We study the radial structure of the stellar mass surface density ($mu$) and stellar population age as a function of the total stellar mass and morphology for a sample of 107 galaxies from the CALIFA survey. We use the fossil record to recover the st
ar formation history (SFH) in spheroidal and disk dominated galaxies with masses from 10$^9$ to 10$^{12}$ M$_odot$. We derive the half mass radius, and we find that galaxies are on average 15% more compact in mass than in light. HMR/HLR decreases with increasing mass for disk galaxies, but is almost constant in spheroidal galaxies. We find that the galaxy-averaged stellar population age, stellar extinction, and $mu$ are well represented by their values at 1 HLR. Negative radial gradients of the stellar population ages support an inside-out formation. The larger inner age gradients occur in the most massive disk galaxies that have the most prominent bulges; shallower age gradients are obtained in spheroids of similar mass. Disk and spheroidal galaxies show negative $mu$ gradients that steepen with stellar mass. In spheroidal galaxies $mu$ saturates at a critical value that is independent of the galaxy mass. Thus, all the massive spheroidal galaxies have similar local $mu$ at the same radius (in HLR units). The SFH of the regions beyond 1 HLR are well correlated with their local $mu$, and follow the same relation as the galaxy-averaged age and $mu$; suggesting that local stellar mass surface density preserves the SFH of disks. The SFH of bulges are, however, more fundamentally related to the total stellar mass, since the radial structure of the stellar age changes with galaxy mass even though all the spheroid dominated galaxies have similar radial structure in $mu$. Thus, galaxy mass is a more fundamental property in spheroidal systems while the local stellar mass surface density is more important in disks.
In a companion paper we have presented many products derived from the application of the spectral synthesis code STARLIGHT to datacubes from the CALIFA survey, including 2D maps of stellar population properties and 1D averages in the temporal and spa
tial dimensions. Here we evaluate the uncertainties in these products. Uncertainties due to noise and spectral shape calibration errors and to the synthesis method are investigated by means of a suite of simulations based on 1638 CALIFA spectra for NGC 2916, with perturbations amplitudes gauged in terms of the expected errors. A separate study was conducted to assess uncertainties related to the choice of evolutionary synthesis models. We compare results obtained with the Bruzual & Charlot models, a preliminary update of them, and a combination of spectra derived from the Granada and MILES models. About 100k CALIFA spectra are used in this comparison. Noise and shape-related errors at the level expected for CALIFA propagate to 0.10-0.15 dex uncertainties in stellar masses, mean ages and metallicities. Uncertainties in A_V increase from 0.06 mag in the case of random noise to 0.16 mag for shape errors. Higher order products such as SFHs are more uncertain, but still relatively stable. Due to the large number statistics of datacubes, spatial averaging reduces uncertainties while preserving information on the history and structure of stellar populations. Radial profiles of global properties, as well as SFHs averaged over different regions are much more stable than for individual spaxels. Uncertainties related to the choice of base models are larger than those associated with data and method. Differences in mean age, mass and metallicity are ~ 0.15 to 0.25 dex, and 0.1 mag in A_V. Spectral residuals are ~ 1% on average, but with systematic features of up to 4%. The origin of these features is discussed. (Abridged)
