Context :

Aims : We perform a comprehensive study of the stellar population properties ( formation epoch , age , metallicity , and extinction ) of quiescent galaxies as a function of size and stellar mass to constrain the physical mechanism governing the stellar mass assembly and the likely evolutive scenarios that explain their growth in size .

Methods : After selecting all the quiescent galaxies from the ALHAMBRA survey by the dust-corrected stellar mass-colour diagram , we built a shared sample of \sim 850 quiescent galaxies with reliable measurements of sizes from the HST .
This sample is complete in stellar mass and luminosity , I \leq 23 .
The stellar population properties were retrieved using the fitting code for spectral energy distributions called MUlti-Filter FITting for stellar population diagnostics ( MUFFIT ) with various sets of composite stellar population models .
Age , formation epoch , metallicity , and extinction were studied on the stellar mass–size plane as function of size through a Monte Carlo approach .
This accounted for uncertainties and degeneracy effects amongst stellar population properties .

Results : The stellar population properties of quiescent galaxies and their stellar mass and size since z \sim 1 are correlated .
At fixed stellar mass , the more compact the quiescent galaxy , the older and richer in metals it is ( 1 Gyr and 0.1 dex , respectively ) .
In addition , more compact galaxies may present slight lower extinctions than their more extended counterparts at the same stellar mass ( < 0.1 mag ) .
By means of studying constant regions of stellar population properties across the stellar mass-size plane , we obtained empirical relations to constrain the physical mechanism that governs the stellar mass assembly of the form M _ { \star } \propto r _ { \mathrm { c } } ^ { \alpha } , where \alpha amounts to 0.50 – 0.55 \pm 0.09 .
There are indications that support the idea that the velocity dispersion is tightly correlated with the stellar content of galaxies .
The mechanisms driving the evolution of stellar populations can therefore be partly linked to the dynamical properties of galaxies , along with their gravitational potential .

Conclusions :