The Clouds in the "Middle Ages" I. Star formation history and chemical abundances in the LMC

The LMC is a benchmark galaxy for studying stellar evolution, chemical enrichment, and galaxy interactions due to its proximity and intermediate metallicity. While its star formation history (SFH) has been extensively studied using colour-magnitude diagram (CMD) fitting techniques and the chemical enrichment is largely based on red giant branch (RGB) stars, the asymptotic giant branch (AGB) population - a key tracer of intermediate-ages - has received less attention in these analyses. We aim to reconstruct the SFH of the LMC using AGB stars and to study their reliability as tracers of chemical abundances. The initial sample of 879 AGB stars from the Gaia DR3 long-period variable catalog was extended to 2047 fundamental-mode pulsators by applying separate O-rich and C-rich period-Wesenheit relations; OGLE-III cross-matching then showed that only 256 of these stars are Mira variables. We reconstructed the SFH using two period-age calibrations: the theoretical relation of Trabucchi and Mowlavi (2022) and the empirical calibration of Zhang and Sanders (2023). For the chemical abundance analysis, we used APOGEE DR17 spectra for 296 AGB and 271 RGB stars, applying a refined line-by-line abundance pipeline with a tailored line selection to derive Mg, Si, and Ca abundances. The two calibrations yield significantly different SFHs, and neither matches independent CMD-based results equally well, so we present both rather than one fiducial choice. Our SFH reveals three distinct phases: an ancient population at 9-10 Gyr, a quiescent phase at 4-8 Gyr, and a starburst peaking at 1.5-2 Gyr. Our chemical analysis demonstrates that carefully selected Mg, Si, and Ca lines yield significantly reduced intrinsic scatter compared to APOGEE DR17 results. AGB stars prove to be reliable tracers of both the SFH and chemical enrichment of the LMC, provided that careful line selection and calibration are applied.