Dust formation and mass loss around intermediate-mass AGB stars with initial metallicity Zini ≤ 10-4 in the early Universe - I. Effect of surface opacity on stellar evolution and the dust-driven wind

Dust formation and the resulting mass loss around asymptotic giant branch (AGB) stars with initial metallicity in the range 0 <= Z(ini) <= 10(-4) and initial mass 2 <= M-ini/M-circle dot <= 5 are explored by hydrodynamical calculations of the dust-driven wind (DDW) along the AGB evolutionary tracks. We employ the MESA code to simulate the evolution of stars, assuming an empirical mass-loss rate in the post-main-sequence phase and considering three types of low-temperature opacity (scaled-solar, CO-enhanced and CNO-enhanced opacity) to elucidate the effect on stellar evolution and the DDW. We find that the treatment of low-temperature opacity strongly affects dust formation and the resulting DDW; in the carbon-rich AGB phase, the maximum. M of M-ini >= 3M(circle dot) stars with the CO-enhanced opacity is at least one order of magnitude smaller than that with the CNO-enhanced opacity. A wide range of stellar parameters being covered, the necessary condition for driving efficient DDW with. M >= 10(-6) M-circle dot yr(-1) is expressed as effective temperature T-eff less than or similar to 3850 K and log(delta L-C/kappa M-R) greater than or similar to 10.43 log T-eff -32.33, with the carbon excess delta(C) defined as epsilon(C) - epsilon(O), the Rosseland mean opacity.R in units of cm(2) g(-1) in the surface layer and the stellar mass (luminosity) M(L) in solar units. The fitting formulae derived for gas and dust mass-loss rates in terms of input stellar parameters could be useful for investigating the dust yield from AGB stars in the early Universe being consistent with stellar evolution calculations.