Context : In the \Lambda CDM cosmological framework , massive galaxies are the end-points of the hierarchical evolution and are therefore key probes to understand how the baryonic matter evolves within the dark matter halos .

Aims : The aim of this work is to use the ” archaeological ” approach in order to infer the stellar population properties and star formation histories of the most massive ( M > 10 ^ { 10.75 } M _ { \sun } ) and passive early-type galaxies ( ETGs ) at 0 < z < 0.3 ( corresponding to a cosmic time interval of \sim 3.3 Gyr ) based on stacked , high signal-to-noise ratio ( SNR ) , spectra extracted from the Sloan Digital Sky Survey ( SDSS ) .
Our study is focused on the most passive ETGs in order to avoid the contamination of galaxies with residual star formation activity and extract the evolutionary information on the oldest envelope of the global galaxy population .

Methods : Differently from most previous studies in this field , we did not rely on individual absorption features such as the Lick indices , but we exploited the information present in the full spectrum by means of the STARLIGHT public code , adopting different stellar population synthesis models .
Successful tests have been performed in order to assess the reliability of STARLIGHT to retrieve the evolutionary properties of the ETG stellar populations such as age , metallicity and star formation history .
The results indicate that these properties can be derived with a percentage accuracy better than 10 ~ { } \% at SNR ~ { } \gtrsim~ { } 10 – 20 , and also that the procedure of stacking galaxy spectra does not introduce significant biases on their retrieving .

Results : Based on our spectral analysis , we found that the ETGs of our sample are very old systems with ages almost as old as the age of the Universe in the case of the most massive ones .
The stellar metallicities are slightly supersolar , with a mean of Z \sim 0.027 \pm 0.002 and Z \sim 0.029 \pm 0.0015 ( depending on the spectral synthesis models used for the fit ) and do not depend on redshift .
Dust extinction is very low , with a mean of A _ { V } \sim 0.08 \pm 0.030 ~ { } mag and A _ { V } \sim 0.16 \pm 0.048 ~ { } mag .
The ETGs show an anti-hierarchical evolution ( downsizing ) where more massive galaxies are older .
The SFHs can be approximated with a parametric function of the form SFR ( t ) \propto \tau ^ { - ( c + 1 ) } t ^ { c } ~ { } exp ( - t / \tau ) , with typical short e -folding times of \tau \sim 0.6 - 0.8 Gyr ( with a dispersion of \pm~ { } 0.1 Gyr ) and c \sim 0.1 ( with a dispersion of \pm~ { } 0.05 ) .
Based on the reconstructed SFHs , most of the stellar mass ( \gtrsim 75 ~ { } \% ) was assembled by z \sim 5 and \lesssim 4 ~ { } \% of it can be ascribed to stellar populations younger than \sim~ { } 1 Gyr .
The inferred SFHs are also used to place constraints on the properties and evolution of the ETG progenitors .
In particular , the ETGs of our samples should have formed most stars through a phase of vigorous star formation ( SFRs \gtrsim 350 - 400 M _ { \sun } ~ { } yr ^ { -1 } ) at z \gtrsim 4 - 5 and are quiescent by z \sim 1.5 - 2 .
The expected number density of ETG progenitors , their SFRs and contribution to the star formation rate density of the Universe , the location on the star formation ” Main Sequence ” and the required existence of massive quiescent galaxies at z \lesssim 2 , are compatible with the current observations , although the uncertainties are still large .

Conclusions : Our results represent an attempt to demonstrate quantitatively the evolutionary link between the most massive ETGs at z < 0.3 and the properties of suitable progenitors at high redshifts .
Our results also show that the full-spectrum fitting is a powerful and complementary approach to reconstruct the star formation histories of massive quiescent galaxies .