We compute the mass and composition of dust produced by stars with masses in the range and with a metallicity of Z= 0.001 during their asymptotic giant branch (AGB) and super-AGB phases. Stellar evolution is followed from the pre-main-sequence phase using the code aton which provides, at each time-step, the thermodynamics and the chemical structure of the wind. We use a simple model to describe the growth of the dust grains under the hypothesis of a time-independent, spherically symmetric stellar wind. Although part of the modelling which describes the stellar outflow is not completely realistic, this approach allows a straight comparison with results based on similar assumptions present in the literature, and thus can be used as an indication of the uncertainties affecting the theoretical investigations focused on the dust formation process in the surroundings of AGB stars.
We find that the total mass of dust injected by AGB stars in the interstellar medium does not increase monotonically with stellar mass and ranges between a minimum of for the 1.5- stellar model up to , for the 6- case. Dust composition depends on the stellar mass: low-mass stars () produce carbon-rich dust, whereas more massive stars, experiencing Hot Bottom Burning, never reach the C-star stage, and produce silicates and iron. This is in partial disagreement with previous investigations in the literature, which are based on synthetic AGB models and predict that, when the initial metallicity is Z= 0.001, carbon-rich dust is formed at all stellar masses. The differences are due to the different modelling of turbulent convection in the super-adiabaticity regime. Also in this case, like for other physical features of the AGB, the treatment of super-adiabatic convection shows up as the most relevant issue affecting the dust formation process.
We also investigate super-AGB stars with masses in the range that evolve over an ONe core. Due to a favourable combination of mass-loss and Hot Bottom Burning, these stars are predicted to be the most efficient silicate-dust producers, releasing masses of dust.
We discuss the robustness of these predictions and their relevance for the nature and evolution of dust at early cosmic times.