parent cloud that formed the disk, this suggests that $^{26}$Al was
heteregeneously distributed in the cloud. We model the collapse of such an
heterogeneous cloud, using two different $^{26}$Al distributions (monotonic and
non-monotonic), and follow its re-distribution in the first condensates and
bulk dust that populate the forming disk.
  We find that CAIs inherit the $^{26}$Al/$^{27}$Al ratio of the matter
infalling at the time of their formation, so that variations of
$^{26}$Al/$^{27}$Al among primordial CAIs can be accounted for, independently
of radioactive decay. The prevalence of a canonical ratio among them and its
necessity for the differentiation of the first planetesimals suggest a
(monotonic) scenario where $^{26}$Al sharply rose relatively close to the
center of the protosolar cloud and essentially remained at a high level outward
(rather than decreased since). As the $ ^{26}$Al abundance would be relatively
homogeneous after cessation of infall, this would warrant the use of the Al-Mg
chronometer from the formation of "regular" CAIs onward, to chondrules and
chondrite accretion.

Earth and Planetary Astrophysics