Stellar populations of galaxies in the ALHAMBRA survey up to $z \sim 1$. III. The stellar content of the quiescent galaxy population during the last $8$ Gyr

We aim at unveiling the stellar content properties of quiescent galaxies, as well as how these galaxies evolved and assembled their stellar populations since $z\sim1$ up to the present days. Using the multi-filter photometric data from ALHAMBRA and the SED-fitting code MUFFIT, we built a complete catalogue of quiescent galaxies through the dust-corrected stellar mass-colour diagram. This catalogue includes stellar population properties, such as ages, metallicities, extinctions, stellar masses and photo $z$, which were retrieved using two sets of SSP models to construct composite models of stellar populations. We develop a novel methodology to provide, for the first time, the analytic probability distribution functions of mass-weighted ages, metallicities, and extinctions of quiescent galaxies as a function of redshift and stellar mass. In the analysis, we explore different assumptions for the SFH to discard potential systematics of the population synthesis models. There is an increasing number of quiescent galaxies since $z\sim1$ that is more prominent for decreasing stellar masses. Quiescent galaxies present extinction values of $A_V<0.6$ with median values in the range $A_V = 0.15$--$0.3$. At increasing stellar mass, quiescent galaxies are older and more metal rich since $z\sim1$. A detailed analysis of the PDFs reveals that the evolution of quiescent galaxies is not compatible with a passive evolution and there is striking evidence for a slight decrease in the median metallicity of $0.1$--$0.2$~dex. The intrinsic dispersions of the age and metallicity PDFs show a dependence with stellar mass and redshift. These results are qualitatively consistent with both set of SSP models and the alternative SFH assumptions explored. To reconcile the observed trends, the quiescent population must undergo an evolutive pathway including mergers, remnants of star formation and the "progenitor" bias.