Title: CAI formation in the early Solar System

Abstract: Ca-Al-rich inclusions (CAIs) are the oldest dated solid materials in the solar system, found as light-coloured crystalline ingredients in meteorites. Their formation time is commonly associated with age zero of the Solar System. Yet, the physical and chemical processes that once led to the formation of these sub-millimetre to centimetre-sized mineral particles in the early solar nebula are still a matter of debate. This paper proposes a pathway to form such inclusions during the earliest phases of disc evolution. We combine 1D viscous disc evolutionary models with 2D radiative transfer, equilibrium condensation, and new dust opacity calculations. We show that the viscous heating associated with the high accretion rates in the earliest evolutionary phases causes the midplane inside of about 0.5 au to heat up to limiting temperatures of about 1500-1700 K, but no further. These high temperatures force all refractory material components of the inherited interstellar dust grains to sublimate - except for a few Al-Ca-Ti oxides such as Al2O3, Ca2Al2SiO7, and CaTiO3. Once the Mg-Fe silicates are gone, the dust becomes more transparent and the heat is more efficiently transported to the disc surface, which prevents any further warm-up. This thermostat mechanism keeps these minerals above their annealing temperature for hundreds of thousands of years, which creates large, pure and crystalline particles. These particles are dragged out by the viscously spreading disc. Beyond about 0.5 au, the silicates re-condense on the Ca-Al-rich particles, adding an amorphous silicate matrix. We estimate that this mechanism to produce CAIs works during the first 50000 years of disc evolution. These particles then continue to move outward and populate the entire disc up to radii of about 50 au, before, eventually, the accretion rate subsides, the disc cools, and the particles start to drift inwards.