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The O-rich Asymptotic Giant Branch (AGB) stars experience strong mass losswith efficient dust condensation and they are major sources of dust in theinterstellar medium. Alumina dust (Al$_2$O$_3$) is an important dust componentin O-rich circumstellar shells and it is expected to be fairly abundant in thewinds of the more massive and O-rich AGB stars. By coupling AGB stellarnucleosynthesis and dust formation, we present a self-consistent exploration onthe Al$_2$O$_3$ production in the winds of AGB stars with progenitor massesbetween $\sim$3 and 7 M$_{\odot}$ and metallicities in the range 0.0003 $\le$ Z$\le$ 0.018. We find that Al$_2$O$_3$ particles form at radial distances fromthe centre between $\sim2$ and 4 R$_*$ (depending on metallicity), which is inagreement with recent interferometric observations of Galactic O-rich AGBstars. The mass of Al$_2$O$_3$ dust is found to scale almost linearly withmetallicity, with solar metallicity AGBs producing the highest amount (about10$^{-3}$ M$_{\odot}$) of alumina dust. The Al$_2$O$_3$ grain size decreaseswith decreasing metallicity (and initial stellar mass) and the maximum size ofthe Al$_2$O$_3$ grains is $\sim$0.075 $\mu m$ for the solar metallicity models.Interestingly, the strong depletion of gaseous Al observed in thelow-metallicity HBB AGB star HV 2576 seems to be consistent with the formationof Al$_2$O$_3$ dust as predicted by our models. We suggest that the content ofAl may be used as a mass (and evolutionary stage) indicator in AGB starsexperiencing HBB.

On the alumina dust production in the winds of O-rich Asymptotic Giant Branch stars