© ESO, 2015

1. Introduction

Galaxies are a complex mix of stars, gas, dust, and dark matter distributed in different components (bulge, disk, and halo) whose present day structure and dynamics are intimately linked to their assembly and evolution over the history of the Universe. Different observational and theoretical approaches can be followed to learn how galaxies form and evolve.

Theoretically, the formation of large-scale structures arise through the evolution of cold dark matter. In this picture, small-scale density perturbations in the dark matter collapse and form the first generation of dark matter halos, which subsequently merge to form larger structures such as clusters and superclusters 126; 34. This basic hierarchical picture explains the global evolution of the star formation rate density of the universe, with galaxy peak formation epoch at redshift 2−3 e.g. 82, and references therein. The stellar components formed at earlier epochs likely evolved into elliptical galaxies and bulges through mergers of the primordial star-forming disks 37; 16. However, this framework fails to explain how the galaxy population emerges at z ~ 1, and how the present day Hubble sequence of galaxies was assembled.

The growth of galaxies is not related in a simple way to the build up of dark matter; the interplay of energy and matter exchange (between the process of gas accretion and cooling and star formation) is essential for the growth the gaseous and stellar components in galaxies. Feedback mechanisms resulting from stellar winds, supernova explosions, and AGN are relevant to stop the gas collapse and cooling, quenching the star formation and hence galaxy growth 124; 67. Although these processes are difficult to implement in theoretical models, they are essential to explain the masses, structures, morphologies, stellar populations, and chemical compositions of galaxies, and the evolution of these properties with cosmic time.

Recently, a new set of cosmological hydrodynamic simulations have started to predict how the spatially resolved information of the properties of stellar populations in galaxies can constrain the complex interplay between gas infall, outflows, stellar migration, radial gas flows, and star formation efficiency, in driving the inside-out growth of galactic disks 19; 48; 43; 105; 89. Radiative cooling, star formation, feedback from supernovae, and chemical enrichment are also included in simulations to predict radial metallicity gradients as a function of merging history. Shallow metallicity gradients are expected if elliptical galaxies result from major mergers e.g. 74, but a minor merger picture for the formation of ellipticals can successfully explain the strong size evolution of massive galaxies 98. This late-time accretion of low-mass and metal poor galaxies (dry mergers) into the already formed massive galaxy can produce a variation of the age and metallicity radial structure of the galaxy as it increases in size. Galactic stellar winds and metal cooling also have an important effect on these ex situ star formation models, predicting different behavior of the mass and metallicity assembly in massive early-type galaxies, and in the radial gradient of present stellar populations properties of galaxies 64; 65.

In summary, these theoretical works show that observational data with spatial information of the mass and metallicity assembly and their cosmic evolution, and the present radial structure of stellar population properties (stellar mass surface density, age, metallicity) contain relevant information to constrain the formation history of galaxies and the physics of feedback mechanisms involved.

Observationally, a first step is to study what kinds of galaxies are there in the Universe, and which are their physical properties. Attending to their form and structure, galaxies can be grouped into a few categories. Results show that most of the massive nearby galaxies are ellipticals, S0’s, or spirals 14 following the Hubble tuning-fork diagram. In this scheme, S0’s are a transition between spirals and ellipticals 23, and the bulge/disk ratio increases from late to early-type spirals. At the same time, galaxy properties such as color, mass, surface brightness, luminosity, and gas fraction are correlated with Hubble type 110, suggesting that the Hubble sequence somehow reflects possible paths for galaxy formation and evolution. However, the processes structuring galaxies along the Hubble sequence are still poorly understood.

Integral field spectroscopy (IFS) enables a leap forward, providing 3D information (2D spatial + 1D spectral) on galaxies. These datacubes allow one to recover two-dimensional maps of stellar mass surface density, stellar ages, metallicities, extinction and kinematics, as well as a suit of nebular properties, such as gas kinematics, metallicity, excitation, etc. Until a few years ago, IFS was used to target small samples of galaxies. Detailed programs, such as SAURON 7, VENGA 13, (U)LIRs at z ≤ 0.263, PINGS 111, or DiskMass Survey 12, have been limited to less than a hundred galaxies, but it is more than fair to recognize that to get these amounts of IFU data was a challenge at the time. ATLAS3D 22 represented a step forward, with the observation of a volume-limited sample of 260 galaxies, but with three important limitations: the sample only includes early-type galaxies, the field of view is limited to 1 effective radius, and the spectral range is restricted from Hβ to [NI]λ5200.

CALIFA (Calar Alto Legacy Integral Field Area) is our ongoing survey of 600 nearby galaxies at the 3.5 m at Calar Alto 114¹. The data set provided by the survey (see Husemann et al. , for DR1; García-Benito et al. for DR2) is unique to advance in these issues not only because of its ability to provide spectral and spatial information, but also because of the following: a) It includes a large homogeneous sample of galaxies across the color-magnitude diagram, covering a large range of masses 10⁹ to 10¹² M_⊙, 56, and morphologies from Ellipticals (E0-E7), Lenticulars (S0-S0a), to spirals (Sa to Sm; see Walcher et al. for a general description of the sample). b) It has a large field of view (74′′ × 65′′) with a final spatial sampling of 1 arcsec, and a resolution of ~ 2.5 arcsec, allowing it to spatially resolve the stellar population properties well, and to obtain the total integrated properties, such as galaxy stellar mass, and stellar metallicity. c) It covers the whole rest-frame optical wavelength at intermediate spectral resolution, including the most relevant absorption diagnostics for deriving the stellar population properties.

Previous papers in this series used the first ~100 datacubes of the survey to derive spatially resolved stellar population properties by means of full spectral fitting techniques. We obtained the following: 1) massive galaxies grow their stellar mass inside-out. The signal of downsizing is shown to be spatially preserved, with both inner and outer regions growing faster for more massive galaxies. The relative growth rate of the spheroidal component (nucleus and inner galaxy), which peaked 5–7 Gyr ago, shows a maximum at a critical stellar mass M_⋆ ~ 7 × 10¹⁰ M_⊙104. 2) The inside-out scenario is also supported by the negative radial gradients of the stellar population ages 56. 3) Global and local relations between stellar mass, stellar mass surface density, and stellar metallicity relation were investigated, along with their evolution (as derived from our fossil record analysis). In disks, the stellar mass surface density regulates the ages and the metallicity. In spheroids, the galaxy stellar mass dominates the physics of star formation and chemical enrichment 56; 54. 4) In terms of integrated versus spatially resolved properties, the stellar population properties are well represented by their values at 1 HLR 56; 54. The CALIFA collaboration has also compared the age and metallicity gradients in a subsample of 62 face-on spirals and it was found that there is no difference between the stellar population properties in barred and unbarred galaxies 119.

In this paper, we extend our study of the spatially resolved star formation history (SFH) of CALIFA galaxies to derive the radial structure of the stellar population properties as a function of Hubble type, and galaxy stellar mass, M_⋆. The goals are: 1) to characterize in detail the radial structure of stellar population properties of galaxies in the local universe; 2) to find out how these properties are correlated with Hubble type, and if the Hubble sequence is a scheme to organize galaxies by mass and age, and/or mass and metallicity; 3) to establish observational constraints to galaxy formation models via the radial distributions and gradients of stellar populations for disk and bulge dominated galaxies.

This paper is organized as follows: Sect. 2 describes the observations and summarizes the properties of the CALIFA galaxies analyzed here. In Sect. 3 we summarize our method for extracting the SFH, based on the fossil record method, and we explain the main differences between the analysis presented here and that in previous works. Section 4 presents results on the galaxy stellar mass, half-light, and half-mass radii (HLR, HMR, respectively), and galaxy averaged stellar metallicity. Section 5 deals with the spatially resolved properties of the stellar population: stellar mass surface density, μ_⋆; luminosity weighted mean age, ⟨log age⟩_L; mass weighted mean metallicity, ⟨log Z_⋆⟩_M; and stellar extinction, A_V. We discuss the results in Sect. 6; and Sect. 7 presents the conclusions.

2. Sample, observations, and data reduction

2.1. Sample and morphological classification

The CALIFA mother sample consists of 939 galaxies selected from SDSS survey in the redshift range z = 0.005–0.03, and with r-band angular isophotal diameter of 45−80′′. These criteria guarantee that the objects fill the 74′′ × 64′′ FoV well. The sample includes a significant number of galaxies in different bins in the color-magnitude diagram (CMD), ensuring that CALIFA spans a wide and representative range of galaxy types.

The galaxies were morphologically classified as Ellipticals (E0–7), Spirals (S0, S0a, Sab, Sb, Sbc, Sc, Scd, Sd, Sm), and Irregulars (I). The classification was carried out through visual inspection of the r-band images averaging the results (after clipping outliers) from five members of the collaboration. Galaxies are also classified as B for barred, otherwise A, or AB if it is unsure, and as M if it shows “merger” or “interaction features” 138.

The sample for this paper comprises the 312 CALIFA galaxies observed in both V1200 and V500 setups as of January 2014. The 12 galaxies showing “merger or interacting features” are not discussed here, leaving a main sample of 300 objects with a well defined morphology. For this work we have grouped galaxies into seven morphology bins: E, S0 (including S0 and S0a), Sa (Sa and Sab), Sb, Sbc, Sc (Sc and Scd), and Sd (13 Sd, 1 Sm and 1 Irr).

Figure 1 shows that these 300 galaxies provide a fair representation of the CALIFA survey as a whole. The left panel shows scaled histograms of the Hubble type in the mother sample (empty bars) and in our sample (filled bars). The number of objects in each morphology bin for our sample is indicated at the top, with a brown to blue color palette that represents Hubble types from ellipticals to late spirals. This same color scheme is used throughout this paper. The similarity of the distributions reflects the random sampling strategy of CALIFA, with targets picked from the mother sample on the basis of visibility criteria alone. The right panel in Fig. 1 shows the u − r versus M_r CMD, with grey points representing the mother sample and colored points the 300 galaxies. As for the Hubble type distribution, a simple visual inspection shows that our subsample is representative of the full CALIFA sample in terms of CMD coverage.

2.2. Observations and data reduction

The observations were carried out with the Potsdam Multi-Aperture Spectrometer 112, PMAS in the PPaK mode 137 at the 3.5 m telescope of Calar Alto observatory. PPaK contains 382 fibers of 2.7′′ diameter each, and a 74′′ × 64′′ FoV 73. Each galaxy is observed with two spectral settings, V500 and V1200, with spectral resolutions ~ 6 Å (FWHM) and 2.3 Å, respectively. The V500 grating covers from 3745 to 7300 Å, while the V1200 covers 3650−4840 Å. Detailed descriptions of the observational strategy and of the data can be found in Sánchez et al. , and Husemann et al. .

The datacubes analyzed here have been calibrated with version 1.5 of the reduction pipeline. The main issues addressed by this new version are: (i) correction of the sensitivity curve for the V500 grating; (ii) new registering method to determine, for each galaxy, the relative positioning of the three pointings of the dithering pattern, and absolute WCS registration; (iii) a new cube interpolation method. CALIFA pipeline v1.5 improves the flux calibration to an accuracy of 2−3% and is the current official data release. A detailed account of this new pipeline is presented in the Data Release 2 article 46.

To reduce the effects of vignetting on the data, we combine the observations in the V1200 and V500 setups. The combined datacubes were processed as described in Cid Fernandes et al. . Our analysis requires that spectra have signal-to-noise ratio S/N ≥ 20 in a 90 Å window centered at 5635 Å (rest-frame). When individual spaxels do not meet this S/N threshold, they are coadded into Voronoi zones 21. Further pre processing steps include spatial masking of foreground and background sources, rest-framing, and spectral resampling. The resulting 253 418 spectra were then processed through starlight and pycasso (the Python CALIFA starlight Synthesis Organizer), producing the stellar population properties discussed here as described in detail in the next section.

3. Stellar population analysis: differences with respect to previous work

Our method to extract stellar population properties from datacubes has been explained and applied to CALIFA in Pérez et al. , Cid Fernandes et al. ; , and González Delgado et al. ; . In short, we analyze the data with the starlight code 30, which fits an observed spectrum (O_λ) in terms of a model (M_λ) built by a nonparametric linear combination of N_⋆ simple stellar populations (SSP) from a base spanning different ages (t) and metallicities (Z). Dust effects are modeled as a foreground screen with a Cardelli et al. reddening law with R_V = 3.1. Windows around the main optical emission lines and the NaI D absorption doublet (because of its interstellar component) are masked in all spectral fits². Bad pixels (identified by the reduction pipeline) are also masked. Results for each spectrum are then packed and organized with the pycasso pipeline.

This working scheme is preserved here, but with three new developments:

• 1.

  The datacubes come from the version 1.5 of the reduction pipeline 46.

• 2.

  Larger and more complete SSP bases are employed.

• 3.

  A somewhat different definition of mean stellar metallicity is adopted see 54.

This section describes the novelties related to the stellar population synthesis. Improvements resulting from the new reduction pipeline are described in Appendix A.

3.1. SSP spectral bases

SSP models are a central ingredient in our analysis, linking the results of the spectral decomposition to physical properties of the stellar populations. Our previous applications of starlight to CALIFA explored spectral bases built from three sets of SSP models, labeled as GM, CB, and BC in Cid Fernandes et al. . The first two are used again here, but extended to a wider range of metallicities, producing what we denote as bases GMe and CBe.

Base GMe is a combination of the SSP spectra provided by Vazdekis et al. for populations older than t = 63 Myr and the González Delgado et al. models for younger ages. The evolutionary tracks are those of Girardi et al. , except for the youngest ages (1 and 3 Myr), which are based on the Geneva tracks 121; 120; 28. The Initial Mass Function (IMF) is Salpeter. In our previous studies of the first 100 CALIFA galaxies, we defined base GM as a regular (t,Z) grid of these models, with 39 ages spanning t = 0.001−14 Gyr and four metallicities from 0.2 to 1.5 Z_⊙. We now extend the Z range to use of all seven metallicites provided by Vazdekis et al. models: log Z/Z_⊙ = −2.3, −1.7, −1.3, −0.7, −0.4, 0, and + 0.22. Because these models lack ages below 63 Myr, these young ages are only covered by the four largest metallicities, such that our extended GM base is no longer regular in t and Z. Base GMe contains N_⋆ = 235 elements.

Base CBe is built from an update of the Bruzual & Charlot models (Charlot & Bruzual 2007, private communication), replacing STELIB 81 with a combination of the MILES 116; 41 and granada 85 spectral libraries (the same ones used in base GMe). The evolutionary tracks are those collectively known as Padova 1994 1; 17; 39; 40; 50. The IMF is that of Chabrier . Whereas in previous works we limited the Z range to ≥ 0.2 solar, we now extend this base to six metalicities: log Z/Z_⊙ = −2.3, −1.7, −0.7, −0.4, 0, and + 0.4. Base CBe contains N_⋆ = 246 elements (41 ages from 0.001 to 14 Gyr and the six metallicities above).

The main similarities and differences between bases GMe and CBe are the same as between the original GM and CB bases, which are thoroughly discussed in Cid Fernandes et al. . Throughout the main body of this paper we focus on results obtained with base GMe, but we anticipate that our overall qualitative findings remain valid for base CBe. The role of base CBe is to enable a rough assessment of the uncertainties associated with the model choice.

A minor technical difference with respect to our previous analysis is that we now smooth the spectral bases to 6 Å FWHM effective resolution prior to the fits. This is because the kinematical filter implemented in starlight operates in velocity-space, whereas both CALIFA and the SSP model spectra have a constant spectral resolution in λ-space, so that effects of the instrumental broadening can only be mimicked approximately by starlight. We have verified that this modification does not affect the stellar population properties used in this paper.

Appendix B presents some comparisons of the results obtained with these two bases. Experiments were also performed with bases which extend the age range to 18 Gyr and configure starlight to allow negative values of A_V. These tests are also discussed in Appendix B, which adds to the collection of “sanity checks” on the results of our analysis.

4. Galaxy mass, metric, and stellar metallicity

This section addresses three relatively unrelated aspects, which are all important to better understand the results presented in the next section, where we examine how the spatial distribution of stellar population properties relates to a galaxy’s stellar mass and morphology. First, Sect. 4.1 reviews the relation between stellar mass and morphological type for our sample. This strong relation is imprinted on virtually all results discussed in Sect. 5. Second, Sect. 4.2 compares our measurements of the HLR and HMR. As discussed by González Delgado et al. , these two natural metrics for distances are not identical because of the inside-out growth of galaxies. Here we inspect how the HMR/HLR ratio varies as a function of Hubble type and stellar mass in our sample. Finally, Sect. 4.3 presents our definition of mean stellar metallicity. González Delgado et al. showed that stellar mass surface densities, mean ages, and extinction values defined from the integrated spectrum, from galaxy-wide spatial averages, and measured at R = 1 HLR all agree very well with each other. Here we extend this test to stellar metallicities. Throughout this section, results for the two SSP models discussed in Sect. 3.1 are presented.

4.1. Stellar masses

To obtain the total stellar mass of a galaxy, we add the mass in each zone, thus taking spatial variations of the stellar extinction and M/L ratio into account. Masked spaxels (e.g., foreground stars) are accounted for using the μ_⋆ radial profile as explained in González Delgado et al. .

Figure 2 shows the distribution of M_⋆ as a function of Hubble type. Table 1 shows the distribution of galaxies by Hubble type in several bins of M_⋆. The masses range from 7 × 10⁸ to 7 × 10¹¹ M_⊙ for fits with GMe (Salpeter IMF). CBe-based masses (Chabrier IMF) are on average smaller by a factor 1.84. As for the general galaxy population, mass is well correlated with Hubble type, decreasing from early to late types. High bulge-to-disk ratios (E, S0, Sa) are the most massive ones (≥ 10¹¹ M_⊙), while galaxies with small bulges (Sc–Sd) have M_⋆ ≤ 10¹⁰ M_⊙. The average log M_⋆(M_⊙) is 11.4, 11.1, 11.0, 10.9, 10.7, 10.1, and 9.5 for E, S0, Sa, Sb, Sbc, Sc, and Sd, respectively. The dispersion is typically 0.3 dex, except for Sc galaxies, which have a dispersion of ~ 0.5 dex.

Because CALIFA is not complete for M_r ≥ −19.5, this distribution in mass is not completely representative of the local Universe. In particular, it is important to remember that dwarf ellipticals are not included, so M_⋆ or any other property discussed here for E’s are restricted to massive ellipticals.

4.2. The HMR/HLR

As explained in Cid Fernandes et al. , we define the HLR as the semi-major axis length of the elliptical aperture which contains half of the total light of the galaxy at the rest-frame wavelength 5635 Å. Similarly, the HMR is derived from the 2D distribution of the stellar mass, as the elliptical aperture at which the mass curve of growth reaches 50% of its asymptote. The ratio between the HMR and the HLR (/) reflects the spatial variation of the SFH in a galaxy. This ratio is lower than 1 in almost all cases 56, a signpost of the inside-out growth found by Pérez et al. .

Figure 3 shows the relation between / and Hubble type (left panel), and galaxy stellar mass (right panel). These plots confirm our earlier finding that galaxies are more compact in mass than in light. If the gradient in stellar extinction is taken into account, the average / for base GMe (CBe). Figure 3 shows that the ratio decreases from late to early-type spirals; while lenticulars and ellipticals have similar /.

These results are also in agreement with our previous result, which / shows a dual dependence with galaxy stellar mass: it decreases with increasing mass for disk galaxies, but is almost constant in spheroidal galaxies, as confirmed in the right panel of Fig. 3. Sb–Sbc galaxies are those with the lowest /.

4.3. Stellar metallicity

Metallicity is one of the most difficult stellar population properties to estimate. Reasons for this include: (i) the coarse metallicity grid of the SSP bases; (ii) the limitation of the stellar libraries to the solar neighborhood; and (iii) inherent degeneracies like the dependence of the continuum shape on extinction, age, and metallicity, whose effects are hard to disentangle. Notwithstanding these difficulties, meaningful estimates of Z_⋆ can be extracted from observed spectra, particularly by means of full spectral synthesis methods (Sánchez-Blázquez et al. ).

starlight-based estimates of Z_⋆ for the same CALIFA sample used in this paper were previously used by González Delgado et al. to study global and local relations of Z_⋆ with the stellar mass and stellar mass surface density. We have shown there that: (i) our sample follows a well defined stellar mass-metallicity relation (MZR); (ii) this relation is steeper that one obtained from O/H measurements in HII regions, but that considering only young stellar populations the two MZR’s are similar; and (iii) Z_⋆ is strongly related to μ_⋆ in galaxy disks and to M_⋆ in spheroids. All these results lend confidence to our Z_⋆ estimates.

Here we review our definition of the mean stellar metallicity, and test whether its value at 1 HLR matches the galaxy wide average value as well as at obtained from the spatially collapsed data cube.

4.3.1. Mean stellar metallicity

The main properties analyzed in this paper are the stellar mass surface density (μ_∗), stellar extinction (A_V), mean age (⟨log age⟩_L), and metallicity of the stellar population, whose spatial distributions are studied as a function of Hubble type and total stellar mass (M_⋆). These properties were defined in previous articles in this series. For instance, the mean light weighted log stellar age is defined as (1)Eq. (9) of 31, where x_tZ is the fraction of flux at the normalization wavelength (5635 Å) attributed to the base element with age t and metallicity Z. The mass-weighted version of this index, ⟨ log age⟩_M, is obtained by replacing x_tZ by its corresponding mass fraction m_tZ.

While Cid Fernandes et al. average the base metallicities linearly (their Eq. (10)), as in González Delgado et al. , we employ a logarithmic average: (2)for the mass-weighted mean log Z_⋆ and (3)for the luminosity-weighted mean log Z_⋆. The motivation to use this definition is that the extended SSP bases used in this study span a much wider dynamical range in Z_⋆ (nearly three orders of magnitude, compared to barely one in our previous papers), which is better handled with a geometric mean (implicit in the use of the logarithm). This is the same reasoning behind the use of ⟨ log age ⟩ instead of log ⟨ age ⟩.

To some degree, the definition of mean Z is largely a matter of taste (albeit one with mathematical consequences because of the inequality of the arithmetic and geometric means, ⟨ log Z ⟩ ≤ log  ⟨ Z ⟩), so much so that one finds both types of averaging in the literature. For instance, in Gallazzi et al. metallicities are averaged logarithmically, whereas Asari et al. work with arithmetic averages.

As shown in González Delgado et al. (2014; see also Fig. 4), our metallicities span about 1 dex for galaxy masses ranging from 10⁹ to 10¹² M_⊙, with an MZR which matches well the stellar metallicities of both Milky Way and LMC-like galaxies.

4.3.2. Galaxy averaged stellar metallicity

González Delgado et al. obtained the important result that galaxy-averaged stellar ages, mass surface density, and extinction are well matched by the corresponding values of these properties at R = 1 HLR and also with the values obtained from the analysis of the integrated spectrum (i.e., the one obtained by collapsing the datacube to a single spectrum). The general pattern, therefore, is that galaxy averaged properties match both the values at 1 HLR and those obtained from integrated spectra. Do our stellar metallicities comply with this rule?

To answer this question, we first define the galaxy-wide average stellar metallicity following Eq. (2) in González Delgado et al. , which gives the mass-weighted mean value of ⟨ log Z_⋆,xy⟩_M as (4)where M_⋆,xy is the stellar mass in spaxel xy.

Figure 4 compares our results for with the mass-weighted mean ⟨ log Z_⋆⟩_M values obtained at R = 1 HLR (, bottom panels) and those derived from the integrated spectrum (, top panels), analyzed in the exact same way as the individual zone spectra. Results are shown for both base GMe (left panels) and CBe (right).

The agreement is remarkable. The galaxy averaged metallicity and at 1 HLR are the same to within a dispersion of 0.1 dex. The integrated metallicity also matches the galaxy averaged value with only slightly larger dispersions. The largest deviations occur for low-metallicity systems. Similar conclusions are reached if the comparison in Fig. 4 is done using the light weighted version of Eq. (4), (5)where L_⋆,xy is the luminosity (corrected by stellar extinction) in each spaxel evaluated at a reference wavelength (5635 Å in our case).

The stellar metallicities behave as expected, in the sense that like other properties, their galaxy-wide averages match the values at R = 1 HLR, and also the values derived from integrated spatially unresolved spectroscopy 56. We thus conclude that galaxy-wide spatially averaged stellar population properties (stellar mass, mass surface density, age, metallicity, and extinction) match those obtained from the integrated spectrum, and that these spatially averaged properties match those at R = 1 HLR, proving that effective radii are really effective 55.

5. Spatially resolved stellar population properties as a function of morphology and mass

This section presents a series of results derived from our spatially resolved spectral synthesis analysis of CALIFA galaxies. We focus on the following four stellar populations properties: mass surface density (μ_∗, Sect. 5.1), mean ages (⟨log age⟩_L, Sect. 5.2), metallicities (⟨log Z_⋆⟩_M, Sect. 5.3), and extinction (A_V, Sect. 5.4). Each of these properties is studied by means of (i) 2D maps of the individual galaxies; (ii) radial profiles; and (iii) radial gradients. Throughout the section, the emphasis is on evaluating and comparing the roles of morphology and total stellar mass in shaping the observed behavior of these four properties. Before discussing the results, we briefly explain how these quantities are obtained and how they are presented.

2D maps in the CMD: using pycasso we obtain, for each galaxy, 2D maps of each of the four properties. The results for all the galaxies are presented in the framework of the color-magnitude diagram, where each map is placed at the galaxy’s coordinates in the u − r vs. M_r CMD. Because absolute magnitude is related to M_⋆ and redder galaxies are (usually) older and more metal rich, these plots show the correlations M_⋆-μ_⋆, M_⋆-age, and M_⋆-metallicity in a 2D fashion. Because in our sample the galaxy Hubble type is correlated with color and luminosity, these plots not only show how the galaxy averaged properties and their radial structure change with the galaxy stellar mass, but also with the morphological type. These maps are shown in the Appendix C (Figs. C.1−C.4).

Radial profiles: each 2D map is azimuthally averaged to study the radial variations of each of the four stellar population properties. Elliptical apertures 0.1 HLR in width are used to extract the radial profiles, with ellipticity and position angle obtained from the moments of the 5635 Å flux image. Expressing radial distances in units of HLR allows the profiles of individual galaxies to be compared on a common metric, as well as averaging (“stacking”) them as a function of Hubble type or stellar mass. Radial profiles expressed in units of the HMR were also analyzed and lead to similar shapes, so all profiles presented below use HLR as the unit for radius.

Radial gradients: inner and outer gradients are defined as differences between the values at R = 1 and 0 (▽ _in), and R = 2 and 1 (▽ _out), respectively. For instance, for log μ_⋆, and similarly for ⟨log age⟩_L, ⟨log Z_⋆⟩_M and A_V. Defined in this way, the gradients have units of dex/HLR (mag/HLR for ▽ A_V). Since the stellar population properties of galaxies at 1 HLR represent very well the galaxy-wide average, ▽ _in (▽ _out) effectively measures how the bulge (disk) properties change with respect to those of the galaxy as a whole³.

Unless otherwise noted, all results reported below are for the GMe base, although the whole analysis was carried out with properties derived with both sets of SSP models discussed in 3.1. Differences between GMe and CBe SSPs are as: (a) The stellar mass surface density is lower with CBe than with GMe by 0.27 dex on average, mostly due to the different IMFs (Salpeter in GMe versus Chabrier in CBe). (b) Variations in stellar extinction are negligible. (c) CBe yields somewhat younger ages and higher metallicities than GMe, by an average of 0.14 dex in ⟨log age⟩_L and 0.12 dex in ⟨log Z_⋆⟩_M. These shifts reflect the age-metallicity degeneracy, and are mainly a consequence of the different sets of metallicities available in these bases. However, radial gradients are not affected by this degeneracy. A detailed comparison of properties derived with the two bases is given in Appendix B.

5.1. Stellar mass surface density

2D maps of the stellar mass surface density for the 300 individual galaxies of our sample are presented in the Appendix C (Fig. C.1). Here we discuss the radial structure of log μ_⋆ as a function of Hubble type and M_⋆.

5.1.1. μ_⋆-morphology and μ_⋆-mass relations

Figure 5 shows how μ_⋆ measured at 1 HLR changes with Hubble type (left panel), and with the galaxy stellar mass (right). Recall from González Delgado et al. that properties measured at 1 HLR match the corresponding galaxy-wide average value very well, so these plots ultimately show how the global μ_⋆ depends on the morphology and on M_⋆.

The plot shows increasing from late spirals to spheroids, with average and dispersion values of 3.1 ± 0.2, 3.10 ± 0.18, 3.05 ± 0.25, 2.70 ± 0.17, 2.65 ± 0.24, 2.40 ± 0.28, 2.04 ± 0.27, for E, S0, Sa, Sb, Sbc, Sc, and Sd, respectively. Note that E and S0 are remarkably similar.

Surface densities also increase with M_⋆, as seen in the right panel of Fig. 5. The overall relation is relatively smooth, with no evidence of an abrupt change of behavior as that discussed by Kauffmann et al. for SDSS galaxies. Figure 5, however, reveals that morphology is also behind the dispersion in the μ_⋆ − M_⋆ relation. The black line shows the relation for the full sample, obtained by averaging log μ_⋆ in 0.4 dex-wide bins in mass, while the big circles break this general relation into different (color-coded) morphological types for the same mass bins. Despite the reduced statistics, it is evident that: (a) for the same stellar mass, early-type galaxies are denser than late-type galaxies; and (b) Sa and earlier type galaxies exhibit a much flatter μ_⋆ − M_⋆ relation than later types. The overall impression from these results is that morphology, and not only stellar mass, plays a fundamental role in defining stellar surface densities, and it is responsible for the change of slope in the SDSS μ_⋆ − M_⋆ relation.

5.1.2. Radial profiles

Azimuthally averaged radial profiles of log μ_⋆ are shown in Fig. 6. Results are stacked by Hubble type (left panel) and mass (right). In the left panel galaxies are grouped in our seven morphological classes. The typical dispersion within these bins is illustrated by the error bar, which shows the standard deviation in log μ_⋆ (R = 1 HLR) for galaxies of the Sa class.

A clear trend with Hubble type is seen: the μ_⋆(R) profiles scale with Hubble type from late to early spirals, and this modulation with morphology is preserved at any given distance. E and S0 have remarkably similar profiles, with core and extended envelope equally dense at any given distance, suggesting that the disk of S0 galaxies and the extended envelope of ellipticals have grown their mass by similar processes.

The right panel of Fig. 6 shows the radial profiles grouped in seven bins of stellar mass spanning the log M_⋆(M_⊙) = 9.1−11.8 range. These also show that the average of log μ_⋆(R) is modulated by M_⋆. However, this μ_⋆(R)–M_⋆ modulation breaks for early-type galaxies (concentration index C (r₉₀/r₅₀) ≥ 2.8; see also Fig. 13 in González Delgado et al. ), which in our sample are populated mainly by E and S0, and some Sa. On the other hand, these early types are all massive, with M_⋆ ≥ 10¹¹ M_⊙.

5.1.3. Radial gradients

Inner (0–1 HLR) and outer (1–2 HLR) gradients in log μ_⋆, as defined by Eqs. (6) and (7), are plotted as a function of morphology and stellar mass in Fig. 7. ▽ _inlog μ_⋆ values (corresponding to the core region) are plotted in grey-red, while ▽ _outlog μ_⋆ (which trace the disks of spirals and S0 and the extended envelope of ellipticals) are plotted in grey-blue. Circles and stars show results for bases GMe and CBe, respectively, illustrating that the resulting gradients are nearly identical even though these bases yield different absolute values of μ_⋆.

A clear correlation exists between ▽ _inlog μ_⋆ and Hubble type. The gradient in the inner HLR increases (in absolute values) significantly from late to early spirals, converging to a constant value for E and S0. This relation reflects the variation of the bulge to disk ratio in spirals, and the dominance of the bulge component in spheroids (S0 and E). The outer gradient is weaker (smaller in absolute value) than the inner gradient, as expected if a disk component dominates the mass outward of 1 HLR.

The right panel of Fig. 7 shows the relation between the inner gradient and stellar mass. There is a clear increase (in absolute values) of ▽ _inlog μ_⋆ with M_⋆, with the more massive galaxies having a steeper increase of the central density. The dispersion with respect to the average values (black crosses) within M_⋆-bins is significant. To check the effect of morphology on this dispersion we have averaged ▽ _inlog μ_⋆ in mass intervals for each Hubble type and plotted the resulting averages (large colored circles). The general trend that emerges is that, for galaxies of the same mass, early type galaxies tend to be overall centrally denser than later types, in agreement with Fig. 5; although, there are a few intervals of stellar mass (e.g. log M_⋆ = 11.4 M_⊙), in which the variations in ▽ _inlog μ_⋆ with Hubble type are not significant.

It is also worth mentioning that ▽ _inlog μ_⋆ in Sa and Sb is very close to that in S0 and E, and in this sense it would be easy to fade early-type spirals into S0’s.

5.2. Ages of the stellar populations

2D maps of the luminosity-weighted mean log stellar ages (Eq. (1)) for the 300 galaxies are presented in Fig. C.2. Here we discuss the radial structure of ⟨log age⟩_L and its relation to Hubble type and M_⋆. The presentation follows the same script used in the presentation of μ_⋆-related results in Sect. 5.1.

5.2.1. Age-morphology and age-mass relations

Figure 8 shows how the mean age of the stellar populations at 1 HLR changes along the Hubble sequence (left panel), and with the galaxy stellar mass (right). Similar to , ⟨log age⟩_L^HLR represents well the galaxy-wide averaged stellar population age (⟨log age⟩_L^galaxy, González Delgado et al. ).

Clearly, ⟨log age⟩_L^HLR scales with Hubble type, increasing steadily from Sd to Sa. S0 and ellipticals have stellar populations of similar mean age, and they are older than spirals. The average and dispersion values of ⟨log age⟩_L^HLR (yr) are 8.62 ± 0.22, 8.89 ± 0.22, 9.07 ± 0.19, 9.33 ± 0.21, 9.55 ± 0.19, 9.71 ± 0.11, and 9.74 ± 0.11, for Sd, Sc, Sbc, Sb, Sa, S0, and E, respectively.

Mean ages also increase with the galaxy mass (right panel of Fig. 8), a “downsizing” behavior that has been confirmed with widely different samples and methods. For instance, our age-mass relation is similar to that derived for SDSS galaxies by Gallazzi et al. , their Fig. 8;. They found that there is a transition at M_⋆ ~ 3 × 10¹⁰ M_⊙⁴, below which galaxies are typically young and above which they are old. This is the same mass at which Kauffmann et al. find the μ_⋆ − M_⋆ relation to flatten.

Unlike in these SDSS-based works, we do not see sharp transitions as a function of M_⋆ in neither μ_⋆ nor ⟨log age⟩_L, although differences in sample selection and statistics prevent a proper comparison. We do, however, note a common behavior in the right panels of Figs. 5 and 8, in the sense that the dispersion above ~ 10¹⁰M_⊙ is strongly related to morphology.

Like in Fig. 5 (right panel), the black line in the right panel of Fig. 8 shows the age-mass relation for the whole sample, obtained by averaging ⟨log age⟩_L^HLR values in M_⋆ bins. Small dots show individual galaxies, while the large colored circles represent the mass-binned average ⟨log age⟩_L^HLR for each Hubble type. As with the μ_⋆ − M_⋆ relation, breaking the age-mass relation into morphological types reveals clean trends. In this case, we see that, for a fixed M_⋆, earlier type galaxies are older than later types. The corollary is that mass is not the sole property controlling the SFH of a galaxy. In fact, given the ~flat age-mass relations for Sa, S0, and E, morphology seems to be a more relevant factor, at least in these cases.

5.2.2. Radial profiles

Figure 9 shows the age radial profiles obtained by stacking galaxies as a function of Hubble type and mass. The ⟨log age⟩_L(R) profiles scale with Hubble type, but by different amounts at the center than at 1 HLR. At any radial distance, however, the early-type galaxies are older than later-ype galaxies. E and S0 are again very similar at all radii. This suggests that E and S0 have similar histories not only on average, but also spatially resolved, at least in the inner 2 HLR. Negative age gradients are detected in all galaxies (except perhaps in Sd, whose ages profiles are flatter than in the other spirals⁵). These negative gradients reflect the inside-out growth of galaxies. Furthermore, the decrease of ⟨log age⟩_L with R indicates that quenching happens earlier at the galaxy center; and also earlier in early-type galaxies (spheroids and Sa) than in later-type spirals (Sbc–Sc).

The radial profiles also show a clear trend with M_⋆ (Fig. 9, right), with the more massive galaxies being older everywhere, hence preserving the downsizing pattern at all radial distances. Comparing the left and right panels in Fig. 9, one sees that grouping galaxies by their stellar mass leads to a reduced vertical stretch in their ⟨log age⟩_L(R) profiles than when the averaging is done by morphology. But the profiles expand to a similar vertical scale if galaxies earlier than Sd and more massive than 10^9.6 M_⊙ are considered indicating that the effect of morphology and stellar mass are not easily disentangled here. However, in Sect. 6.3, Fig. 20 shows that the dispersion in the ⟨log age⟩_L(R) profiles between galaxies of the same M_⋆ and different Hubble type is significant, and larger than between the ⟨log age⟩_L(R) profiles of galaxies of different M_⋆ but the same Hubble type. These results, in agreement with Fig. 8, indicate that the age profiles are more related to morphology than to M_⋆. Since ⟨log age⟩_L(R) is essentially a first moment of the spatially resolved SFH, we can conclude that the SFH and its radial variation are modulated primarily by the galaxy morphology, with mass playing a secondary role.

5.2.3. Radial gradients

Gradients in ⟨log age⟩_L, computed as indicated in Eqs. (6) and (7), are plotted in Fig. 10 against Hubble type (left panel) and stellar mass (right). The figure layout is exactly as in Fig. 7. Whilst in that plot results obtained with bases GMe and CBe (circles and stars in the left panel, respectively) could hardly be distinguished, here the results for these two sets of SSPs do not overlap so precisely, although the differences in ▽ ⟨ log age⟩_L are clearly very small (see Sect. B.2).

A clear relation exists between ▽ _in ⟨ log age⟩_L and morphology: the inner age gradient increases from early-type galaxies to Sb–Sbc spirals, which are the galaxies with the largest variation between the age of the stellar population at the bulge and the disk. Spirals of later type (Sc and Sd) have flatter radial profiles than Sb–Sbc. The outer (between 1 and 2 HLR) age gradient shows a similar bimodal behavior as ▽ _in ⟨ log age⟩_L, but with a smaller amplitude.

The right panel of Fig. 10 shows the behavior of ▽ _in ⟨ log age⟩_L with M_⋆. The gradient tends to increase (become more negative) from low-mass galaxies (which have roughly flat profiles) up to about 10¹¹ M_⊙, at which point the trend reverses and ▽ _in ⟨ log age⟩_L decreases with increasing M_⋆. This is best seen following the black crosses, which trace the mass-binned mean relation. The dispersion with respect to this relation is significant and is related to the morphology, as seen through the large colored circles. The tendency is that, at a given mass, S0 and early-type spirals have weaker ▽ _in ⟨ log age⟩_L than Sb–Sbc. This dependence of age gradients with the Hubble type at a fixed M_⋆ indicates again that the spatial variation of the SFH is mainly driven by morphology and not by stellar mass.

However, the morphology (understood as the B/D ratio Graham & Worley ) cannot be the only driver of the spatial variation of the SFH along all the Hubble sequence. Figure 10 shows that there is not a monotonic relation between the B/D ratio and ▽ _in ⟨ log age⟩_L, with galaxies with the smaller B/D ratio having the largest variations in ⟨log age⟩_L between the central core and the disk. This bimodal behavior seen in Fig. 10 suggests that other physical properties are also important in establishing the spatial variation of the SFH, which on the other hand is reflecting the different bulge formation processes along the Hubble sequence.

5.3. Stellar metallicity

Figure C.3 presents the images of the mass-weighted mean (logarithmic) stellar metallicity (cf. Eq. (2)). Here we discuss the radial structure of ⟨log Z_⋆⟩_M as a function of Hubble type and M_⋆.

5.3.1. Metallicity-morphology and mass-metallicity relations

Figure 11 shows how the stellar metallicity measured at 1 HLR changes with the Hubble type (left panel) and with the galaxy stellar mass (right).

Stellar metallicities grow systematically from late to early-type galaxies. The statistics within each Hubble type are ⟨log Z_⋆⟩_M^HLR(Z_⊙) = −0.05 ± 0.13, −0.05 ± 0.33, −0.21 ± 0.16, −0.10 ± 0.18, −0.05 ± 0.15, + 0.06 ± 0.08, and + 0.10 ± 0.08 for Sd, Sc, Sbc, Sb, Sa, S0, and E, respectively.

Not surprisingly, metallicities also grow with M_⋆, as shown in the right panel of Fig. 11. Since we have shown in Sect. 4.3.2 that the galaxy-wide average stellar metallicity is well represented by the metallicity at 1 HLR, this plot is in fact equivalent to the global mass-stellar metallicity relation (MZR). We have previously found that this relation is steeper than that derived from HII regions, which is similar to the flatter stellar MZR obtained when we consider only young stars 54. As in Fig. 5, the smoothed black curve is obtained by averaging ⟨log Z_⋆⟩_M^HLR in 0.4 dex bins of log M_⋆. The dispersion in the MZR is significant, and larger than the dispersion produced by the galaxy morphology as shown by the distribution of large colored circles. These circles are the average ⟨log Z_⋆⟩_M^HLR in each mass bin for each Hubble type, and show the tendency of earlier type galaxies to be more metal rich than late-type galaxies of the same stellar mass.

5.3.2. Radial profiles

Figure 12 shows the results of stacking the radial profiles of ⟨log Z_⋆⟩_M as a function of Hubble type and M_⋆. Outwards decreasing ⟨log Z_⋆⟩_M is detected for most morphological classes, but flat profiles are found for Sc–Sd galaxies. Intermediate type-spirals (Sb–Sbc) stand out as those with the largest variations in stellar metallicity.

The behavior of the radial variation of the stellar metallicity with M_⋆ (right panel in Fig. 12) is similar to the behavior with morphology. Most galaxies have ⟨log Z_⋆⟩_M that decreases with R, except for the two lowest mass bins, which show flat profiles. The largest spatial variations are also found in galaxies in the intermediate mass bins (10 ≤ log M_⋆(M_⊙) ≤ 11).

These negative radial gradients of the metallicity are also an indicator of the inside-out formation processes in galaxies. The inversion of the gradient in late-type spirals and in low-mass spirals may be an indicator of the secular processes or the outside-in formation scenario in these galaxies 104.

5.3.3. Radial gradients

Figure 13 clones Figs. 7 and 10 for ⟨log Z_⋆⟩_M gradients. On the left panel, one sees that, as for stellar densities and ages, results for bases GMe and CBe are very similar. On average, galaxies have ⟨log Z_⋆⟩_M gradients ~−0.1 dex/HLR similar to the value obtained from nebular oxygen abundances 115. Outer and inner gradients are not significantly different. Despite the large scatter, there is a hint of a bimodal distribution as that found for stellar ages, also with intermediate-type spirals in a pivotal position and late-type spirals with the flattest gradients, at least in a statistical sense.

The right panel of Fig. 13 shows ▽ _in ⟨ log Z_⋆⟩_M as a function of M_⋆. The dispersion is significant, but on average there is a tendency to turn flat profiles into negative gradient profiles as M_⋆ increases from 10⁹ to 10¹⁰ M_⊙. The largest gradients are found between 10¹⁰ and 10¹¹ M_⊙. More massive galaxies tend to have weaker stellar metallicity gradients. The dispersion is significant throughout this relation. A trend with morphology is seen in the sense that, for a given mass, early types are those with weaker gradients.

5.4. Stellar extinction

starlight models the stellar extinction as a foreground screen, parametrized by A_V and following the Galactic reddening law. Images showing the spatial distribution of A_V for our 300 galaxies are presented in Fig. C.4. Here we present A_V related results as a function of Hubble type and M_⋆, following the same script adopted in the discussion of μ_⋆, ⟨log age⟩_L, and ⟨log Z_⋆⟩_M in the previous subsections, thus completing the list of stellar population properties studied in this work. Unlike masses, ages, and metallicities, extinction is more easily affected by inclination effects, so the results reported below should be interpreted with caution. Section 5.5 explores this issue in depth.

5.4.1. Extinction-morphology and extinction-mass relations

Figure 14 shows how the stellar extinction at 1 HLR changes with Hubble type (left panel) and with stellar mass (right panel). As with other properties, represents well the mean extinction of the galaxy⁶ as well as the A_V value derived from spectral fits of the integrated spectra⁷. The left panel in Fig. 14 shows as a function of morphology. Ellipticals and S0s have almost no extinction, with mean , and 0.06 ± 0.07 mag, respectively. Sa, Sb, and Sc galaxies have around 0.25 mag, and somewhat smaller (0.19 ± 0.08 mag) in Sd’s.

There is no clear behavior of stellar extinction with galaxy stellar mass. In general, galaxies with M_⋆ ≤ 10¹¹ M_⊙ have –0.3 mag. More massive galaxies are less extinguished, and for fixed mass early types tend to have smaller , but the dispersion is large.

5.4.2. Radial profiles

Figure 15 shows A_V(R) profiles stacked by Hubble type (left panel), and mass (right). Spirals have A_V ~ 0.2 mag in the disk and up to 0.6 mag in the center. Their A_V profiles are similar for all Hubble types except for Sd’s, where A_V does not change much from disk to center. Ellipticals and S0’s also show negative A_V gradients, although at distances larger than 1 HLR they are almost dust-free. The radial profiles in different bins of M_⋆ (right panel) show a similar behavior to that with morphology. Except for the most massive bins, shifted to lower extinction values, all other mass-binned A_V(R) profiles are similar.

5.4.3. Radial gradients

A_V gradients are shown in Fig. 16, which is formatted as Figs. 7, 10 and 13. As for the previous properties, results for bases GMe and CBe are nearly indistinguishable, as illustrated by the overlap of circles and stars in the left panel. ▽ _inA_V and ▽ _outA_V show similar behavior with morphology, although the inner gradient is always higher than the outer gradient. In Ellipticals the gradient of A_V only exists in the central region. With the exception of Sd galaxies, spirals have ▽ _inA_V ~ −0.25 mag/HLR.

On average, ▽ _inA_V gets stronger with increasing M_⋆ up to 10¹¹ M_⊙ (Fig. 16, right) and weakens toward higher mass, spheroid dominated systems. The dispersion with respect to the mass-binned relation (traced by the black crosses) is large, and not clearly related to morphology (coded by the colored circles).

As a whole, and despite the general trends summarized above, of the four properties analyzed in this section, A_V is the one for which tendencies with Hubble type and stellar mass are less clear. A major reason for this is that, unlike for μ_⋆, ⟨log age⟩_L, and ⟨log Z_⋆⟩_M, A_V estimates are sensitive to inclination effects, as explained next.

5.5. Effect of inclination on the radial profiles

An implicit hypothesis throughout the analysis presented so far is that galaxy inclination does not affect our estimates of the stellar population properties and their radial distributions. One expects this assumption to break down in the case of A_V, which should increase from face on to edge on galaxies, although it is not unreasonable to conceive that inclination effects propagate to the spectral synthesis-based estimates of stellar mass surface densities, mean ages, and metallicities. It is therefore relevant to evaluate if and how inclination affects our results.

In order to do so, we have divided the 300 galaxies in three subsamples on the basis of the b/a ratio (minor to major isophotal axes), as measured in SDSS R-band images. The three subsamples, each containing 100 galaxies, cover (i) b/a ≤ 0.39, edge on; (ii) 0.39 <b/a ≤ 0.63; and (iii) b/a> 0.63, face on. Galaxies in each subsample were grouped by Hubble type, and their radial profiles of log μ_⋆, ⟨log age⟩_L, ⟨log Z_⋆⟩_M, and A_V averaged as previously done for the whole sample in the left panels of Figs. 6, 9, 12, and 15.

Figure 17 shows the resulting stacked profiles of log μ_⋆, ⟨log age⟩_L, ⟨log Z_⋆⟩_M, and A_V. Solid, dashed and dotted lines show profiles for the “face-on” (b/a> 0.63), intermediate inclination (0.39 <b/a ≤ 0.63), and “edge-on” (b/a ≤ 0.39) samples, respectively, and each column is for one of the seven Hubble types used throughout the paper. Average profiles were only computed for morphology-inclination bins containing at least four galaxies.

Stellar mass surface density, age, and metallicity profiles show a negligible variation among the b/a-based subsamples. This result indicates that inclination does not affect the estimates of these properties in any systematic way. Any difference is at a level not significant insofar as this paper is concerned. The exception is the ⟨log Z_⋆⟩_M profiles for “edge-on” Sc’s, which differ substantially from the profiles of less inclined Sc’s. It so happens, however, that the sub-group of b/a ≤ 0.39 Sc’s has a mean stellar mass 0.4 dex lower than other Sc’s, which could explain their lower metallicities without implying inclination effects.

The one property that does vary systematically with b/a is A_V, and it does so in the expected sense: spirals with lower b/a have larger extinction. This is particularly evident in Sb’s. This dependence hinders the interpretation of the stacking results presented in Sect. 5.4, and explains why no clean tendencies of the A_V values and profiles with morphology and stellar mass were identified.

6. Discussion

This section is divided into four main parts. First we summarize our results in the context of related studies. We then discuss our findings in the context of the growth of galaxies – theoretical expectations, high-redshift observations, and previous results of inside-out growth for CALIFA galaxies. In the third part, we explore what the results tell us about the quenching of star formation in galaxies. Finally, we discuss the theoretical predictions for the radial variations of age and metallicity in early types and in spirals from different simulations of galaxy formation. We compare our results for variations of the radial structure in the inner (R ≤ 1 HLR) and outer (1 ≤ R ≤ 3 HLR) parts with other observational results in the literature.

6.1. Age and metallicity of bulges and disks

The analysis of SDSS data has generated a general knowledge of how the age and metallicity of galaxies change with M_⋆, color, or concentration index e.g. 71; 45; 86. These studies have confirmed that, in general, early-type galaxies are old and metal rich, while late-type galaxies are younger and more metal poor. Numerous (single spectra or longslit) studies have reported also that ellipticals are metal rich, and have a range of ages, 2–10 Gyr, which depend on stellar velocity dispersion e.g. 132; 131; 116; 58; 69.

Our spatially resolved analysis introduces a significant improvement in the study of the structure of galaxies. For example, we compute ages and metallicities of bulges in disk galaxies and compare them with elliptical galaxies in a systematic way, avoiding problems derived from the lack of spatial resolution prevalent in some of the previous studies.

We compute the luminosity-weighted and the mass-weighted age and metallicity: (i) in the central part of galaxies (values averaged within 0.25 HLR) as representative of the stellar population properties of bulges and central core of ellipticals; and (ii) in the outer part of galaxies, values averaged in a ring at 1.5 ± 0.1 HLR, as representative of disks. Figure 18 plots the individual results as small dots; large dots represent the average values for each (color-coded) Hubble type, and the error bars show the dispersion. While ⟨log age⟩_L gives information about the globally “averaged” SFH, ⟨log age⟩_M informs when most of the stellar mass was formed.

Figure 18 shows that the bulges of Sa–Sb and the cores of E-S0 formed at a similar epoch; they are very old (~10 Gyr) and metal rich (≳1 Z_⊙). Thus, they probably formed through common processes, that occurred rapidly and early on. However, the bulges in Sc–Sd galaxies (shown as the two darkest shade of blue) are younger and have a more extended SFH (both ⟨log age⟩_M and ⟨log age⟩_L are smaller), and have lower stellar metallicities. Thus, Sc–Sd galaxies formed in later times and/or with different processes.

Many bulges in late-type spirals are in fact pseudo–bulges. Unlike true bulges, pseudo–bulges are thought to grow by secular processes, where material from the disk (by the loss of angular momentum) is the main source of star formation in the central parts of these galaxies e.g. 76. We may see this effect at work in Figs. 9 and 12, as a flattening of the radial profiles of ⟨log age⟩_L and ⟨log Z_⋆⟩_M, and the positive ⟨log age⟩_L gradient in the core of Sc galaxies. Some effects of the secular processes due to the disk may also be present in the bulges of Sa–Sb. For example, Fig. 18 shows that bulges of Sa–Sb have ⟨log age⟩_L~ 6 Gyr, younger than the 10 Gyr epoch of formation derived from ⟨log age⟩_M; and this may be understood if some disk stars are rearranged into the bulges or if dissipation processes bring gas triggering new star formation in the center.

Figure 18 also shows that disks are younger and more metal poor than bulges. Both ⟨log age⟩_L and ⟨log age⟩_M are lower in disks than in their respective bulges, indicating that disks formed later than bulges, and that star formation continues for a longer time in disks that in bulges, probably as a consequence of a continuing availability of gas in disks 110. This indicates a general scenario of inside-out formation.

6.2. Inside-out growth of spheroids and spirals

6.2.1. Theoretical expectations and recent results from high redshift galaxies

Models of galaxy formation predict a common inside-out view for the mass assembly in galaxies e.g. 70; 5. First, the bulge formed at high redshift; then, the disk was built around the bulge in the case of spirals. In the case of ellipticals, the central core formed at z ≥ 2, and the envelope grew later through minor mergers e.g. 97; 63. Observational evidence come from the significant size evolution in early-type galaxies (ETG), which grow in size 134; 102.

More recently, van Dokkum et al. find evidence against the inside-out formation scenario for spirals. For a sample of MW-like spirals at redshift z = 2.5, they estimate the dependence of the radius with M_⋆, and find that their size-M_⋆ relation is similar to the size-M_⋆ of similar galaxies at z = 0. They conclude that the mass growth took place in a fairly uniform way, with the galaxies increasing their mass at all radii, thus, their R_eff barely grows. These results seem to be supported by numerical simulation by Elmegreen et al. , which find that bulges can be formed by migration of unstable disks. Other observational evidence come from the detection of clumpy star-forming disks in galaxies at z ~ 247; 44, which may indicate an early build up of bulges by secular evolution. Thus, studies at high redshift are providing new results that draw a complex landscape of galaxy build up. For example, Wuyts et al. also find clumpy disk star formation, but at the same time conclude that there is a Hubble sequence in place at least since z ~ 2.5. On the other hand, there is other evidence that galaxies rapidly assemble inside-out at z = 195; 129; 130; while Hammer et al. find evidence that MW-like galaxies have rebuilt their disk at z ≤ 1 in a major merger epoch that drastically reshapes their bulges and disks, and is consistent with earlier cumply evolution.

In summary, there is mounting evidence of the major processes responsible for the assembly and shaping of galaxies at different epochs, and these are complemented with a variety of processes that modify the inside-out formation scenario: stellar migration, bar induced gas inflows, gas-rich minor merger, angular momentum loss due to reorientation of the disk, infall of gas with misaligned angular momentum, etc. 6.

6.2.2. CALIFA view of the inside-out growth of galaxies

Our results favor an inside-out growth of spirals. Pérez et al. studied the stellar mass growth as a function of the radius and cosmic time in galaxies with 10¹⁰ ≲ M_⋆ ≲ 5 × 10¹¹ M_⊙, and showed that the nuclei grow faster than the inner 0.5 HLR, which, in turn, grow faster than the outer 1 HLR. This conclusion is supported by the stellar age radial profiles presented in González Delgado et al. , and confirmed here in Fig. 10 for most spirals and spheroidals. Further support comes from the ratio HMR/HLR (Fig. 3), a good probe of the spatial variation of the SFH in galaxies 56. This ratio is lower than 1 (Fig. 3), a fingerprint of the inside-out growth found by Pérez et al. .

Figure 19 shows how the radial profiles of ⟨log age⟩_M decrease outward for all the Hubble types. Most of the stellar mass in the center was formed 10 Gyr ago or earlier (z ≥ 2). However, at 1.5 HLR, ⟨log age⟩_M ranges from 7 Gyr (z ~ 1) in E–S0 to 4.5 Gyr (z ~ 0.4) in Sbc, suggesting that, both early type and MW-like, galaxies have continued accreting or forming in situ stars in their disks until more recent times, thus supporting the inside-out scenario in these galaxies.

This trend, however, changes beyond 1.5−2 HLR, where ⟨log age⟩_M and ⟨log age⟩_L flatten. This may be interpreted as indicating that the mass was formed in a more uniformly distributed manner across the outer disk, or that stellar migration shuffles inner born stars to the outer disk, washing out the inside-out formation signs so clearly seen in the inner 1.5 HLR. In the case of E–S0, this may be understood if beyond 2 HLR most of the stellar mass in the galaxies was already accreted at z = 1.

6.3. Quenching

Several mechanisms have been proposed to explain the shutdown of star formation in galaxies. Halo mass quenching is one of the most popular explanations of the bimodal distribution of the properties of galaxies, and it is required to explain the green valley as a pathway towards quenching of star formation in early and late type galaxies e.g. 122. In this scheme, galaxies with a halo mass below a critical value (a few ×10¹² M_⊙) accrete cold gas conducive to star formation. Above this critical mass, the infalling gas reaches the sound speed and cannot form new stars e.g. 26; 35. The dependence with environment and clustering strongly supports this quenching mechanism e.g. 139; 103.

The differential dependence of the stellar mass surface density (Figs. 5 and 6) with the galaxy stellar mass (a proxy of the halo mass) provides further evidence of the halo quenching e.g. 9. Estimating of the properties of the stellar populations in SDSS galaxies, Kauffmann et al. found that there is a critical mass (M_⋆ = 3 × 10¹⁰M_⊙, equivalent to ~ 6 × 10¹⁰ M_⊙ for our Salpeter IMF) below which log μ_⋆ scales with M_⋆, and above which log μ_⋆ is independent of the galaxy stellar mass. The right panels of Figs. 5 and 6 support this scenario because the radial profiles of log μ_⋆ scale with log M_⋆, and furthermore they do so all along their extent. Our results also show that log μ_⋆ saturates at high M_⋆ because the high-mass end of the distribution is dominated by early type galaxies (Sa–S0–E); this suggests that the spheroidal component plays a significant role in the quenching of star formation in high-mass galaxies.

The importance of morphology in the quenching of galaxies has also been reported in the literature e.g. 10; 11; 8; 99; 140. Martig et al. found that the dependence of quenching with morphology is a consequence of the bulge-building mechanism. The steep potential well induced by the formation of a large spheroid component results in the stabilization of the disk, which cuts the supply of the gas, preventing its fragmentation into bound, star-forming clumps. Our results support this scenario, as it is explained below, because the dependence of the SFH of galaxies with the morphology.

If the halo mass is the main property responsible for quenching, we should expect that the radial structure of ⟨log age⟩_L (both, the age values and the gradients) to change more with M_⋆ than with Hubble type. On the contrary, if quenching is driven by morphology, galaxies of similar stellar mass would have very different ⟨log age⟩_L structure depending on Hubble type. We explore the relevance of morphology versus M_⋆ in Fig. 20: age radial profiles are shown as a function of M_⋆ and of morphology, in four mass bins (log M_⋆ = 11.5−11.2, 11.2−10.9, 10.9−10.6, 10.6−10.1). Clearly, morphology is the main driver: it can account for up to 0.75 dex change in age at a given mass (top panels); conversely, at a fixed morphology, mass accounts for less than 0.25 dex (bottom panels). Further, morphology accounts not only for changes in absolute values, but also for changes in the gradients at a given galaxy mass.

This confirms the similar result obtained above with log μ_⋆, and it implies that galaxies of similar M_⋆ (equivalent to have similar M_halo) and with a large spheroid have shut down their star formation (outside their central core) earlier than galaxies of later morphology. These results indicate that the SFH and their radial variations are modulated primarily by galaxy morphology, and only secondarily by the galaxy mass, suggesting that the bulge formation has a relevant role in quenching the star formation in galaxies.

6.4. Radial structure of the stellar population properties in ETG and their relation with galaxy formation models

6.4.1. Theoretical predictions from cosmological simulations

Classical chemical evolution models of the formation of early-type galaxies (ETG) are based on two possible scenarios: 1) dissipative formation, the well-known monolithic collapse; and 2) the non-dissipative collapse. These scenarios produce very different radial gradients of ages and abundances, being very steep in the first case, with values of ▽[Fe/H] ~−0.5 to −1.0 [dex/dex] 79; 80; 25⁸, but (almost) flat when there are pure stellar mergers. This second case may even erase a previously existing radial gradient.

The most recent cosmological simulations propose a two-phase formation scenario for ETG’s in which the central core formed at z ≥ 2, and the envelope grows after this through minor mergers e.g. 93; 98; 62; 94. As follows: 1) galaxies assemble their mass through dissipative processes and star formation occurs in situ. Starbursts formed at the center as a consequence, for example, of large major mergers or monolithic collapse. The star formation is induced by cold flow of accretion or by gas-rich mergers. 2) Galaxies grow in size by mass assembly through the external accretion of satellites; ex situ star formation formed by dry mergers of galaxies toward the central most massive galaxies.

Observationally, there is evidence of a significant size evolution in ETG. The growth of the galaxy size with supports this proposal. A transition region is expected between the in situ central core of ETG and ex situ outer regions. Since the central core of these ETG is enriched very quickly due to major mergers at high redshift (z ≥ 2), and the satellites that are accreted are less metal rich than the central massive galaxies, a negative radial gradient of the metallicity is expected, even with a change of the slope in the transition region. Thus, values as ▽[Fe/H] = −0.5 [dex/dex] 107 or ▽[Fe/H] = −0.3 [dex/dex] 72 are predicted.

However, the merger history may change an existing radial gradient: while dry major mergers can flatten the pre-existing gradient 74; 36; 66, dry minor mergers can steepen the metallicity gradient. Thus, Kobayashi SPH chemodynamical simulations of elliptical galaxies which include radiative cooling, star formation and feedback from SNII-Ia, and chemical enrichment (but do not include kinematic feedback), found that the steep negative radial metallicity gradient, established during the initial starburst at z ≥ 2, can flatten significantly by later major-mergers in the galaxy. Following these simulations, the average gradient at the present time is ▽[Fe/H] = −0.3 [dex/dex], but it may decrease to a value of −0.2 [dex/dex] when major mergers appear.

Beside the merger history, feedback can change the inner and outer metallicity gradients. Thus, a strong AGN feedback can stop the star formation in the central core of massive galaxies, flattening the inner gradients. Feedback from in situ star formation can alter the outer metallicity gradient. Also, the existence of galactic winds may modify the composition of the ISM in a galaxy. Hirschmann et al. performed cosmological simulations, which include an empirical model for the momentum driven galactic winds, to investigate the dependence of the age and metallicity outer gradients with metal cooling and galactic winds; in principle, required to explain the mass-metallicity relation, MZR. These simulations including winds predict ▽[Fe/H] = −0.33 [dex/dex], steeper than the simulations without winds that predict ▽[Fe/H] = −0.11 [dex/dex]. The main explanation is that in wind models the stars accreted are of lower metallicity than in the simulations with no winds. In both cases, however, they predict a positive age gradient of ~0.03−0.04 [dex/dex].

6.4.2. Implications from this work and comparison with other results from the literature

Following our own results, E and S0 have formed their central core at similar cosmic time since they have similar central ages (see Fig. 18). Further they must have formed through similar processes since their radial profiles of log μ_⋆, ⟨log age⟩_L, and ⟨log Z_⋆⟩_M are remarkably similar. They both show small but negative ⟨log age⟩_L, and ⟨log Z_⋆⟩_M gradients in the central core. In the central 1 HLR, E and S0 in our sample have ▽⟨log Z_⋆⟩_M~−0.1 [dex/dex] (std = 0.15)⁹. Slightly steeper, ▽⟨log Z_⋆⟩_M = −0.2 [dex/dex], when CBe models are used. These are within the range of values found in other studies based on long-slit or IFS data up to one effective radius e.g. 87; 117; 2; 109; 125; 77. However, they are shallow compared with theoretical expectations if minor mergers are relevant in growing up the central core of E and S0 galaxies. This may indicate that major mergers are more likely the main process building the central regions (up 1 HLR) of ETGs.

Between 1 and 3 HLR, the radial profile of ⟨log Z_⋆⟩_M is of similar slope or slightly shallower than in the inner 1 HLR. We do not find any evidence of a transition region where the metallicity radial profile steepens to metallicities below solar. If the 1 to 3 HLR envelope of ETG had grown through the accretion of low-mass satellites a steepening of metallicity would be expected, as explained before, because the mass-metallicity relation implies that low-mass satellites would be of low metallicity. In our results there is no evidence either of an inversion of the age radial profile toward older ages beyond 1−2 HLR, as expected if these satellites were formed very early on like the core of E and S0 (see Figs. 9 and 18). These results are in contrast with recent results by Greene et al. ; : for a sample of ~30 early type galaxies they find at 2 R_eff an old (10 Gyr) stellar population with [ Fe / H ] ~ −0.5, and interpret this as the stellar outskirts of these galaxies being built up through minor mergers. Coccato et al. ; La Barbera et al. ; Montes et al. observing a few massive ellipticals reported a decline of the metallicity to under solar in an old stellar population in their outskirts (≥10 R_eff) suggesting that these galaxies are formed in two phases, the central core through major mergers, and through minor mergers farther out. However, other recent works show examples of ETG with an old and metal-rich stellar population and a very shallow metallicity gradient up to 3 R_eff133 in contrast with the results by Greene et al. ; .

Our results do not support the minor merger scenario for the size growth of ETG. Thus, the ages ⟨log age⟩_L~ 9.7 (yr) and metallicity ⟨log Z_⋆⟩_M~Z_⊙ at 1−3 HLR, and the shallow metallicity gradient, ▽⟨log Z_⋆⟩_M~−0.1 [dex/dex], that we obtain are more consistent with the growth of the 1−3 HLR envelope of ETGs through major mergers.

Another interesting result reported in the literature that can be compared with ours is the correlation between the metallicity gradient and the galaxy mass (or stellar velocity dispersion, σ_⋆) found for E and S0. Spolaor et al. have found that the relation between σ_⋆ and the metallicity gradient shows two regimes of behavior: (i) for galaxies with log σ_⋆ ≤ 2.2 km s^-1, the metallicity gradient steepens with σ_⋆; (ii) galaxies with log σ_⋆> 2.2 km s^-1 (the most massive ellipticals), have a metallicity gradient that does not correlate with σ_⋆ (or galaxy mass), with a mean value ~−0.15 [dex/dex]. On the other hand, Pastorello et al. derive the [ Z/H ] gradient in the outer 1−2.5R_eff of a sample of ellipticals, and they find that the gradient covers a wide range of values, from negative very steep (~−2) to flat or even positive; these values correlate with the galaxy stellar mass and stellar velocity dispersion, with galaxies of lower M_⋆ (or σ_⋆) having the steeper metallicity gradient. However, the most massive galaxies exhibit the flattest gradients and an average value of ▽⟨log Z_⋆⟩_M~−0.2 [dex/dex] (std = 0.38) for galaxies with M_⋆ ≥ 10¹¹ M_⊙. Both works show a significant scatter in the ▽⟨log Z_⋆⟩_M−M_⋆ relation for M_⋆ ≥ 10¹¹ M_⊙, and reasonable doubts of the existence of the correlation for high-mass ellipticals.

Our results (Fig. 13) indicate that there is no correlation between the metallicity gradient and M_⋆ for the CALIFA early-type galaxies (E and S0). Even so, our results are compatible with Spolaor et al. and Pastorello et al. because E and S0 in our sample are all above 10¹¹M_⊙ (and σ_⋆> 100 km s^-1), for which no correlation is found between the metallicity gradient and M_⋆ in Spolaor et al. or Pastorello et al. . We find that CALIFA ellipticals have a shallow gradient. This behavior is also in agreement with Hirschmann et al. simulations and their interpretation of the lack of correlation between the metallicity gradient and M_⋆ in massive ellipticals. Following these authors, massive galaxies accrete higher mass satellites, and because of their deeper potential well they retain their own gas against stellar winds, producing a shallower metallicity gradient in the outer regions of massive ellipticals.

Because the metallicity at 2−3 HLR in E and S0 are similar to the metallicity in the bulge of early spirals, and the stars at these distances are as old as the bulges of Sa–Sb galaxies (see Fig. 9), the 1−3 HLR envelope of early-type galaxies might have built from the centers of early-type spirals. In summary, the negative but shallow gradients of the metallicity and ages suggest that massive (M_⋆ ≥ 10¹¹M_⊙) early-type galaxies built their inner 3 HLR through mergers with massive and metal-rich spirals.

6.5. Radial structure of the stellar population properties in spirals and their relation with galaxy formation models

New insights into the structure of the Milky Way disk, in particular through the measurements of chemical abundances of large sample of stars, are provided by the spectroscopic surveys undertaken in recent times e.g., SEGUE, RAVE, Gaia-ESO survey, HERMES, APOGEE, LAMOST, etc.; 142; 127; 49; 144; 83; 143. Radial Velocity Experiment 127; 15, RAVE; is studying the radial and vertical chemical gradients using a very large sample of dwarf stars. Close to the Galactic plane, RAVE shows a negative radial gradient of Fe abundance, −0.054 dex/kpc¹⁰, which becomes flatter or even positive when measured above the disk. So, the [Fe/H] gradient ranges from −0.039 to + 0.047 dex/kpc when measured at heights 0.4−0.8 kpc, or 1.2−2 kpc above the Galactic plane, respectively.

The radial gradient of abundances in the different regions of a spiral galaxy are important because they are directly related to the formation process. Obviously, not all scenarios of disk/spiral formation are valid, since it is necessary that they produce a radial gradient of abundances in the disk but not in the halo, as observed in the MW and in M 31. Thus, the formation of the halo from different fragments or minor mergers with very short free fall times does not create a radial gradient but a dispersion of abundances, and therefore it was concluded early on that the MW halo may be formed from mergers or from the accretion of low-mass galaxies (or part of them). However, disks are more likely formed from a single cloud falling on and from inside out.

6.5.1. Theoretical predictions from “classical” chemical evolution models

Most classical chemical evolution models claim that the infall of gas with a radial dependence, implying an inside-out scenario for the disk formation, is essential to reproduce the observed radial gradient of abundances. The key ingredient is the dependence of the disk infall time scale with the radial distance, which makes the gas to accumulate faster in the inner disk. Since the star formation rate depends on the gas density, these assumptions produce a radial dependence of the star formation rate and a negative radial metallicity gradient 42; 91; 29; 90. Thus Molla et al. give a value −0.08 for a MW-like galaxy, reproducing the value found by Shaver et al. and other Hii regions studies. Chiappini et al. models predict a gradient of −0.04 dex/kpc for a MW-like galaxy. In fact, as theoretical equations show 52, the radial gradient of abundances appears in the disk when there is an adequate ratio between star formation rate to infall rate. It also implies, therefore, that a dependence of the radial gradient on the morphological type of galaxies may exist. 91 models already predicted radial gradients for galaxies of different morphological types, with values in the range −0.025 (for a M 31-like galaxy) to −0.183dex kpc^-1 (for a late type galaxy like NGC 300). More recent works 90 calculate models in which the infall rate was a function of the mass distribution (or rotation curve) of the galaxy, assuming a stronger radial dependence of the infall timescales than in Chiappini et al. . Moreover Mollá & Díaz models also depend on an efficiency factor to condense the molecular gas, and to convert the gas reservoir into stars. The metallicity gradients range −0.02 to −0.15dex kpc^-1 with flat gradients for galaxies with the largest efficiency factor, or the most massive galaxies, although in the extreme end the low-mass and lowest efficiencies models also show flat radial distributions. Thus, the steepest gradients appear in the intermediate-mass or intermediate-type galaxies. However, there is no dependence on the morphological type when the gradient is normalized to a characteristic value, such as the effective radius, as recent results by CALIFA have found based on HII regions abundances 115.

6.5.2. Theoretical predictions from cosmological simulations

Recently, hydrodynamical cosmological simulations have provided evidence in support of the imposed inside-out disk growth scenario adopted within the “classical” chemical evolution models. Like spheroidals, spirals are formed in two phases. In the first phase, the bulge formed in a similar way as the core of E-S0. In the second phase, the disk grows by star formation in situ from the infalling gas 70; 5. Metal poor gas with higher angular momentum at lower redshifts is turned into stars at larger radii. Negative radial metallicity gradients are expected, as the classical models predict. This assumption is a natural outcome of the mass, momentum, and energy conservation laws imposed in the simulations of disks in a cosmological context 18; 19; 43; 105; 106; 48.

Pilkington et al. examined a set of 25 simulations, from several groups, using different codes and initial conditions 128; 108; 75; 43 to predict the present-day metallicity gradient in MW-like galaxies and its evolution. Although the evolution of the simulated metallicity gradients depends strongly on the choice of the subgrid physics employed, most of the simulated galaxies tend to a similar present-day gradient of ~−0.05 dex kpc^-1, in agreement with the Chiappini et al. and Mollá & Díaz models for normal galaxies as the MW.

6.5.3. Implications from this work

Our findings show that spiral galaxies (excluding Sd) have negative radial gradients as indicative of the inside-out growth of the disk (see Fig. 12). The average ▽ _out⟨log Z_⋆⟩_M for spirals (excluding Sd and later type) is −0.08 dex/HLR or −0.02 dex/kpc. These values are compatible with the results obtained by Sánchez-Blázquez et al. , which have already derived the metallicity gradients for 62 CALIFA face-on spiral galaxies to study the effect of bars on the properties of the stellar populations. For these galaxies, they find a metallicity gradient of −0.025 dex/kpc (std = 0.05), equal (−0.027 dex/kpc) to the gradient that we derive for the same group of galaxies.

To compare the RaDES simulated galaxies 43 with our results, 19 galaxies of the Pilkington et al. sample, have been analyzed, measuring the HLR and the gradients in a similar way as we have done with the CALIFA galaxies (Ruiz-Lara, in prep.; Ruiz-Lara et al., priv. comm.). However, these 19 simulated galaxies analyzed cover a narrow range of morphologies, mainly Sbc–Sc, in comparison with CALIFA. Therefore, these results cannot be extrapolated to the full work presented here, but they are representative of the state-of-art of cosmological simulations of disk galaxies, and can be used to compare them to similar disks from our observations. Mock B-band images are used to derive the HLR and to perform a bulge-disk decomposition used as a proxy for the morphology. Metallicities are calculated for disk particles using Eq. (2) and the gradient is derived between 0−1 HLR and also between 1 and 2 HLR. The stellar metallicity and age gradients of the simulated galaxies are compatible with the results presented here. Keeping in mind that the morphological range covered by these simulations is rather narrow and that they use B/D as a proxy for a morphological classification, the results show a slight dependence of ▽ _out⟨log Z_⋆⟩_M with B/D ratio, with a steeper slope for B/D = 1 (Sbc galaxies) for which ▽ _out⟨log Z_⋆⟩_M~−0.1 dex/HLR. Later type spirals have a flatter gradient of ▽ _out⟨log Z_⋆⟩_M~−0.046 dex/HLR. These results go in line with those found here, namely, that the metallicity radial gradient of spirals shows a dependence on morphology, with the steepest gradient found in the intermediate Sb–Sbc spirals (see Figs. 12 and 13). However, a larger set of cosmological simulations is required covering from early Sa to late Sd, and a large range of galaxy masses (from 10⁹ to 10¹¹M_⊙), to confirm the general trend found here. On the other hand, these results indicate that the feedback recipes used in these simulations are able to recover realistic galaxies with small bulges and are fully in agreement with the work presented here.

Furthermore, our results are also compatible with classical chemical models, and certainly, the CALIFA Sb–Sbc galaxies have stellar metallicity gradients (−0.025 dex/kpc) in the range observed in the MW disk, but somewhat shallower than the [Fe/H] gradient measured in the Galactic disk. However, it is necessary to take into account that the gradient usually given in the literature is obtained for young stars or HII regions, while here it is an average value obtained for all stellar populations existing in the studied galaxy or region. Besides that, the number of objects has increased compared with the old studies and, more importantly, all of them have been self-consistently analyzed using the same reduction technique and spectral models.

In any case our results favor an inside-out growth of spirals. This conclusion is supported by the stellar age radial profiles presented here: the age decreases outwards for all Hubble types studied¹¹. Beyond 1.5−2 HLR the radial distribution of ages flattens, suggesting that the mass forms more uniformly in those regions, or that the stellar mixing brings stars born in the inner disk to the outskirts. This last possibility has been recently investigated by Minchev et al. ; , who have performed N-body hydrodynamical models with the chemical evolution implementation 88; 89. They simulated MW-like galaxies with the aim to investigate whether the Galactic disk can be understood as a single structure with kinematic and chemical features that are continuously distributed, being the thin and thick disks two extreme cases of these structures. Furthermore, they investigate the effect of stellar migration and kinematic heating in the scatter of the age-metallicity relation, and how it changes with the Galactic radius. In fact, an increase of the scatter in the age-metallicity relation and a flattening of the stellar metallicity gradient is produced by the stellar radial migration, which causes a radial mixing in the older stellar population and creating the appearance of a flatter gradient in early times, leading to a decoupling of the stellar population from their birth interstellar medium 113. These results also indicate that even though radial mixing has a significant effect in flattening the metallicity gradient, it can not destroy the negative gradient.

7. Summary and conclusions

We analyzed the stellar population properties of 300 galaxies, observed by CALIFA with the V500 and V1200 gratings and IFU PPak at the 3.5 m telescope of Calar Alto, to investigate the trends in the stellar populations properties with radial distance as a function of Hubble type and galaxy stellar mass. The sample includes ellipticals, S0, and spirals from early (Sa–Sb) to late types (Sc–Sd). They cover a stellar mass range from 0.7 × 10⁹ to 7 × 10¹¹M_⊙ if Salpeter IMF is assumed, and a factor 1.78 (0.25 dex) lower for a Chabrier IMF. A full spectral fitting analysis was performed using the starlight code and a combination of SSP spectra from González Delgado et al. , Vazdekis et al. , or Charlot & Bruzual (2007, priv. comm.). Our pipeline pycasso is used to process the spectral fitting results to produce present day maps of the spatial distribution of the stellar population properties. For each galaxy, these maps are azimuthally averaged to produce radial profiles (in units of the half light radius, HLR: ) of the stellar mass surface density (log μ_⋆), stellar ages (light-weighted, ⟨log age⟩_L, and mass-weighted, ⟨log age⟩_M), metallicity (⟨log Z_⋆⟩_M), and extinction (A_V). The radial profiles are stacked as a function of Hubble type and of galaxy mass. Radial gradients of these properties measured within the inner 1 HLR and between 1 and 2 HLR are also obtained.

Our main results are:

• 1.

  Spatially averaged vs. integrated galaxy properties: the metallicity, ⟨log Z_⋆⟩_M, galaxy-wide spatially averaged matches the metallicity obtained from the integrated spectrum, and the metallicity at R = 1 HLR. This result is equivalent to that obtained for the other stellar population properties, log μ_⋆, ⟨log age⟩_L, and A_V, as reported by González Delgado et al. ; , proving that effective radii are indeed effective.

• 2.

  Mass-weighted size: we confirm our earlier finding 56 that galaxies are more compact in mass than in light by ~20%. The HMR/HLR ratio shows a dual distribution with Hubble type, that breaks the galaxies with the smaller HMR/HLR in the Sb–Sbc. This ratio also shows a dual dependence with M_⋆: it decreases with increasing mass for disk galaxies, and becomes almost constant in spheroidal galaxies. These results are a signpost of the inside-out growth previously found by Pérez et al. .

• 3.

  Stellar mass surface density: log μ_⋆(R) shows declining profiles that scale with morphology and with M_⋆; this behavior is preserved at any given distance. At constant M_⋆, log μ_⋆(R) is higher in early-type than in late-type spirals. E and S0 show equal log μ_⋆(R) profiles, independently of M_⋆. The inner gradient, ▽ _inlog μ_⋆, correlates with Hubble type. The negative gradients steepen from late type spirals to spheroids, as well as with galaxy total mass in galaxies with M_⋆ ≤ 10¹¹M_⊙. At a constant M_⋆, ▽ _inlog μ_⋆ steepens with morphology, with E and S0 having the steepest gradients. These results indicate that morphology, and not only M_⋆, plays a relevant role in defining μ_⋆, and the μ_⋆ − M_⋆ relation.

• 4.

  Stellar ages: ⟨log age⟩_L(R) shows declining profiles that scale with morphology; this behavior is preserved at any given distance. Early-type spirals are always older than late spirals. E and S0, although older than spirals, both have similar ⟨log age⟩_L(R) profiles, indicating that these galaxies have similar SFH. The more massive are also the older galaxies; this “downsizing” behavior is always preserved at any given distance. The negative ▽ _in⟨log age⟩_L depends on Hubble type in different ways: steeper from E and S0 to Sbc, and shallower from Sbc to Sd. Thus, Milky Way-like galaxies have the steepest age gradient. A ▽ _in⟨log age⟩_L−M_⋆ relation exists, increasing the gradient from the low mass galaxies (which have roughly flat profiles) up to about 10¹¹M_⊙, at this point the trend reverses and ▽ _in⟨log age⟩_L decreases with increasing M_⋆. However, the dispersion in the ▽ _in⟨log age⟩_L−M_⋆ relation and ⟨log age⟩_L^HLR − M_⋆ is significant and it is strongly related to the morphology. Even more, the dispersion of the ⟨log age⟩_L(R) profiles of galaxies of equal mass is significant and larger than between the ⟨log age⟩_L(R) profiles of galaxies of different M_⋆ but the same Hubble type. Thus, the SFHs and their radial variations are modulated primarily by the Hubble type, with mass playing a secondary role.

• 5.

  Stellar metallicity: ⟨log Z_⋆⟩_M(R) shows mildly decreasing profiles for most Hubble types, except Sd that show little, if any, radial dependence. Milky Way-like galaxies (Sbc) stand out as those with the steepest radial profiles. ⟨log Z_⋆⟩_M(R) scales with M_⋆ similar to the way as it scales with the morphology. This can be understood as a consequence of the global mass metallicity relation, which is a primary dependence of the metallicity with M_⋆. The metallicity gradients are negative but shallow on average, with ▽ _in⟨log Z_⋆⟩_M~−0.1 dex/HLR, and show a small dependence with M_⋆ up to M_⋆ ~ 10¹¹M_⊙, steepening with increasing mass. Above 10¹¹M_⊙ (Sa’s, S0’s and E’s) they have similar metallicity gradient. The dispersion in the ▽ _in⟨log Z_⋆⟩_M–M_⋆ relation is significant and a trend with morphology is seen, in the sense that, for a given mass, intermediate-type spirals are those with steeper gradients.

• 6.

  Stellar extinction: all the galaxies show A_V(R) declining profiles, but do not have a clear trend with morphology or with galaxy mass. Most spirals show similar radial variations, and similar average extinction, A_V ~ 0.2 mag at the disk and up to 0.6 mag in the center, with the inner gradient ▽ _inA_V ~−0.25 mag/HLR. However, Sd galaxies show a shallow central gradient. E and S0 also show a negative gradient in the inner 1 HLR (shallower than in early-type spirals), but they are almost dust free out of the core. On average, ▽ _inA_V gets stronger with increasing M_⋆ up to 10¹¹M_⊙, and weakens toward higher mass. However, the dispersion with respect to the binned mass relation is not related to Hubble type. A major reason for this is that A_V(R) profiles are sensitive to inclination effects, unlike μ_⋆, ⟨log age⟩_L, or ⟨log Z_⋆⟩_M. Thus, spirals with larger inclination have larger extinction. This is particularly evident in Sb that have the largest and the steepest central gradient.

From these results, we conclude that:

• Evidence in favor of the inside-out growth of galaxies is found in the negative radial stellar age gradients. Metallicity gradients and the fact that galaxies are more compact in mass than in light also support this scenario. On the other hand, the flattening of the ⟨log age⟩_L(R) profiles beyond 1.5−2 HLR may be interpreted as indicative that the mass was formed in a more uniformly distributed manner across the outer disk of spirals. In the case of E and S0 this may be understood if beyond 2 HLR most of the stellar mass was accreted at z = 1.

• The mean stellar ages of disks and bulges are correlated with disks covering a large range of ages, and late-type spirals hosting the younger disks. The bulges of S0 and early type spirals are old and metal rich as the core of E. They formed with similar processes, through mergers. Later-type spirals, however, have younger bulges, and larger contributions from secular evolution are expected. Disks are younger and more metal poor than bulges, as an indicative of the inside-out formation scenario of these galaxies.

• S0 in this sample (all are massive galaxies) act as a transition class between E and spirals, with μ_⋆(R), ⟨log age⟩_L(R), and A_V(R) between massive E and Sa. The gradient in μ_⋆ and ⟨log age⟩_L of S0 is so similar to Sa galaxies that they can result from the same formation process.

• The Hubble type rather M_⋆ drives differences in the galaxy averaged ages, and radial age gradients. These results indicate that the SFH and their radial variations are modulated primarily by galaxy morphology, and only secondarily by the galaxy mass. This suggests that galaxies are morphologically quenched and that the shutdown of star formation occurs outward and earlier in galaxies with a large spheroid than in galaxies of later Hubble type.

From the comparison of the results with the theoretical predictions from cosmological simulations, we conclude:

• Major mergers are likely the main process in building the central regions of ETGs. The metallicity gradient within 1 HLR is shallow compared with the theoretical expectation of whether minor mergers are relevant in the growth of the central core of E’s and S0’s. In our results there is no evidence either of an inversion of ⟨log age⟩_L toward older ages beyond 1−2 HLR, or of a steepening of the metallicity if these galaxies were growing in size through minor dry mergers. Massive galaxies probably accreted massive satellites that were able to retain their metal rich gas against winds, producing flatter metallicity gradients 65. Alternatively, the flattening of the metallicity radial profile can result from the quenching of star formation. When this happens, the metal cycle stops and only stars of that last star formation event remain.

• Through the negative metallicity gradients, spirals show evidence of growing inside-out. These gradients are flatter than the predictions by the classical chemical evolution models (e.g. Chiappini et al. ; Mollá & Díaz ), but are similar to those measured above the Galactic disk. The largest gradient happens in intermediate types and intermediate galaxy mass, as predicted by the Mollá & Díaz models. However, Sbc galaxies have a ⟨log Z_⋆⟩_M gradient similar to the predictions by RaDES simulations 43; 105. This indicates that the feedback recipes used in these simulations are able to recover realistic galaxies with small bulges. However, a larger set of cosmological simulations is required, covering from early-type Sa to late Sd, and a large range of galaxy mass (from 10⁹ to 10¹¹M_⊙), to confirm the general trend with the Hubble type found in this work.

Thanks to the uniqueness of the CALIFA data in terms of spatial coverage and resolution, large sample spanning all morphological types, and homogeneity and quality of the spectral analysis, we are able to characterize the radial structure of the stellar population properties of galaxies in the local universe. The results show that the Hubble sequence is a useful scheme to organize galaxies by their spatially resolved stellar density, ages, and metallicity; however, stellar extinction cannot discriminate between the different Hubble types so well. Stellar mass, although responsible for setting the average stellar population properties in galaxies, is less responsible for the quenching processes. Morphology is, however, more strongly connected with the shut down of the star formation activity in the bulges and disks of galaxies.

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Acknowledgments

CALIFA is the first legacy survey carried out at Calar Alto. The CALIFA collaboration would like to thank the IAA-CSIC and MPIA-MPG as major partners of the observatory, and CAHA itself, for the unique access to telescope time and support in manpower and infrastructures. We also thank the CAHA staff for the dedication to this project. Support from the Spanish Ministerio de Economía y Competitividad, through projects AYA2010-15081 (PI R.G.D.), and Junta de Andalucía FQ1580 (PI R.G.D.), AYA2010-22111-C03-03, and AYA2010-10904E (S.F.S.). We also thank the Viabilidad, Diseño, Acceso y Mejora funding program, ICTS-2009-10, for funding the data acquisition of this project. R.C.F. thanks the hospitality of the IAA and the support of CAPES and CNPq. R.G.D. acknowledges the support of CNPq (Brazil) through Programa Ciencia sem Fronteiras (401452/2012-3). A.G. acknowledges support from EU FP7/2007-2013 under grant agreement n.267251 (AstroFIt) and from the EU Marie Curie Integration Grant “SteMaGE” Nr. PCIG12-GA-2012-326466. C.J.W. acknowledges support through the Marie Curie Career Integration Grant 303912. E.P. acknowledges support from the Guillermo Haro program at INAOE. Support for L.G. is provided by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. L.G. acknowledges support by CONICYT through FONDECYT grant 3140566. J.I.P. acknowledges financial support from the Spanish MINECO under grant AYA2010-21887-C04-01 and from Junta de Andalucía Excellence Project PEX2011-FQM7058. I.M., J.M. and A.d.O. acknowledge support from the project AYA2013-42227-P. RAM is funded by the Spanish program of International Campus of Excellence Moncloa (CEI). J.M.A. acknowledges support from the European Research Council Starting Grant (SEDmorph; P.I. V. Wild)

References

Online material

Appendix A: Improvements resulting from the new reduction pipeline

The quality of the starlight fits to CALIFA version 1.3c spectra was assessed in Cid Fernandes et al. by averaging R_λ = O_λ − M_λ residual spectra of 107 galaxies (~ 10⁵ spectra). Inspection of these residuals revealed low amplitude (a few %) but systematic features related to unmasked weak emission lines, SSP deficiencies, and data calibration imperfections. This exercise needs updating now that the reduction pipeline has changed to version 1.5.

Figure A.1 summarizes the results of this re-evaluation. The plots show stacked R_λ = O_λ − M_λ residual spectra, in units of the median flux in the 5635 ± 45 Å window. The top panel shows results for the nuclear extractions, while the middle and bottom panels are built using spectra from zones within radial distances R = 0−1 and 1−2 half light radius (HLR, computed in the same wavelength range), respectively. Residuals are colored according with the Hubble type of the galaxies. When all galaxies are stacked, the residuals are colored according with the spatial zone extracted. These subdivisions are presented to get a sense of how the residuals relate to position within a galaxy and its Hubble type, which are two central aspects of this paper.

No matter which panel one looks at, the improvement with respect to version 1.3c is evident to the eye when compared

to figure 13 of Cid Fernandes et al. . The broad trough around Hβ present in the 1.3c spectra, for instance, is much shallower now. In fact, it is confined to late types (compare blue and red lines in the lower panel in Fig. A.1), indicating that its origin is related to calibration, and also to the SSP spectra of young stellar populations (as previously reported by Cid Fernandes et al. for SDSS data). Residuals are also visibly smaller towards the blue, including the CaII K line, which is now well fitted whereas in version 1.3c a small systematic residual subsisted¹². The humps around 5800 Å, on the other hand, are still present in version 1.5, particularly noticeable for outer regions, indicating that further refinement of the sky subtraction are warranted.

In short, the spectral fits have improved substantially with the new reduction pipeline. We attribute this to the updated sensitivity curve used in version 1.5. A more extended discussion of these and other aspects of the data reduction are presented in García-Benito et al. .

Despite these changes, the stellar population properties derived from the spectral fits did not change much in comparison to those obtained for version 1.3c data. The most noticeable changes were in mean ages, which become 0.1 dex older, and extinction, which is now 0.2 mag smaller on a global average.

Appendix B: Base experiments and uncertainties due to SSP templates

To derive the stellar population properties of these 300 CALIFA galaxies we have fitted ~253000 spectra with the GMe and CBe using the cluster Grid-CSIC at the Instituto de Astrofísica de Andalucía and the cluster Alphacrucis at IAG-USP Sao Paulo. Examples of the quality of the spectral fits as a function of the Hubble type and radial distance are presented in Fig. A.1.

Appendix B.1: Mass-metallicity relation

Here we want to find out how well our metallicity definitions follow a MZR which guarantees that galaxies like the MW or Andromeda (log M_⋆(M_⊙) ~ 11) have solar metallicity at the disk, while LMC-SMC-like galaxies (log M_⋆(M_⊙) ~ 9) have ~ 1 / 4 Z_⊙. We do this with mass-weighted and luminosity-weighted definitions of Eqs. (2) and (3), and with the two sets of SSP models (GMe or CBe).

Similarly, the correlation between the galaxy averaged stellar metallicities and the metallicity measured at 1 HLR, and the MZR, guarantee that the metallicity radial profiles scale with the galaxy stellar mass. However, the MZR in González Delgado et al. was derived using the galaxy averaged stellar metallicity instead of the metallicity measured at 1 HLR, and using the mass-weighted definition of the metallicity and only the results with the base GMe. For these reasons, we derive the MZR that results from using the mass-weighted and the light-weighted definition of the metallicity, and the GMe and CBe bases.

Figure B.1 shows the correlation of M_⋆ and (upper panels), and (lower panels) for the GMe (left panels) and CBe (right panels) SSP models. The mass-metallicity relation found by Panter et al. and Gallazzi et al. are the magenta and brown lines, respectively¹³. Note that in the four cases, the metallicities are well in the range of the dispersion given by Gallazzi et al. ; brown dashed line represent the 16th and 84th percentiles of their distribution. To compare the general trend of these values, we derived a smoothed mass-binned relation, represented by a solid black or grey-black line. As expected from the global MZR derived in González Delgado et al. , base GMe and ⟨ log Z_⋆⟩_M predict stellar metallicities for MW and LMC-SMC with the expected values. But ⟨ log Z_⋆⟩_L gives a MZR that predict higher metallicities. The opposite happens for the MZR using the base CBe, which gives mass-weighted metallicities higher on average than the SDSS metallicities. But the MZR with ⟨ log Z_⋆⟩_L goes close to the Gallazzi et al. relation, and also predicts stellar metallicities for MW-Andromeda-like and LMC-SMC galaxies with the expected values.

In summary, ⟨ log Z_⋆⟩_M with GMe and ⟨ log Z_⋆⟩_L with CBe provide a mass-metallicity relation similar to the SDSS MZR, and predict metallicities between −0.7 and −0.4 dex for galaxies with mass between ~10⁹ and 10¹⁰M_⊙, the expected values for LMC and SMC-like galaxies, and solar for MW-like galaxies.

Appendix B.2: Variations over bases GMe and CBe

Although the two sets of models are built with the same stellar libraries (MILES and granada), base GMe stops at 1.5 Z_⊙, while CBe goes up to 2.5 Z_⊙. Because MILES is built with stars in the solar neighborhood, it does not contain stars as metal rich as 2.5 Z_⊙, so CBe results in over solar metallicity should be interpreted with care. On the other hand, the central parts of galaxies can be as metal rich as 2−3 Z_⊙, and the base GMe may be too low to fit spectra of these regions, leading to saturation effects. To avoid these problems, we also fitted the spectra with another two sets of SSP, are identical to GMe and CBe, but where for each metallicity bin, two SSPs of age 16 and 18 Gyr are added to our “standard” bases. These extra bases, which we name GMd and CBd, allow galaxies older than the age of the universe if their bulges are very metal rich. Furthermore, results at very low metallicity also must be taken with care. MILES contain only few stars of metallicity below 1/100 Z_⊙. For this reason, Vazdekis et al. provide a safe age range for each metallicity bin, being the models with log Z_⋆(Z_⊙) ≤ −1.7 only valid between 10 and 18 Gyr. This safety margin is provided to avoid the cases when, because of age-metallicity degeneracy, these old metal poor models fit young metal-rich populations, may happen if the base does not include SSP younger than 100 Myr. Our fits do not suffer this problem because bases GMe and CBe both have spectra of ages as young of 1 Myr.

Appendix B.3: Global results and uncertainties associated with SSP models

To evaluate to which extent the spectral synthesis results depend on the choice of SSP models, we now compare the global properties derived with bases GMe and CBe. Using our pipeline pycasso we obtained the radial distribution of the stellar population properties for each galaxy with a spatial sampling of 0.1 HLR. Here we compare the stellar population properties of the 0.1 HLR radially sampled points, instead of comparing the results obtained from the individual 253 418 fitted spectra. Figure B.2 shows the results for a total of 6000 points corresponding to a maximum of 20 radial points (from nucleus to 2 HLR) for each of the 300 galaxies analyzed in this work. The figure compares the results for base GMe in the x-axis, with CBe in the y-axis, in the bottom and middle panels. The upper panels compare the results of GMe with GMd. Each panel quotes the mean Δ and its standard deviation, where Δ = property(CBe) − property(GMe) or Δ = property(GMd) − property(GMe).

GMe-based μ_⋆-values are higher than CBe by 0.27 dex on average, reflecting the different IMF used. Apart from this offset, the two stellar mass surface density agree to within 0.08 dex. Mean extinction is also in good agreement with a dispersion of 0.05 mag. Ages are higher in GMe than CBe by 0.14 dex for ⟨log age⟩_L and 0.08 dex for ⟨log age⟩_M, with dispersion 0.18 dex and 0.12 dex, respectively. This result is expected since base GMe also differs from CBe in IMF and isochrones. The differences in opacities in the equation of state between Padova 2000 (GMe) and 1994 (CBe) tracks produce somewhat warmer stars in the red giant branch in the former. Thus, older ages are expected with GMe than with CBe. However, the metallicities are lower in GMe than in CBe by 0.13 dex for ⟨log (Z_⋆/Z_⊙)⟩_M and very similar (on average) for ⟨log (Z/Z_⊙)⟩_L. In both cases, the dispersion is similar, 0.11 and 0.13 dex, respectively. Note that for Z_⋆ ≥ Z_⊙, the metallicities (weighted in light or in mass) are always higher with CBe than GMe, reflecting the saturation effects in the base GMe due its limitation to Z ≤ 1.5 Z_⊙. The shift at under-solar metallicities may be reflecting the age-metallicity degeneracy, CBe giving higher metallicity and younger ages.

The upper panels compare the results of GMe with the GMd. Here, we see two relevant effects. The results of GMd also differ from GMe in the range of extinctions allowed to starlight. While with GMe and CBe starlight always assumes A_V ≥ 0, with GMd, starlight can bluer the SSP spectra by up to A_V = −0.5 mag. This is allowed to avoid the effect of saturation at A_V = 0. The global effect is that ages can be 0.11 dex younger with GMe than GMd. Metallicity is not affected by this choice of A_V; but the extension to ages older than the age of the Universe in GMd has some effect on the metallicity above Z_⊙, so metallicities are slightly lower and ages slightly older.

Appendix C: 2D maps and tables

Appendix C.1: 2D maps of logμ_⋆

Figure C.1 shows the M_r vs. u − r CMD for the 300 CALIFA galaxies of our sample. Each galaxy is represented by its 2D map of the log μ_⋆ located at the position of its integrated M_r and u − r values. In this plot, the SFH is compressed into the present-day stellar mass surface density, which measures the end product of the SFH. Because our analysis accounts for extinction, these log μ_⋆ values and their radial variations are free from extinction effects. Figure C.1 clearly shows¹⁴ that log μ_⋆ correlates with M_r, and spheroids are significantly denser than late-type galaxies by one to two orders of magnitude at the center, and by one order of magnitude at distances 1−2 HLR. At the center, 2.0 ≤log μ_⋆ (M_⊙ pc^-2) ≤ 4.7, while ≤log μ_⋆ (M_⊙ pc^-2) ≤ 3.4 at 1 HLR, and 1.0 ≤log μ_⋆ (M_⊙ pc^-2) ≤ 2.9 at 2 HLR.

Appendix C.2: 2D maps of ⟨log age⟩_L

Similarly to Figs. C.1, C.2 shows the 2D maps of ⟨log age⟩_L. It portrays the correlation between the average age of the stellar populations and M_r and colors, with the most luminous and red galaxies being older, while the bluest galaxies are the youngest. Gradients of the stellar population ages are also clearly detected within each galaxy in these 2D maps, and more remarkably in galaxies located in the green valley. At the center, 7.3 ≤⟨log age⟩_L (yr) ≤ 10.1, while 8.3 ≤⟨log age⟩_L (yr) ≤ 10.1 at 1 HLR, and 7.5 ≤⟨log age⟩_L≤ 9.9 at 2 HLR.

Appendix C.3: 2D maps of ⟨log Z_⋆⟩_M

Similar to Figs. C.1, C.3 presents the 2D maps of ⟨log Z_⋆⟩_M. It clearly shows the correlation between the stellar metallicity and galaxy luminosity, equivalent to the mass metallicity

relation. Gradients of the stellar metallicities are more clearly seen in these 2D maps in galaxies with intermediate luminosity (−22 ≤ M_r ≤ −20). The most luminous galaxies have solar or over solar metallicity producing a visual saturation in the 2D maps. The stellar metallicities range from ⟨log Z_⋆⟩_M = –1.4 to 0.22.

Appendix C.4: 2D maps of A_V

Similarly to Figs. C.1, C.4 presents 2D maps of A_V. Effects of spatial binning are visible in the A_V maps, where all the pixels within a Voronoi zone have the same value. These effects are not noticeable in the μ_⋆ images (Fig. C.1) because μ_⋆ is an extensive property, and the zoning effect was softened by scaling the value at each pixel by its fractional contribution to the total flux in the zone; this is not possible for A_V (Fig. C.4), ⟨log age⟩_L (Fig. C.2), or ⟨log Z_⋆⟩_M (Fig. C.3), because these are intensive properties. Figure C.4 shows how A_V changes across the CMD: the most luminous galaxies are little affected by extinction, while A_V is higher in spirals of intermediate type and with blue colors. The mean (dispersion) A_V values at the nuclei, 1 HLR, and 2 HLR are 0.47 (0.37), 0.19 (0.16), and 0.13 (0.13), respectively. 2D maps and the difference in the mean values at different distance indicate that stellar extinction shows radial gradients.

All Tables

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