Studying the resolved stellar populations of the different structuralcomponents which build massive galaxies directly unveils their assemblyhistory. We aim at characterizing the stellar population properties of arepresentative sample of bulges and pure spheroids in massive galaxies($M_{\star}>10^{10}$ M$_{\odot}$) in the GOODS-N field. We take advantage ofthe spectral and spatial information provided by SHARDS and HST data to performthe multi-image spectro-photometrical decoupling of the galaxy light. We derivethe spectral energy distribution separately for bulges and disks in theredshift range $0.14<z\leq1$ with spectral resolution $R\sim50$. Analyzingthese SEDs, we find evidences of a bimodal distribution of bulge formationredshifts. We find that 33% of them present old mass-weighted ages, implying amedian formation redshift $z_{\rm{form}}={6.2}_{-1.7}^{+1.5}$. They are relicsof the early Universe embedded in disk galaxies. A second wave, dominant innumber, accounts for bulges formed at median redshift$z_{\rm{form}}={1.3}_{-0.6}^{+0.6}$. The oldest (1$^{\rm{st}}$-wave) bulges aremore compact than the youngest. Virtually all pure spheroids (i.e., thosewithout any disk) are coetaneous with the 2$^{\rm{nd}}$-wave bulges, presentinga median redshift of formation $z_{\rm{form}}={1.1}_{-0.3}^{+0.3}$. The twowaves of bulge formation are not only distinguishable in terms of stellar ages,but also in star formation mode. All 1$^{\rm st}$-wave bulges formed fast at$z\sim6$, with typical timescales around 200 Myr. A significant fraction of the2$^{\rm{nd}}$-wave bulges assembled more slowly, with star formation timescalesas long as 1 Gyr. The results of this work suggest that the centers of massivedisk-like galaxies actually harbor the oldest spheroids formed in the Universe.

We investigate the assembly history of massive disk galaxies and describe howthey shape their morphology through cosmic time. Using SHARDS and HST data, wemodeled the surface brightness distribution of 91 massive galaxies at redshift$0.14<z\leq 1$ in the wavelength range $0.5-1.6$ $\mu$m, deriving theuncontaminated spectral energy distributions of their bulges and disksseparately. This spectrophotometric decomposition allows us to compare thestellar populations properties of each component in individual galaxies. Wefind that the majority of massive galaxies ($\sim85\%$) builds inside-out,growing their extended stellar disk around the central spheroid. Some bulgesand disks could start forming at similar epochs, but these bulges grow morerapidly than their disks, assembling $80\%$ of their mass in $\sim0.7$ Gyr and$\sim3.5$ Gyr, respectively. Moreover, we infer that both older bulges andolder disks are more massive and compact than younger stellar structures. Inparticular, we find that bulges display a bimodal distribution of mass-weightedages, i.e., they form in two waves. In contrast, our analysis of the diskcomponents indicates that they form at $z\sim1$ for both first and second-wavebulges. This translates to first-wave bulges taking longer in acquiring astellar disk ($5.2$ Gyr) compared to second-wave less-compact spheroids ($0.7$Gyr). We do not find distinct properties (e.g., mass, star formation timescale,and mass surface density) for the disks in both types of galaxies. We concludethat the bulge mass and compactness mainly regulate the timing of the stellardisk growth, driving the morphological evolution of massive disk galaxies.