  Whereas it is generally accepted that calcium-aluminum-rich inclusions (CAIs)
from chondritic meteorites formed in a hot environment in the solar
protoplanetary disk, the conditions of their formation remain debated. Recent
laboratory studies of CAIs have provided new kind of data: their size
distributions. We show that size distributions of CAIs measured in laboratory
from sections of carbonaceous chondrites have a power law size distribution
with cumulative size exponent between -1.7 and -1.9, which translates into
cumulative size exponent between -2.5 and -2.8 after correction for sectioning.
To explain these observations, numerical simulations were run to explore the
growth of CAIs from micrometer to centimeter sizes, in a hot and turbulent
protoplanetary disk through the competition of coagulation and fragmentation.
We show that the size distributions obtained in growth simulations are in
agreement with CAIs size distributions in meteorites. We explain the CAI sharp
cut-off of their size distribution at centimeter sizes as the direct result
from the famous fragmentation barrier, provided that CAI fragment for impact
velocities larger than 10 m/s. The growth/destruction timescales of millimeter-
and centimeter-sized CAIs is inversely proportional to the local dust/gas ratio
and is about 10 years at 1300 K and up to 104 years at 1670K. This implies that
the most refractory CAIs are expected to be smaller in size owing to their long
growth timescale compared to less refractory CAIs. Conversely, the least
refractory CAIs could have been recycled many times during the CAI production
era which may have profound consequences for their radiometric age.
