© ESO, 2014

1. Introduction

The separation of galaxies in a red sequence and a blue cloud according to their location in the color−magnitude diagram (CMD) has been well established since the work of Strateva et al. (2001). This location correlates with stellar population properties (Kauffmann et al. 2003a,b; Baldry et al. 2004; Bell et al. 2004; Brinchmann et al. 2004; Gallazzi et al. 2005; Mateus et al. 2006, 2007; Blanton & Moustakas 2009). Red galaxies are usually composed of metal rich and old stars, and have very little gas and recent star formation. In contrast, galaxies in the blue cloud are actively forming stars, and have a large gas fraction and a metal poor and young stellar population. This bimodal distribution of galaxy properties reflects the Hubble sequence, because red galaxies are mainly spheroidal dominated systems, while blue galaxies are disk dominated systems. This distribution also depends on the galaxy stellar mass (M_∗) which has become the most important parameter for galaxy evolution studies (e.g., Brinchmann & Ellis 2000; Dickinson et al. 2003; Fontana et al. 2006; Pérez-González et al. 2008), although environment can also play a relevant role (e.g., Peng et al. 2010).

Sorting galaxies by their stellar mass is a way to start to classify galaxies and to check if their properties scale among the different subsamples. Earlier results from the analysis of Sloan Digital Sky Survey (SDSS) data (Strateva et al. 2001) have reported the existence of a critical mass, ~3 × 10¹⁰ M_⊙, that divides the local population of galaxies in two distinct families: lower mass galaxies with young stellar populations, low mass surface density and low concentration index typical of disks, and higher mass galaxies with old stellar populations, high mass surface density, and concentration index typical of bulges (Kauffmann et al. 2003a,b). This dependence of the galaxy properties on the stellar mass distribution points to morphology as a secondary parameter (Balogh et al. 2001; Boselli et al. 2001). Later works have also pointed out that μ_∗ is a more fundamental parameter than M_∗. Kauffmann et al. (2006) found that there is also a critical μ_∗ ~ 3 × 10⁸ M_⊙ kpc^-2 that divides galaxies in disk-dominated and bulge-dominated systems. Below this critical surface density, μ_∗ scales with the stellar mass, while above it μ_∗ is almost constant. These results suggest that the conversion of baryons into stars in low mass galaxies increases with their halo mass, but in massive galaxies the star formation efficiency decreases in the highest mass haloes, with little star formation occurring in massive galaxies after they have assembled.

These SDSS results were obtained by analyzing a single central spectrum per galaxy, with a 3 arcsec diameter covering from nuclear regions to not more than 70% of the total galaxy light, depending on distance. Because of the radial structure of galaxy properties, such as the mass-to-light (M/L) ratio, results based on SDSS spectroscopy can be greatly affected by aperture losses and fiber location within the galaxy (Ellis et al. 2005; Iglesias-Páramo et al. 2013).

Based on spatially resolved surface photometry, Bell & de Jong (2000) found that μ_∗ is a more fundamental parameter than M_∗ in driving the star formation history (SFH). They analyzed a sample of 121 nearby S0−Sd galaxies, and concluded that the SFH of a disk galaxy is primarily driven by its local surface density, with the total stellar mass as a secondary parameter that correlates with metallicity, but not with age. This suggests that galaxy mass dependent feedback is an important process in the chemical evolution of galaxies, as has also been suggested by the mass-metallicity relation (Tremonti et al. 2004), although recent works point out that this relation is a scaled-up integrated effect of a local μ_∗ – oxygen abundance relation (Rosales Ortega et al. 2012; Sánchez et al. 2013). We note, however, that Bell & de Jong (2000) use K-band surface brightness as a proxy of the stellar mass surface density, and their results are based on color gradients, which can be affected by spatial variation of the extinction, and even by emission lines contributing to optical bands.

In a pioneering work, Zibetti et al. (2009) carried out a detailed analysis of nine nearby galaxies using SDSS ugriz plus J, H, K images, devising a method to derive the spatially resolved H-band M/L ratio as a function of the g − i color. Comparing the total stellar mass obtained from the spatially resolved μ_∗ map with the mass inferred from the integrated photometry, they find that the former can be up to 0.2 dex larger. However, because of the limited number of galaxies in their sample, they could not study how the radial structure of μ_∗ changes with M_∗ or with galaxy type.

More recently, μ_∗ profiles have been obtained for individual galaxies at different redshifts, made possible by the high spatial resolution provided by WFC3 on board Hubble Space Telescope. Now it is possible to measure the rest frame optical emission of galaxies at redshift z ~ 2, and to obtain spatially resolved maps of the stellar mass by fitting the SED in each individual pixel (Wuyts et al. 2012), or simply using an empirical relation between the rest-frame color and stellar M/L ratio (Szomoru et al. 2012). Stellar mass surface density radial profiles have been used to trace the mass distribution, concluding that galaxies at z ~ 2 are growing inside-out.

We note, however, that these works estimate not only μ_∗ but also the average age of the stellar population based on broad band photometry. The average age is a crude but robust way to represent the SFH of galaxies, and rest-frame optical colors are used extensively to obtain ages. Radial gradients of colors have been detected in bulges (Peletier et al. 1990; Silva & Bothun 1998; La Barbera et al. 2004; Menanteau et al. 2004; Wu et al. 2005; Moorthy & Holtzman, 2006; Roche et al. 2010) and disks (Peletier & Balcells 1996; de Jong 1996; Peletier & de Grijs 1998; Bell & de Jong 2000; MacArthur et al. 2004; Muñoz-Mateos et al. 2007; Tortora et al. 2010; Bakos et al. 2008). Usually, a color gradient is interpreted as due to radial variations in age or metallicity, but because of the age-metallicity-extinction degeneracy, color gradients can also be related to metallicity and/or extinction gradients that are certainly present in the disks and central regions of massive galaxies.

Spectroscopic data and measured line-strength stellar indices can help to break these degeneracies (Trager et al. 2000; Proctor & Sansom 2002; Sánchez-Blázquez et al. 2007; MacArthur et al. 2009). Pioneering three-dimensional spectroscopic surveys like SAURON (Bacon et al. 2001; de Zeeuw et al. 2002), and ATLAS3D (Capellari et al. 2011) have taken this approach to spatially resolve the stellar population properties of mainly early-type galaxies (Peletier et al. 1997; McDermid et al. 2006; Chilingarian 2009; Kuntschner et al. 2010; see also Ganda et al. 2007, for a few spiral galaxies). Unfortunately, the short spectral range in these works limits the analysis to a few spectral indices, with little leverage to trace extinction effects and to use long-range continuum shape to further constrain stellar populations properties. Surveys covering a larger spectral range exist (e.g., Chilingarian 2009; Blanc et al. 2013; Yoachim et al. 2012; Greene et al. 2012; Sil’chenko et al. 2012), but they are still based on a small number of galaxies.

It is clear from this summary that spatially resolved spectroscopy covering the whole optical wavelengths for a large homogenous sample is needed to better map the radial structure of the stellar population properties, and to ascertain the roles that μ_∗ and M_∗ play in the SFH of galaxies. The Calar Alto Integral Field Area (CALIFA, Sánchez et al. 2012; Husemann et al. 2013) is the largest 3D spectroscopic survey to date of galaxies in the local Universe, providing a unique set of data for galaxies covering a large range of masses (10^9 − 12 M_⊙) and morphological types (from E to Sc), spatially resolved up to three half-light radii (HLR).

We have already obtained the spatially resolved history of the stellar mass assembly for the first 105 galaxies of CALIFA. In Pérez et al. (2013) we applied the fossil record method of spectral synthesis to recover the spatially and time resolved SFH of each galaxy, finding that galaxies more massive than 10¹⁰ M_⊙ grow inside-out. We also show that the signal of downsizing is spatially preserved, with both inner and outer regions growing faster for more massive galaxies. Furthermore, we show that the relative growth rate of the spheroidal component, nucleus, and inner galaxy, which happened 5−7 Gyr ago, shows a maximum at a critical stellar mass of ~7 × 10¹⁰ M_⊙.

We use the full spectral fitting technique because it has been proven to reduce the age-metallicity degeneracy (Sánchez-Blázquez et al. 2011). In addition, this technique, which has been extensively applied to single SDSS spectra of galaxies (e.g., Cid Fernandes et al. 2005, 2007; Asari et al. 2007), successfully produces the 2D distribution of the stellar population properties when applied to CALIFA data cubes (Cid Fernandes et al. 2013). Additionally, we have studied extensively the uncertainties associated with the estimation of the radial distribution of the stellar population properties (Cid Fernandes et al. 2014).

In this paper we extend our study of the spatially resolved stellar population properties of galaxies in the CALIFA survey; we obtain the radial structure of the stellar mass surface density and ages of the stellar population and their dependence on the galaxy stellar mass and morphology; we compare the averaged and integrated properties of the galaxies, and find out where and in which galaxies the total stellar mass and/or the local stellar mass surface density is more connected to their history.

This paper is organized as follows. Section 2 describes the observations and summarizes the properties of CALIFA galaxies and of the subsample studied here. In Sect. 3 we summarize the fossil record method of extracting the SFH, and the single stellar population models used as ingredients for the full spectral fitting. Section 4 presents the 2D maps of μ_∗ and age, as well as their radial structures. Section 5 deals with the total stellar mass. Section 6 compares the galaxy-averaged with the integrated stellar population properties, and links them with their values at one HLR. In Sect. 7 we obtain the mass weighted size, and we discuss the ratio of half-mass (HMR) to half-light radii as a function of galaxy mass and the spatial variation of the M/L ratio. Section 8 presents the radial structures of age and μ_∗ stacking galaxies according to their M_∗, and concentration index, and we discuss the roles of M_∗ and μ_∗ in the history of disk and spheroidal galaxies. Finally, Sect. 9 summarizes the results obtained and presents our conclusions. Throughout we adopt a Salpeter IMF (Salpeter 1955), resulting in stellar masses a factor of 1.78 larger than in the case of a Chabrier IMF (Chabrier 2003).

2. Observations, data reduction, and sample

2.1. Observations and data reduction

The observations were carried out with the Potsdam Multi-Aperture Spectrophotometer (PMAS, Roth et al. 2005) in the PPak mode (Verheijen et al. 2004) at the 3.5 m telescope of the Calar Alto Observatory (CAHA); PPak is a fiber bundle of 382 fibers of diameter each, covering a 74″ × 64″ field of view (FoV, Kelz et al. 2006).

Observations for CALIFA are obtained in two different spectral settings using the V500 and V1200 gratings. The V500 grating achieves a spectral resolution of ~6 Å (FWHM) with a nominal wavelength coverage from 3745−7300 Å, while the V1200 achieves a higher spectral resolution of ~2.3 Å, covering the 3650−4840 Å range. However, the useful wavelength range is reduced by vignetting of the CCD corners which cannot be fully compensated with the three-dithering scheme. More extended explanations on the observational strategy, effects of vignetting, the reduction pipeline, and data quality can be found in Sánchez et al. (2012) and Husemann et al. (2013).

To reduce the effects of the vignetting on the data, we combine the observations in both setups such that they fully cover the optical range from [OII] λ3727 to [SII] λλ6717, 6732. To combine both spectral setups we first degraded the spectral resolution of the V1200 data set to match the V500 data. This is done within the standard CALIFA pipeline to ensure that the data handling and error propagation matches that of the V500 data. Spatial alignment of the V500 and V1200 datacubes requires only full pixel shifts because both datacubes have been reconstructed during the correction for differential atmospheric refraction such that the central surface brightness peak is centered on a certain pixel. The V500 and V1200 data are always observed under different observing conditions, so that the difference in the seeing will slightly affect the observed surface brightness for each spaxel. Thus, we scale all individual spectra of the V1200 data such that they match with surface brightness of the corresponding V500 data within the unvingetted wavelength range 4500−4600 Å. Finally, a combined V1200 + V500 datacube is produced where the wavelength range shortward of 4600 Å is taken from matched V1200 datacube and long-ward of 4600 Å is taken from the original V500 datacube.

The combined V1200 + V500 datacubes were processed as described in Cid Fernandes et al. (2013). Briefly, spectra adequate for a full spectral synthesis analysis of the stellar population content were extracted in a way that ensures a signal-to-noise ratio S/N ≥ 20 in a 90 Å wide region centered at 5635 Å (in the rest-frame). When individual spaxels do not meet this S/N threshold (typically beyond a couple of half-light radii from the nucleus), they were coadded into Voronoi zones (Cappellari & Copin 2003). On average, we analyzed ~1000 zones per galaxy (to be precise, the 107 galaxies studied in this paper were segmented into 98 291 zones). Pre-processing steps also include spatial masking of foreground/background sources and very low S/N spaxels, rest-framing, and spectral resampling. The whole process takes spectrophotometric errors (ϵ_λ) and bad pixel flags (b_λ) into account. The spectra were then processed through pycasso (the Python CALIFA starlight Synthesis Organizer), producing the results discussed throughout this paper.

2.2. The parent sample and the first 107 galaxies

A detailed characterization of the CALIFA sample will be presented by Walcher et al. (in prep.). Here we summarize its main properties and compare it to the subsample studied in this paper.

CALIFA’s mother sample contains 939 galaxies selected from the SDSS DR7 photometric catalog (Abazajian et al. 2009). In addition to the restriction in declination to ensure good visibility from CAHA, the main selection criteria are: a) angular isophotal diameter in the SDSS r-band in the range D₂₅ = 45 − 80 arcsec, to ensure that objects fill well the PPak FoV; and b) redshift range z = 0.005 − 0.03, guaranteeing that all relevant optical emission lines are covered. The sample includes a significant number of galaxies in the different areas across the CMD, ensuring that CALIFA spans a wide and representative range of galaxy types.

In this paper we present the results of the analysis of the first 107 galaxies observed by CALIFA. The observing order selection is random, but is this subset representative of the mother sample as a whole? To answer this question, Fig. 1 compares the distributions of galaxy properties in the mother sample (empty bars) and in our subsample. The plots show (scaled) histograms of the absolute magnitude, the ratio of the isophotal major-axis to minor-axis diameters, colors, the Petrosian radius, and concentration index (defined as the ratio of Petrosian radii ), as well as the u − r vs. M_r CMD. All data were extracted from the SDSS photometric catalog for the CALIFA mother sample. The histograms are normalized to form a probability density, i.e. each bar scales with the ratio of the number of galaxies in each bin and the total number of galaxies multiplied by the bin width. A simple visual inspection shows that our subsample of 107 galaxies represents well the CALIFA sample. We thus expect that the results reported in this paper will remain valid once the full sample is observed. We note, however, that without applying a volume correction, these distributions do not represent the local galaxy population.

3. Methods, ingredients, and uncertainties

Our method of extracting extract stellar population information from the CALIFA data cubes is based on the full spectral synthesis approach. This section presents a summary of the method, ingredients, and tests that we have carried out (see also Appendix B).

3.1. The spectral synthesis method

Methods of extracting information on stellar populations encoded in galaxy spectra split into two broad categories: those which focus on spectral indices like equivalent widths and/or colors (Bica 1988; Proctor et al. 2004; Gallazzi et al. 2005, 2006), and those which use the whole spectrum (Heavens et al. 2004; Cid Fernandes et al. 2005; Ocvirk et al. 2006; Koleva et al. 2009; Tojeiro et al. 2007; MacArthur et al. 2009). Both have pros and cons. The full spectral synthesis approach has boomed since the first generation of medium spectral resolution evolutionary synthesis calculations became available with the paper by Bruzual & Charlot (2003), and was one of the main tools employed in the mining of the SDSS spectroscopic database, leading to the derivation of physical properties and SFHs of galaxies (e.g., Panter et al. 2003, 2007; Mateus et al. 2007; Vale Asari et al. 2009; Tojeiro et al. 2009). Here, we use the full spectral fitting approach.

We analyze the stellar population properties of CALIFA galaxies with the starlight¹ code (Cid Fernandes et al. 2005), which fits an observed spectrum (O_λ) in terms of a model (M_λ) built by a non-parametric linear combination of N_⋆ simple stellar populations (SSPs) from a base spanning different ages (t) and metallicities (Z). Dust effects are modeled as a foreground screen with a Cardelli et al. (1989) reddening law with R_V = 3.1. Kinematical effects are also accounted for assuming a Gaussian line-of-sight velocity distribution. The fits were carried out in the rest-frame 3800−6850 Å interval, with a Δλ = 2 Å sampling. Windows around the main optical emission lines of [OI], [OII], [OIII], [NII], HeI, and the Balmer series from Hα to Hϵ were masked in all fits. Because of its interstellar absorption component, the NaI D doublet was also masked. A more detailed account of how we process CALIFA data cubes through starlight is given in Cid Fernandes et al. (2013, 2014).

All spectral fits were performed using the cluster Grid-CSIC at the Instituto de Astrofísica de Andalucía. Example spectral fits are presented in Appendix B.

3.2. SSP spectral models

Simple stellar population models are the key ingredient in any spectral synthesis analysis, as it is through them that one transforms observed quantities to physical properties of the stellar populations in galaxies. The SSP spectra result from the combination of an initial mass function (IMF) with stellar isochrones and libraries that provide the spectra of stars with temperature, gravity, and metallicity demanded by the evolutionary tracks (e.g., Tinsley 1980; Bruzual & Charlot 1993; Leitherer et al. 1999; Walcher et al. 2011; Conroy 2013).

All these ingredients involve choices among different options (different IMFs, different tracks, different libraries, and different codes to put them all together), and for this reason we have performed spectral fits using three different sets of SSPs: (a) the GM base is a combination of the SSP spectra provided by Vazdekis et al. (2010) for populations older than 63 Myr and the González Delgado et al. (2005) models for younger ages; (b) base CB is an updated version of the Bruzual & Charlot (2003) models that replaces STELIB (Le Borgne et al. 2003) with a combination of the MILES (Sánchez-Blázquez et al. 2006; Falcón-Barroso et al. 2011b) and granada (Martins et al. 2005) spectral libraries; and (c) base BC comprises the standard Bruzual & Charlot (2003) models.

In Cid Fernandes et al. (2014) we compared the results of fitting the same 98 291 spectra studied here, and the main conclusions are that masses (or mass surface density), mean ages, and extinction are in very good agreement. Some discrepancies are, however, found in metallicity. Comparing GM and CB, the dispersion in luminosity weighted ages is 0.14 dex and the dispersion in A_V is 0.06 dex. GM stellar masses are 0.27 dex higher than CB due to the different IMFs (Salpeter vs. Chabrier), but apart from this offset, the two masses agree to within a dispersion of 0.16 dex. Similar conclusions are obtained when GM and BC results are compared. In short, the differences in mass, age, and extinction obtained with these three sets of SSP models are all relatively small. Uncertainties due to random noise variations and continuum shape errors associated to flux calibration were evaluated through simulations and found to be somewhat smaller than, but of the same order as those associated with the choice of SSP models.

For these reasons, here we present the results obtained with only one set of SSP models. We have chosen base GM, but a comparison of the results obtained with other bases for the most relevant galaxy properties analyzed here is presented in Appendix B. The GM base spans 39 ages from 1 Myr to 14 Gyr, and four metallicities (Z = 0.2,0.4,1,1.5 Z_⊙). They are built with the Girardi et al. (2000) evolutionary tracks, except for the youngest ages (1 and 3 Myr), which are based on the Geneva tracks (Schaeller et al. 1992; Schaerer et al. 1993a,b; Charbonnel et al. 1993). We adopt a Salpeter initial mass function throughout.

4. Spatially resolved properties of the stellar population in galaxies

The spatial distributions of μ_∗ and the luminosity weighted mean stellar age (⟨log age⟩_L, defined in Eq. (9) of Cid Fernandes et al. 2013) are at the heart of the analysis carried out in this paper. For this analysis we prefer to use luminosity weighted ages for two reasons: first because luminosity is more sensitive than mass to age variations and thus provides a wider range of ages; second, because after comparing the ages estimated by starlight for several galaxies with ages estimated using Lick indices, we find that luminosity weighted ages are more in agreement with Lick ages than mass weighted ones, so this choice facilitates comparison with this more traditional school of stellar population analysis in galaxies. This section presents the 2D maps and radial profiles of μ_∗ and ⟨log age⟩_L. The results are presented in the framework of the CMD. Because absolute magnitude is related to M_∗ and color is a proxy for the stellar population age, the CMD is a convenient observational framework for studying the properties of different types of galaxies.

4.1. 2D maps: stellar mass surface density and age

Figures 2 and 3 both show the M_r vs. (u − r) CMD for our sample². Each galaxy is represented by its 2D map of μ_∗ (Fig. 2) and ⟨log age⟩_L (Fig. 3), located at the position of their integrated M_r and (u − r) values. In these plots the SFH of each galaxy is compressed into μ_∗ and ⟨log age⟩_L, with μ_∗ representing the end product of the SFH and ⟨log age⟩_L a measure of the pace with which this end product was achieved.

Cid Fernandes et al. (2013) explain the processes that we follow to convert light into mass and the determination of the ages through the spatially resolved SFH, all included in our analysis pipeline pycasso. Effects of the spatial binning are visible in the mean age maps, where all pixels in a Voronoi zone have the same value. These effects are not noticeable in the μ_∗ images because the zoning effect was softened by scaling the value at each pixel by its fractional contribution to the total flux in the zone, thus producing smoother images.

Figures 2 and 3 show the results obtained with the GM template library. We note that our spectral synthesis analysis accounts for extinction, thus, to the extent that the simple foreground dust screen model works, our μ_∗ values and their radial variation are free of dust effects. This is an improvement compared to most works based on photometry, which estimate μ_∗ from the surface brightness typically assuming that color variations are entirely due to changes in M/L, and dust effects on colors compensate those on luminosity.

Figure 2 shows the stellar mass surface density maps of each of our 107 galaxies. One sees that spheroids are one or two orders of magnitude denser than disks. The gradient is steeper in the luminous and red galaxies than in faint and blue ones. The disk μ_∗ scales well with the luminosity of the galaxy.

Figure 3 shows that ⟨log age⟩_L is correlated both with color (as expected) and luminosity (due to the downsizing effect). Larger age gradients are seen in the galaxies in the green valley than in the more massive red galaxies. The fainter and bluer galaxies either do not show a clear age gradient or seem to have more of an inverted gradient, being younger in the center than in the outskirts.

4.2. Radial profiles of μ_∗ and ⟨log age⟩ _L

In order to study the radial variations with galaxy type, we compressed the 2D maps of μ_∗ and ⟨log age⟩_L in azimuthally averaged radial profiles. A common metric is needed to compare (and stack) the radial profiles, so we expressed the radial distance in units of HLR. Appendix A explains how we derived , defined as the semi-major axis length of the elliptical aperture containing 50% of the light at 5635 Å. There we also compared with the Petrosian radius () and with the half-light radius obtained with circular apertures ().

The pycasso code provides two methods for computing radial profiles: area averaging and spaxel averaging (Cid Fernandes et al. 2013). The second method, which averages a property among all values in the same radial bin, is used here for both μ_∗ and ⟨log age⟩_L, but area averaging yields very similar results.

We divide the CMD into 5 × 5 bins, covering the whole range in absolute magnitude (− 23 ≤ M_r ≤ − 18) and color (1.25 ≤ u − r ≤ 4.25). The individual radial profiles of galaxies located in the same bin are stacked, limiting the radial range to R ≤ 3 HLR. The number of galaxies is shown in the top-right corner in each box.

Figure 4 shows the stacking results for log μ_∗ and ⟨log age⟩_L as solid lines. Values for individual spaxels are shown in blue, intensity coded by the density of points. Unlike for μ_∗, ⟨log age⟩_L images cannot be softened by the zone effects, so we assign the same age to all the spaxels that belong to a given Voronoi zone. Because these spaxels are at different distances within the galaxy, the radial structure of ⟨log age⟩_L shows horizontal stripes that are not seen in the radial profiles of log μ_∗. The consequence is that the dispersion in ⟨log age⟩_L profiles is higher than in log μ_∗, and the radial structure of ⟨log age⟩_L is more uncertain than that of log μ_∗ beyond 2 HLR (where spatial binning becomes prevalent).

The mean stacked profile for all 107 galaxies is shown as the inset in the top-right of each figure. The horizontal and vertical scales of all panels is the same used in this plot. In addition to the mean stacked profile (solid line) in each CMD bin, we plot for reference the mean stacked profile of the 107 galaxies (dashed line), so that systematic trends in the radial structure are more clearly seen.

As expected, μ_∗ exhibits negative radial gradients in all cases. In the nuclei 2.5 ≤ log μ_∗ (M_⊙ pc^-2) ≤ 4.5, while in the outer radii 1.5 ≤ log μ_∗ (M_⊙ pc^-2) ≤ 3. A trend of log μ_∗ with the magnitude and the color of the galaxy is found: red and luminous galaxies are denser than blue and faint galaxies throughout their extent. Disk galaxies show log μ_∗ profiles that scale with M_r. A general trend is also found between the central value of log μ_∗ of each galaxy (or the average log μ_∗) and M_r, as expected since the magnitude correlates with the total mass.

Similarly, ⟨log age⟩_L shows negative gradients, but not for all CMD bins. A strong gradient is found for most of the disk galaxies in the green valley (− 22 ≤ M_r ≤ − 19 and 2 ≤ u − r ≤ 3.5), with mean ages ranging from 5−6 Gyr at the galaxy center to 1 Gyr at R = 1 HLR in the disk. Galaxies in the blue cloud (M_r ≥ − 20 and u − r ≤ 2) show less age gradient, with flat radial profiles at an age ≤1 Gyr beyond 1 HLR. Red galaxies are the oldest (~10 Gyr), not only at the core but also in the extended envelope, and they also show almost flat age gradients.

The CALIFA sample was chosen to cover most of the FoV of PPaK, which corresponds to sizes between 2 and 5 HLR; the typical size is 3 HLR. This is why the radial profiles in Fig. 4 are represented up to 3 HLR, but the 2D maps in Fig. 3, are plotted up the maximum radius observed for each galaxy.

5. Stellar masses

The stellar mass is one of the most important physical properties for galaxy evolution. Armed with the results from our spectral synthesis analysis, we now present total stellar masses derived for the CALIFA subsample of 107 galaxies.

These masses are obtained by adding, for each galaxy, the masses of each zone, hence taking into account spatial variations of the stellar populations and extinction across the face of the galaxies. We take into account areas that were masked in the data cubes (see Appendix A), replacing the missing spaxels by the average of μ_∗ values at the same radial distance. On average, this correction amounts to just ~5%, and for only 3% of the galaxies the correction reaches 0.05−0.1 dex in log M_∗. We have also verified that light outside the PPak FoV does not add much to the stellar masses computed here. As explained in Appendix C, correcting for this effect would increase our masses by 8% on average.

Figure 5a shows the distribution of M_∗. The masses range between 10⁹ and 10¹² M_⊙, with the peak at ~10¹¹ M_⊙. Overall, our sample is dominated by galaxies in the 10¹⁰ − 3 × 10¹¹ M_⊙ range, so CALIFA is successfully sampling Milky Way and M31-like galaxies. Using the concentration index, , to divide the sample in spheroidal (C ≥ 2.8) or disk (C < 2.8) dominated galaxies, we find a clear segregation in mass: galaxies with C ≥ 2.8 are dominated by the most massive ones (≥10¹¹ M_⊙), while disk galaxies are well distributed over the entire CALIFA mass range, with the peak at 10¹¹ M_⊙. This distribution in mass is not meant to be representative of the local universe, since the CALIFA sample is not complete for M_r ≥ − 19.5. Dwarf elliptical or irregular galaxies, for instance, are not sampled.

In the previous section the spatially resolved properties of galaxies were presented as a function of their location in the (M_r, u − r) CMD (Figs. 2−4), where the absolute magnitude plays the qualitative role of galaxy mass. To calibrate this relation in quantitative terms, Fig. 5b shows our stellar masses against M_r. Results are shown for base GM, as are the results obtained with this set of SSP models adopted throughout this paper. As expected, a good correlation is found, but the dispersion in mass is ~0.19 dex with respect to a linear fit. The inset in Fig. 5b shows that residuals correlate with color, revealing the well-known relation between stellar mass and stellar population properties, with massive galaxies being older (and thus having larger M/L) than less massive ones, as previously shown in Fig. 4.

Figure 5c compares the masses estimated from our spatially resolved spectroscopic analysis with those obtained by Walcher et al. (in prep.) through SED fitting using just SDSS photometry (blue symbols) or 2MASS plus SDSS bands (red). gray points represent photo-masses obtained by fitting the SDSS bands with the kcorrect code (Blanton & Roweis 2007). Our starlight-based masses correlate well with the photometric masses, but with systematic offsets: red, blue, and gray points in Fig. 5c are shifted from the one-to-one line by − 0.20, − 0.33, and − 0.39 dex, respectively. Of this offset, a factor of − 0.25 dex can be accounted for by the Salpeter IMF used in our spectral fits with base GM versus the Chabrier IMF adopted in the photo-masses. Also, the photo-masses are not corrected for extinction, so they are expected to be a factor of 0.16−0.2 dex lower than the starlight values if we assume an average A_V = 0.4 − 0.5 mag. Alternatively, the spectroscopic and photometric methods obtain SFHs that weight the contribution of old stellar populations in different ways, resulting in M/L ratios larger in starlight than obtained with SED fitting. The dispersion around the best linear fits (dashed lines in Fig. 5c) are 0.16−0.19 dex, which is of the same order as the dispersion between different photo-masses.

Table 1 lists the masses for all 107 galaxies obtained for the base GM. Figure B.2 shows the comparison of mass distributions for other SSP bases.

6. Spatially resolved properties vs. galaxy-averaged and integrated stellar population properties

In this section we take advantage of our spatially resolved information to address two inter-related questions: (a) what radial location can be considered typical of a galaxy as a whole in terms of its stellar population properties? and (b) how do properties derived from an integrated spectrum (obtained from the spatially collapsed data cube) relate to the typical (spatially averaged) properties within a galaxy?

The relevance of these questions resides in the fact that spatially unresolved spectra of galaxies will always be more abundant than IFS data like CALIFA. It is therefore important to understand precisely what it is that an integrated spectrum represents.

6.1. Galaxy-averaged stellar population properties

Let us define galaxy-wide average values for ⟨log age⟩_L and μ_∗ as follows:

• Galaxy-averaged age: the luminosity weighted mean value of ⟨log age_xy⟩_L over all spaxels is computed as (1)where L_xy is evaluated at our reference wavelength 5635 Å.

• Galaxy-averaged stellar mass surface density: we simply divide the total mass (summing the contributions from all the spaxels) by the total area of these spaxels to obtain the galaxy-averaged stellar mass density (2)

Figure 6 compares these galaxy-wide averages with the corresponding values at R = 0.1 (red crosses), 1 (gray circles), and 2 HLR (blue crosses). The left panel shows a very good agreement between ⟨log age⟩_L at 1 HLR and the galaxy-wide average. The relations for other radii exhibit offsets and larger dispersions. As expected (see Fig. 4), the nuclei are older by an average of 0.2 dex than the galaxy-averaged age (red crosses). We note that because of the variation of the age gradient with the galaxy mass and Hubble type, the nuclei of spheroidal galaxies (C ≥ 2.8) are only about 0.16 dex older than , whereas for disk galaxies this difference increases to 0.23 dex. On the other hand, the outer 1−3 HLR of either disk or spheroidal galaxies are more similar to the average galaxy age (blue crosses), with an average offset of − 0.08 dex.

Figure 6b repeats these comparisons, but now for the stellar mass surface density. Again, the galaxy-averaged values are well matched by the μ_∗ values at R = 1 HLR. For spheroidal galaxies (marked with black dots), is slightly smaller than μ_∗ at 1 HLR, coinciding better with μ_∗ at 1.2 HLR. In nuclei μ_∗ is significantly larger than , by typically 1.25 dex in disk galaxies and 1.43 in spheroidal galaxies.

In summary, the values of ⟨log age⟩_L and μ_∗ at 1 HLR represent remarkably well the galaxy-averaged age and stellar mass surface density, except that spheroidal galaxies are slightly denser at R = 1 HLR than their spatially averaged value.

Both and correlate with the total stellar mass. The latter relation is shown in the right panel of Fig. 6, where one sees increasing from ~10^1.5 M_⊙/pc² for M_∗ ~ 10⁹ M_⊙ to ~10³ M_⊙/pc² for the most massive galaxies in the sample. The points are well fitted by a power law, . This relation was reported before by Kauffmann et al. (2003b) from the analysis of a much larger SDSS sample. They also reported a sharp change in the slope in the μ_∗ − M_∗ relation at a stellar mass of ~3 × 10¹⁰ M_⊙, finding that below this mass μ_∗ increases as , while above it μ_∗ is constant. Even though Fig. 6c does not show a clear change in slope, we can confirm that in the disk galaxies of our sample, , and in spheroid dominated galaxies (black symbols) the relation follows a much flatter slope, with . Similar results are obtained if we repeat the analysis replacing by the surface density at 1 HLR, except that in this case the slope for early-type galaxies is 0.02 ± 0.11, much closer to the Kauffmann et al. (2003) fit. The transition mass of ~3 × 10¹⁰ M_⊙ reported by Kauffmann et al. (2003) corresponds to ~5 − 6 × 10¹⁰ M_⊙ for our IMF. Our sample does not yet allow us to precisely pinpoint a transition mass. Nonetheless, we will see below that all of the spheroid dominated galaxies in our sample with M_∗ ≥ 10¹¹ M_⊙ show radial variations of μ_∗ that are independent of the stellar mass.

6.2. Integrated vs. galaxy-averaged

Besides the 98291 spectra of all zones of all galaxies, we have also used starlight to fit the 107 total spectra obtained by collapsing the data cube to a single spectrum per galaxy. These integrated spectra, which emulate the situation in integrated spectroscopy surveys, are fitted in the same way as the individual ones, adopting identical assumptions regarding the SSP templates, masks, etc. It is instructive to compare properties derived from the integrated spectra with those derived from our spatially resolved analysis.

Figure 7a compares the total stellar masses derived from the integrated spectra (on the vertical axis) with those obtained by adding the zone masses (horizontal). The two values agree very well. The mean difference in log M_∗ is in fact 0.00, and the dispersion is ± 0.07 dex.

Figure 7b compares the ⟨log age⟩_L values from the integrated spectra to the galaxy-average age (Eq. (1), gray circles). Again, the two values match each other, with no mean offset and a dispersion ± 0.1 dex. Extinction values also agree, as shown in Fig. 7c. The A_V values obtained from spectral fits of integrated spectra are on average only 0.02 mag larger than the mean A_V over all zones, with a dispersion of just ± 0.03 mag. The black symbols in Figs. 7b and c compare integrated ages and extinctions to those at 1 HLR. The integrated minus 1 HLR differences are 0.02 ± 0.12 dex for ⟨log age⟩_L and 0.06 ± 0.09 mag for A_V, only slightly worse than for galaxy-wide averages.

Overall, the total stellar mass, age and extinction estimated from integrated spectroscopy are remarkably robust when compared with those obtained from a spatially resolved analysis.

7. Mass weighted size: the half-mass radius and its relation to the half-light radius

While evolution of galaxies is nowadays characterized by their stellar mass more than their luminosity, galaxy sizes are still estimated from the way light, not mass, is distributed. Just as the stellar mass of a galaxy is a more fundamental property than its luminosity, at least when one considers galaxy evolution, the HMR is a more physical metric than the HLR. These two radii are only equivalent in the idealized case of a spatially uniform M_∗/L ratio. Variations of the SFH and/or extinction within a galaxy produce a spatially dependent M/L ratio, and hence differences in their sizes estimated from mass and from light.

We take advantage of our spatially resolved SFH and extinction maps to investigate the relation between HLR and HMR. We use the 2D distribution of μ_∗ to define the HMR, for both circular () and elliptical () apertures, as the radius at which the mass curve of growth reaches 50% of its asymptote. Figure 8a shows how and relate to their luminosity based counterparts and . The following equations express the best fit relations between these radii (in kpc): These fits and Fig. 8a show that the HMR is generally smaller than the HLR. The histogram of for our 107 galaxies is shown in Fig. 8c (black bars). On average, (std = 0.13), so galaxies are typically 20% smaller in mass than they appear to be in optical light. This number is only slightly smaller than the 25% reported by Szomoru et al. (2012) for a sample of high-redshift galaxies analyzed with multi-band photometry. This agreement gives us a preliminary indication that there is no significant cosmic evolution of the HMR/HLR ratio.

7.1. The relative roles of SFH and extinction gradients

Both SFH and extinction gradients induce differences between HMR and HLR. Our analysis provides a way to disentangle the relative roles of these two effects.

Unlike the HMR, the HLR is sensitive to extinction variations. When A_V increases inwards, which is generally the case, the excess dimming of the central regions with respect to outer ones produces HLR values larger than those which would be measured in the absence of extinction gradients. We use our starlight-derived A_V maps to “dust off” the L_λ5635 images and re-evaluate the HLR from the extinction corrected curve of growth, obtaining . This allows us to quantify the role of dust in the observed difference between HMR and HLR.

Figure 8b compares to both (crosses) and (circles). Except for a slightly smaller scatter, the extinction correction brings the irregular galaxy NGC 3991 (CALIFA 475, the outlier cross with ) to the one-to-one line. On average, however, (std = 0.11) (Fig. 8c, gray histogram), corresponding to HMR 15% smaller than the extinction corrected HLR. Compared to the 20% difference found without this correction, we conclude that dust gradients play a relatively small role in explaining the difference between mass and light based sizes.

The main reason why HMR < HLR is thus that stellar populations produce less light per unit mass in the center than outside it. This is explicitly confirmed in Fig. 9, where is plotted against the difference in log M/ (i.e., the extinction-corrected M/L ratio) between R = 1 HLR and the nucleus. Galaxies with small M_∗/L gradients have , while those with the largest gradients can be up to a factor of two more compact in mass than in light. The points in Fig. 9 are color-coded by the corresponding ▽⟨log age⟩_L, showing that age variations are the main factor behind the difference between HMR and HLR.

Therefore HMR < HLR is ultimately a fingerprint of inside-out growth, previously found for this sample by Pérez et al. (2013). This result explains why effective radii derived in the near infrared are generally smaller than those obtained in optical bands (La Barbera et al. 2004, 2010; Falcón Barroso et al. 2011a). Besides being less sensitive to extinction effects, the near infrared is a better tracer of stellar mass than the optical.

7.2. Relation with galaxy properties

The dispersion in the HMR/HLR ratio is significant (Fig. 8c), which prompts the question of whether it correlates with some global galaxy property. Szomoru et al. (2012) were unable to identify any significant dependence of the ratio on the galaxy properties.

We investigated this issue by examining correlations between (and ) with galaxy mass, luminosity, age, color, concentration index, central surface brightness, and size. Two distinct behaviors are identified: decreases with color, surface brightness, central stellar age, and stellar mass surface density in galaxies that are bluer than u − r ~ 2.5, fainter than M_r ~ − 20.5, younger than ~1−3 Gyr, and less dense than log μ_∗ ≤ 3.5 M_⊙/pc² at their core. This trend can be seen in the relation between and the stellar mass shown in Fig. 10. For galaxies with M_∗ ≲ 10¹¹ M_⊙, decreases with increasing stellar mass, whereas this ratio is almost constant for more massive galaxies. This reflects the bimodal distribution of galaxies found in SDSS (Strateva et al. 2001): for spheroid dominated (C ≥ 2.8), red, old massive galaxies, the ratio is almost constant, independent of the stellar mass, but for disk galaxies, the ratio changes significantly from 1 to 0.5 as galaxies go from the blue cloud to the red sequence through the green valley.

Galaxies with lower / are those with larger M/L gradients and age gradients. These are galaxies dominated by a large central bulge surrounded by an extended luminous blue disk. These results point to the same conclusions obtained in Pérez et al. (2013), where we find that galaxies with M_∗ ≥ 10¹⁰M_⊙ grow their mass inside-out, and galaxies with a critical mass ~6 − 8 × 10¹⁰ M_⊙ have been relatively more efficient growing their central regions. If galaxies grow inside-out, we expect that . In the proposed scenario by van Dokkum et al. (2010), galaxies more massive than 10¹⁰ M_⊙ build their core via short violent bursts at high-redshift, and their envelope via accretion of material since z = 2. The SFH in the core, where half of the galaxy mass formed, results in a stellar population that is quite different from that of the extended envelope, giving . At intermediate masses, ~10¹¹ M_⊙, disk galaxies have the lowest , as expected if the central mass of these galaxies grow at a rate that is significantly larger than their extended envelope. However, for low mass galaxies (M_∗ ≤ 10¹⁰ M_⊙), , as expected if they are not growing their mass inside-out, and the build up of their central mass is probably dominated by secular processes. Thus, HMR/HLR is a good probe of the variation of the SFH in the core with respect to extended envelope in galaxies.

8. Star formation histories in terms of stellar mass, surface density, and morphology

We now explore the dependence of the SFH (represented by the first moment of the age distribution, ⟨log age⟩_L) with the total stellar mass (M_∗), surface density (μ_∗), and morphology (as encoded by the concentration index C). We inspect how the radial structure of ⟨log age⟩_L and μ_∗ varies with M_∗ and C. We discuss first the relation resulting from our spatially resolved analysis between μ_∗ and ⟨log age⟩_L, then their gradients in the inner HLR, and radial profiles. The goal is to ascertain whether galaxies dominated by the spheroid or by the disk are well separated in their spatially resolved stellar population properties, where this takes place, and and which stellar mass or stellar mass surface density is the main independent parameter that preserves the SFH of galaxies.

8.1. Stellar mass surface density − age relation

In a pioneering work, Bell & de Jong (2000) correlate the local surface brightness in the K band of a sample of spirals with the age of each region, derived from optical and near-infrared colors. They find that ages are much better correlated with their local surface brightness than with the galaxy absolute magnitude in the K band, and conclude that the surface density plays a more fundamental role in the SFH of disks than the mass of the galaxy. They suggest that the correlation can be explained through a dependence of the star formation law on the local density (see also Bell & Bowen 2000; Boissier & Prantzos 2000). They assume that colors trace age, and use surface brightness and total luminosity as proxies for μ_∗ and M_∗, respectively. Furthermore, this conclusion was obtained only for spiral galaxies. In the light of this result, and armed with our spectroscopically derived properties, we ask whether this conclusion holds for all types of galaxies, and for all regions within galaxies.

We start by exploring the age-density relation for all regions of all galaxies in our sample. Figure 11 plots μ_∗ as a function of ⟨log age⟩_L for all our 98 291 individual spectra, color coded by the log density of points in the diagram. Large overplotted circles represent the galaxy-averaged ⟨log age⟩_L and log μ_∗ obtained as explained in Sect. 6 (Eqs. (1) and (2)). The color of these circles code M_∗ (as labeled on the left-hand side legend). In this plane, our galaxies are divided into two distinct families that break at a stellar mass of ~6 − 8 × 10¹⁰ M_⊙. Galaxies below this critical mass show a correlation between log μ_∗ and ⟨log age⟩_L, and are usually young disk galaxies. Above the critical mass, the relation is significantly flatter, and galaxies there are increasingly dominated by a spheroidal component. A similar result is found by Kauffmann et al. (2003b, 2006) who analyzed galaxy-averaged ⟨log age⟩_L and μ_∗ for 122808 SDSS galaxies. The critical mass reported by these works (~3 × 10¹⁰ M_⊙), is close to the one we find here once the differences in IMF are accounted for.

Galaxy-averaged values fall where a large fraction of the individual zone results are located because and are well represented by values around 1 HLR, and most of the single spaxel zones are located between 1−1.5 HLR. Figure 11 shows that most of the individual zones follow the same general trend followed by the galaxy-averaged properties. Thus, local ages correlate strongly with local surface density. This distribution also shows that there is a critical value of μ_∗ ~ 7 × 10² M_⊙/pc² (similar to the value found by Kauffmann et al. 2006 once differences in IMF are factored in). Below this critical density, μ_∗ increases with age such that regions of low density formed later (are younger) than the regions of higher surface density, while above this critical density the dependence of μ_∗ on age is very shallow or altogether absent.

Since ⟨log age⟩_L reflects the SFH and it correlates with μ_∗, the general distribution of galaxy zones in Fig. 11 suggests that the local mass density is linked to the local SFH, at least when μ_∗ ≤ 7 × 10² M_⊙/pc². Since these densities are typical of disks (Fig. 7), this result is in agreement with the findings of Bell & de Jong (2000) that explain the correlation through a local density dependence in the star formation law. The large dispersion in the distribution for individual regions is caused mainly by the radial structure of the age and of the stellar mass surface density.

8.2. Radial gradients of stellar mass surface density and age

We now investigate inner gradients in age and μ_∗, and their relation with M_∗. The gradient of log μ_∗ in the inner HLR of each galaxy was computed as ▽ log μ_∗ = log μ_∗ [1 HLR] − log μ_∗ [0], and similarly for ▽⟨log age⟩_L. Figure 12 shows these gradients as a function of the galaxy mass. gray dots denote disk dominated galaxies (C < 2.8) and black dots mark spheroid dominated galaxies (C ≥ 2.8). colored symbols show mean values in eight equally populated mass bins³, with circles and stars representing spheroid and disk dominated systems, respectively.

A clear anti-correlation exists between ▽ log μ_∗ and M_∗. The stellar mass surface density profile becomes steeper with increasing galaxy mass. There does not seem to be a dependence on morphology, with both disk and spheroid dominated galaxies of similar mass having similar gradients ▽ log μ_∗. Thus, at least for galaxies of M_∗ ≥ 10¹¹ M_⊙, ▽ log μ_∗ is independent of the galaxy morphology. We note that this anti-correlation between ▽ log μ_∗ and M_∗ holds only when the gradient is measured between the galaxy center (log μ_∗ [0]) and the galaxy-averaged stellar mass density (log μ_∗ [1 HLR]), but that this result does not hold if the gradient is measured between the center and a fixed physical distance (e.g., 3 kpc) because a fixed distance represents a different position in each galaxy.

Age gradients show a different behavior with galaxy mass. While there is no correlation between ▽⟨log age⟩_L and M_∗ for the sample as a whole, a clear trend emerges when galaxies are separated by their concentration index (colored stars for disks and circles for spheroids). Overall, negative age gradients are detected, but low mass disk dominated galaxies (dark blue star) and high mass spheroidal galaxies (brown circles) have flat age profiles. High M_∗ disk galaxies show negative age gradients that steepen with increasing galaxy mass up to − 0.5 dex/HLR for galaxies of 10¹¹ M_⊙, and then flatten towards the values of spheroidal galaxies of similar mass.

For early-type galaxies, we obtain an average ▽⟨log age⟩_L of − 0.11 and a dispersion ± 0.21 dex/HLR. Restricting to the more massive ones, even smaller gradients are obtained: ▽⟨log age⟩_L = −0.02 ± 0.08 dex/HLR for M_∗ > 2.5 × 10¹⁰M_⊙. These values are in good agreement with the results obtained by fitting stellar indices of several small samples of ellipticals observed with long-slit (eg. Sánchez-Blázquez et al. 2007; Mehlert et al. 2003), or integral field spectroscopy (eg., Rawler et al. 2010; Kuntschner et al. 2006). These authors measure age gradients compatible with zero, ranging from − 0.09 to 0.02 dex per effective radius, also in agreement with some of the results obtained from color gradients (Wu et al. 2005). Some of the CALIFA spheroidal galaxies show a positive central gradient (cf. Fig. 13), but these are certainly smaller than those derived from color gradients recently reported (e.g., Tortora et al. 2010; La Barbera et al. 2012) or from stellar indices (Greene et al. 2012).

For spirals we find that age gradients become increasingly negative for masses up to ~10¹¹ M_⊙. In amplitude, these ▽⟨log age⟩_L values are in agreement with results previously reported by MacArthur et al. (2004) based on color maps of several samples of spiral galaxies. However, our trend with M_∗ and the age-gradient values are not in agreement with those reported by Tortora el al. (2010). They use SDSS radial color profiles to find a bimodal distribution with galaxy mass, negative gradients of ~− 0.2 dex per effective radius for galaxies less massive than 10¹⁰ M_⊙, going through 0 and turning positive for high mass (10¹¹ M_⊙) spirals. There are several possible reasons for this discrepancy, one of which is dust, which is not considered in their analysis. Furthermore, their fits compare colors of galaxy disks to single SSPs, an unrealistic approximation for the SFH of spirals, which are better represented by composite stellar population models such as those we use, or by τ models as in MacArthur et al. (2004).

In summary, we find that there is a good correlation between the μ_∗ gradient and M_∗, and a trend of the age gradient with the mass that breaks at M_∗ ~ 10¹¹ M_⊙, which is also approximately where the M_∗-μ_∗ correlation breaks (Fig. 7c; Kauffmann et al. 2003b). In the next section we inspect if the trend of the age gradient with stellar mass is a consequence of the M_∗ − μ_∗ relation.

8.3. Radial profiles as a function of stellar mass and concentration index

A first glance at how the radial profiles of μ_∗ and ⟨log age⟩_L change with stellar mass is shown in Fig. 4 since M_r scales with the galaxy mass. In more detail, Fig. 13 shows the result of stacking log μ_∗ (left column) and ⟨log age⟩_L (right column) radial profiles sorting the galaxies in seven M_∗ bins, chosen so as to have a similar number of 15 galaxies in each one. The mean radial profiles are obtained by co-adding log μ_∗ or ⟨log age⟩_L in each of the following intervals in log M_∗(M_⊙): 9.2−10.2, 10.2−10.6, 10.6−10.8, 10.8−11.0, 11.0−11.2, 11.2−11.4, and 11.4−11.8.

The top row in Fig. 13 shows that the radial profiles of log μ_∗ and ⟨log age⟩_L scale well with the total stellar mass. Both log μ_∗ and ⟨log age⟩_L show negative gradients, which are flatter in the outskirts, except for the galaxies in the lowest mass bin (blue) which also have a flatter ⟨log age⟩_L gradient in the inner 1 HLR. These negative gradients are also observed if mass weighted age is used instead of luminosity weighted age. This trend confirms again that galaxies more massive than ~10¹⁰ M_⊙ grow inside-out (Pérez et al. 2013). More massive galaxies are denser than lower mass ones, not only in their core but all along their extent. There is also a clear trend of the age profile with the mass. More massive galaxies are older along most of their radial extent. There is some overlapping in the ages at radii between 1 and 2 HLR in galaxies of a few 10¹¹ M_⊙ (red and orange). The mean age shows radial structure, with a generally steeper gradient in the inner HLR. This depends on M_∗, with the largest inner gradient occurring in galaxies of intermediate mass (light blue to red curves). The most massive galaxies of the sample studied here (brown) also show negative age gradients but flatter than those of galaxies that belong to the intermediate mass bins, even though they have the largest log μ_∗ gradient. Thus, the age gradient does not seem to be correlated with the central stellar mass surface density.

To check whether M_∗is the only galaxy property that determines the radial structures of age and μ_∗, or whether these depend on structural properties like the morphological type, we divide the sample into two subclasses according to the galaxy concentration index.

First, we divide the sample into spheroidal (C ≥ 2.8) and disk (C < 2.8) dominated galaxies, and then co-add the radial profiles of galaxies in the same M_∗ bin. The central and bottom rows of Fig. 13 show the results. Now the number of galaxies in each mass bin is smaller and uneven (i.e. there is not the same number of galaxies in each mass bin), and that the highest M_∗ bin (brown) is not populated by disk galaxies. Conversely, there are no spheroidals in the low mass bins (see also Fig. 5a)⁴. The log μ_∗ and ⟨log age⟩_L radial structure of disk galaxies (central panels in Fig. 13) is similar to that for the whole sample for galaxies with mass below 10¹¹ M_⊙. There is a steep age gradient in the inner part of disk galaxies more massive than a few 10¹⁰ M_⊙ (cyan to red), and log μ_∗ scales with the galaxy mass. The difference in the log μ_∗ radial structure of galaxies with M ≥ 10¹¹ M_⊙ (orange and red) is very small in comparison with the difference in the ⟨log age⟩_L radial structure between these same two mass bins. Thus, for similar μ_∗, the more massive disk galaxies have older disks and bulges. Also, the difference in bulge ages is larger than the difference between disk ages for these two high mass bins. This is also clearly shown in Fig. 12, where the largest mass bins show age gradients larger for the late-type than for the early-type galaxies.

Spheroidal galaxies (bottom panels in Fig. 13) show ⟨log age⟩_L and log μ_∗ profiles that clearly differ from disk galaxies. Because low mass bins are not well populated, we concentrate first on comparing the three highest mass bins. The most remarkable result is that, as seen in the bottom-right panel, the SFH of spheroidal galaxies changes with stellar mass, while log μ_∗ shows little variation⁵. In addition, for the same galaxy mass, the extended envelopes of early-type galaxies are denser than in disk galaxies, and formed earlier than the disks, although the bulge of the most massive disk galaxies can be as old as the core of spheroids. It is not only that the average μ_∗ of early-type galaxies is almost constant, but also that the inner gradient of log μ_∗ is independent of the stellar mass (see also Fig. 12).

In summary, we see that stellar mass surface density and total stellar mass play a significant role in determining the ages, and their radial variations, but for most of the early-type galaxies, the age at the core, and the galaxy-averaged age change with the total stellar mass, even though they have similar stellar mass surface density, and similar μ_∗ gradients in the inner HLR. These empirical results imply that, for early-type galaxies, total mass is a more important property than mass surface density to shape the age radial profiles, which in principle reflect the spatial variation of the SFH of galaxies.

8.4. The role of stellar mass in the inner regions of galaxies

Throughout this section we have shown a series of relations between stellar age and mass density, local or galaxy-wide averaged, and their mass stacked radial dependencies, as illustrated in Figs. 11−13. These results show that in early-type galaxies ⟨log age⟩_L scales with M_∗ but not with μ_∗, while in disk dominated systems ⟨log age⟩_L scales with μ_∗ as well as with M_∗. Furthermore, we found that μ_∗ and ⟨log age⟩_L for many of the individual regions in the galaxies follow the same relation found for the galaxy-averaged age and mass density (Fig. 11). These findings indicate that μ_∗ is correlated with the stellar ages, and is thus linked to the SFH. Yet, the apparent disconnection between μ_∗ and age at high masses, coupled to the ⟨log age⟩_L – M_∗ relation (implicit in the right panels of Fig. 13) suggests that M_∗ is more related to the SFH than μ_∗ is.

If μ_∗ is the main parameter defining the mean stellar population age, one would expect that the relation between them holds for any region of any galaxy. However, Fig. 11 shows that there is a large dispersion around the global – ⟨log  age relation, a dispersion that reflects the spatial variations of μ_∗ and ⟨log age⟩_L within galaxies. The scatter is larger for ages older than 2−3 Gyr, which is where the global relation between and ⟨log  age starts to flatten. Figure 14 sheds light on the nature of this dispersion. The figure is analogous to Fig. 11, except that now the color of the small dots indicates M_∗ (upper panel) or the distance to the nucleus (lower panel). As in Fig. 11, the large circles plot the global age relation, and their colors code for M_∗. These plots show that regions that are older than a few Gyr belong to massive galaxies (M_∗ ≥ 7 × 10¹⁰ M_⊙) and/or they are located in the inner 1 HLR of the galaxies. These inner regions are denser than those at 1 HLR (which approximately represent the galaxy-wide average) and the outer ones, even though they all formed in a similar epoch (bottom panel of Fig. 14).

To quantify how much the inner regions are overdense with respect to the galaxy-averaged μ_∗, we have fitted a second-order polynomial to the age relation⁶, shown as a black line in the bottom panel of Fig. 14. If μ_∗ is the main property that determines the local SFH, this fit predicts the expected stellar mass density given the age. Deviations from the relation trace deviations from this assumption, so it is interesting to correlate the residuals with other properties, M_∗ being the obvious contender.

This is done in Fig. 15, where we plot the difference with respect to the fit (Δlog μ_∗) as a function of M_∗. The plot contains two sets of 107 points each. The gray points and their error bars represent the mean and ± 1 sigma values of Δlog μ_∗ for all zones located at R ≥ 1.5 HLR in each of the 107 galaxies in our sample. These points are scattered around Δlog μ_∗ = 0, with a small shift towards a negative residual. This residual would be even smaller if we used only points around 1 HLR (which, as shown in Fig. 6, match the galaxy-averaged properties very well). More importantly, the residuals show little, if any, correlation with M_∗. Black points, however, do correlate strongly with M_∗. These are obtained considering only regions inside R = 0.5 HLR, where (as seen in the bottom panel of Fig. 14) μ_∗ values are generally well above the critical μ_∗ of ~7 × 10² M_⊙/pc². The inner regions show an excess μ_∗ which grows for increasing M_∗, particularly so for galaxies more massive than 10¹⁰M_⊙. In the inner regions of the most massive systems the age relation fails by about an order of magnitude, confirming our earlier conclusion that μ_∗ is basically unrelated to the stellar population age in these cases.

To sum up, we find that the ages and their spatial variations in the inner parts (<1 HLR) of galaxies more massive than 10¹⁰ M_⊙ are primarily related to the total stellar mass, and to the mass surface density in the outer parts (>1 HLR).

9. Summary

We have analyzed the stellar population properties of the first 107 galaxies observed by CALIFA with the V500 and V1200 gratings to investigate the trends in the star formation history with radial distance as a function of the galaxy stellar mass and morphology, as traced by the concentration index. This CALIFA sub-sample is well distributed in the CMD (− 23 ≤ M_r ≤ − 18) covering from the blue cloud to the red sequence. In terms of concentration index, our sample contains a fair representation of early-type (spheroidal) dominated galaxies and late-type (disk) dominated galaxies. A full spectral fitting analysis was performed comparing combinations of SSP spectra with those of our sample galaxies using the starlight code. The fitting results are processed with our pipeline pycasso allowing us to resolve the galaxies in time and space. Here, the time information is collapsed to produce 2D maps of the stellar mass surface density and light weighted ages, azimuthally averaged to produce radial profiles. Throughout we adopt a Salpeter IMF, resulting in stellar masses a factor of 1.78 (0.25 dex) larger than in case of a Chabrier IMF.

Our main conclusions are:

• 1.

  Total stellar mass: the sample is distributed between10⁹ − 10¹² M_⊙ with a peak ~10¹¹ M_⊙ similar to MW and M31. Masses obtained from the integrated spectra match well those obtained from the spatially resolved SFH. This makes integrated masses a robust result. SDSS photometric masses are also well correlated with spectroscopic masses, but the former can be underestimated if the photo-SED fit does not account for stellar extinction.

• 2.

  Spatially averaged vs. integrated galaxy properties: the luminosity weighted age ⟨log age⟩_L and the stellar surface mass density μ_∗ averaged over the whole galaxy, and from integrated spectra, correlate well with the age and local surface density measured at 1 HLR. These results show that the properties of a galaxy at 1 HLR are representative of the integrated and of the averaged galaxy properties.

• 3.

  Mass weighted size: half-mass radii are on average 20% smaller than the half-light radii, with spatial variations in the extinction accounting only for 1/4 of this difference. Thus, galaxies are intrinsically more compact in mass than in light. This average size difference shows a dual dependence on stellar mass, in the sense that in disk dominated galaxies the ratio of the half-mass to half-light radii decreases with stellar mass, but in spheroidal systems, the ratio is independent of total stellar mass. Differences between HLR and HMR arise because of radial variations in the SFHs, reflected in M/L gradients. In spheroidal systems and low mass spirals, where the spatial variation of the SFH are small, the ratio is smaller than in massive spirals. These massive spirals, that are mainly disk-like systems with large central bulges, can be up to a factor of 2 more compact in mass than in luminosity.

• 4.

  Stellar mass surface density: the local stellar mass surface density scales with the total mass in disk dominated galaxies; the more massive galaxies are more compact than galaxies of lower mass, and this result is preserved radially at any given distance. Spheroidal systems saturate at a critical stellar mass surface density of ~7 × 10² M_⊙/pc² (measured at 1 HLR) which is almost independent of the galaxy stellar mass.

• 5.

  Luminosity weighted age: the radial run of ⟨log age⟩_L shows inner regions older than outer ones, changing with the galaxy stellar mass and with concentration index. There is no correlation between the gradient and the total stellar mass, but there is a clear trend with galaxy mass when they are separated in early-type and late-type systems. Low mass disk galaxies (usually the galaxies with lowest galaxy mass) and high mass spheroidals (usually galaxies in the highest mass bins) have relatively flat age profiles. The larger inner gradients are detected in massive disk galaxies. The presence of a massive bulge in spirals imprints a large spatial variation of the age in the inner HLR. This suggests that the SFH of building a massive bulge is quite different to the process in low mass disk dominated galaxies.

• 6.

  Stellar local mass surface age-density relation: the SFH of the regions located beyond 0.5-1 HLR are well correlated with their local μ_∗. They follow the same relation as the galaxy-averaged age and μ_∗. This suggests that it is the local stellar mass surface density that preserves the SFH in disks. However, the radial structure of the age in spheroidal galaxies changes significantly with galaxy mass even if all these galaxies show a similar radial structure in μ_∗. This implies that the SFH of spheroids is more fundamentally related to the stellar mass. Thus, galaxy mass is a more fundamental property in spheroidal systems, while the local stellar mass surface density is more important in disks.

Online material

Appendix A: Structural parameters: Half-light radius

To compare the spatial distribution of any given property in galaxies which are at different distances, the 2D maps need to be expressed in a common metric. We chose the half-light radius (HLR). To compute the HLR, we collapse the spectral cubes in the rest-frame window 5635 ± 45 Å, derive the isophotal ellipticity and position angle, and then integrate a curve of growth from which we derive the HLR. In some galaxies, the integrated image may contain masked regions at the position where the original cube contains foreground stars or some other artifacts (see Cid Fernandes et al. 2013 for further explanations) which may affect the estimation of the different parameters, including the HLR. To correct for these missing data, we build an average surface brightness radial profile for each galaxy using circular apertures. This profile is used to estimate the surface brightness of the spaxels masked in the original cube, assuming a smooth change of surface brightness between the missing data and the averaged values of their near neighbors at the same distance. This reconstructed flux image is used to derive the ellipticity and position angle of the aperture, and to obtain the average azimuthal radial profiles of the stellar population properties. These structural parameters are defined and obtained as follows:

• Galaxy center: we take as the galaxy center the peak flux position. This definition is correct for most of the galaxies, except for the irregular galaxy CALIFA 475 (NGC 3991), where the maximum flux is well outside of the morphological center.

• Ellipticity and position angle: the flux-weighted moments of the 5635 Å image are used to define the ellipticity and position angle (Stoughton et al. 2002). The reconstructed flux image is used to calculate the so-called Stokes parameters in order to obtain the ellipticity and position angle at each radial distance. The values, however, are kept constant beyond 2 HLR, which are taken to define a unique elliptical aperture for each galaxy. The final values do not change significantly after an iteration, filling the missing data with the surface brightness profile resulting from adding the flux with the derived elliptical aperture, and then estimating again the Stokes parameters.

• Half-light radius (HLR): for each galaxy, the reconstructed flux image is used to build the flux curve of growth and to obtain the half-light radius. The flux is integrated in elliptical apertures with a position angle and ellipticity defined as explained above. The semi-major axis length at which the curve of growth reaches 50% of its maximum value is defined as the half-light radius, .

For the sample analyzed here, kpc, with a mean value of 4.6 kpc. These values are higher than the Petrosian radius (obtained from the SDSS data archive), as shown in Fig. A.1. However, the circularized size, defined as , where ϵ is the ellipticity, follows well the one-to-one line, as does the HLR obtained through curve of growth integrating in circular rings, . The linear fit, in fact, deviates from the one-to-one line, giving circular HLR that are on average 5% lower than . The outlier in the correlation is CALIFA 886 (NGC 7311), the central galaxy of a compact group. Given the morphology of the system, is probably overestimated.

Table 1 lists values obtained for our sample. In this paper we will use HLR to refer generally to this metric, whether it is computed in circular or elliptical geometry, unless the specific results depend on the actual definition (as in Sect. 7).

Appendix B: Quality of the spectral fits and uncertainties associated with evolutionary synthesis models

Appendix B.1: Quality of the spectral fits

All stellar population information used throughout this work comes from the starlight fits of the 98 291 individual spectra from 107 CALIFA data cubes. Here we illustrate these spectral fits with example spectra extracted from the nucleus and from a spaxel at 1 HLR for three different galaxies.

The top panels in Fig. B.1 show the nuclear spectra (black) of CALIFA 001 (IC 5376), CALIFA 073 (NGC 776), and CALIFA 014 (UGC 00312). The respective starlight fits are shown by the red line. Each panel also shows the O_λ − M_λ residual spectrum. Examples of fits for regions 1 HLR away from the nucleus are shown in the bottom panels.

As customary in full spectral fitting work, the fits look very good. In these particular examples the figure of merit , defined as the mean value of | O_λ − M_λ | /M_λ (Eq. (6) in Cid Fernandes et al. 2013), is % (5.8%) for the nucleus (at 1 HLR) of IC 5376, 1.3% (5.8%) for NGC 776, and 1.6% (5.0%) for UGC 00312. The median values for the 107 galaxies are at the nucleus and 5.1% at R = 1 HLR. The SSP models used in these examples are from the GM base, built from evolutionary synthesis models by González Delgado et al. (2005) and Vazdekis et al. (2010), as summarized in Sect. 3. Very similar results are obtained with bases CB and BC.

Appendix B.2: Uncertainties associated with using different SSP models

To evaluate to what extent the results of our spectral synthesis analysis depends on the choice of SSP models, we now compare properties derived with bases GM, CB, and BC. Since Cid Fernandes et al. (2014) have already performed this comparison for the same data analyzed here, we focus on comparisons related to specific points addressed in this paper.

First, we compare the results obtained for M_∗. Figure B.2 shows the galaxy stellar mass distribution obtained with the CB and BC bases. The GM mass distribution (see Fig. 5a) is shifted to higher masses than CB and BC by ~0.27 dex, as expected because of the different IMFs (Salpeter in GM and Chabrier in CB and BC). The Salpeter IMF used in GM models has more low mass stars than the Chabrier function used in CB and BC, implying larger initial masses for the same luminosity. In addition, for the Salpeter IMF about 30% of this mass is returned to the ISM through stellar winds and SNe, while for a Chabrier IMF this fraction is 45%. These effects end up producing differences of a factor of ~1.8 in the total mass currently in stars.

In the context of this paper, it is useful to compare the results for μ_∗ and ⟨log age⟩_L at the nucleus and at 1 HLR, as these allow us to estimate the uncertainties associated with the stellar mass surface density and age gradient due to the choice of SSP models. This is done in the top two rows of Fig. B.3, where values obtained with GM bases are plotted in the vertical axis, while CB- and BC-based estimates are in the horizontal. In all panels the labels Δ and σ_Δ denote the mean and rms of the difference of values in the y- and x-axis, and the histogram of these differences is shown in the inset panels.

The μ_∗(0) and μ_∗(1 HLR) values show the same 0.27 dex IMF-induced systematic differences seen in Fig. B.2. The dispersions in log μ_∗ values are ~0.1 dex, much smaller than the ▽ log μ_∗ gradients seen in Fig. 12. IMF factors shift log μ_∗(0) and log μ_∗(1 HLR) by the same amount. We thus conclude that SSP model choice has no significant impact on the μ_∗ gradients discussed in this work.

Dispersions in the ⟨log age⟩_L values are also of the order of 0.1 dex. One sees a small bias whereby the nuclei of mainly low mass galaxies are older with GM than CB by 0.05 dex, whereas the difference at 1 HLR is 0.02 dex. This would make ▽⟨log age⟩_L~ 0.03 larger (i.e. a smaller gradient) with CB than with GM, a small effect which does not affect our conclusion that low mass galaxies show flat age radial profiles. The same small effect is found when comparing GM and BC ages.

Finally, we evaluate the effect of SSP choice on the half-mass and half-light radii dicussed in Sect. 7. We note that depends on the spatial variation of the SFH (through the M/L ratio), while also depends on the radial variation of the stellar extinction. The bottom panels of Fig. B.2 show that the choice of SSP base has no significant impact upon the estimates of either HLR or HMR. Light-based sizes derived from GM, CB, and BC fits agree with each other to within ± 0.01 dex, while HMR have dispersion of 0.05 dex or less.

Appendix C: Missing mass in the CALIFA FoV

The main constraint in the sample selection for the CALIFA survey is a size⁷ isoA_r < 79.2′′, only 7% larger than the PPAK FoV of 74′′. This implies that while some galaxies are completely enclosed within the FoV, others are somewhat larger. The question arises of how much stellar mass is left out of our stellar population synthesis analysis because it is out of the FoV. To estimate this “missing mass”, we proceed in the following manner, depicted in Fig. C.1 for the case of CALIFA 003. We use a 3′ × 3′ copy of the SDSS r-band image to compute and subtract the background around the galaxy; the distribution of the background residual is used to compute the edge of the galaxy as that enclosed above 1σ of the background (red contour in the figure). The missing flux (light blue in the top-right panel) is that contained within this contour and outside the CALIFA image; the points corresponding to this missing flux are represented in green in the radial profile in the bottom-left panel. From our population synthesis analysis of the CALIFA data cube, we compute the M/L ratio as a function of distance from the center of the galaxy (gray points in the bottom-right panel of the figure). The mean M/L value between 1.5 and 2.5 HLR is then used together with the missing flux to compute the missing mass outside the PPaK FoV. This is an approximate method, because we assume a constant value for the M/L in the outer parts of the CALIFA FoV, but the results are quite reliable, given that M/L has generally little or no gradient in these outer reaches, as can be seen in the bottom panels for the case of CALIFA 003.

The overall results for the missing mass are shown in the histogram of Fig. C.2; with a mean value of 8.63%, it shows a lognormal-type shape with a peak at ~5%.

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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 Economia y Competitividad, through projects AYA2010-15081 (PI RGD), AYA2010-22111-C03-03 and AYA2010-10904E (SFS), AYA2010-21322-C03-02 (PSB), AYA2010-21322-C03-02 (JFB), AIB-2010-DE-00227 (JFB), the Ramón y Cajal Program (SFS, PSB and JFB), and FP7 Marie Curie Actions of the European Commission, via the Initial Training Network DAGAL under REA grant agreement number 289313 (JFB, GvdV) are warmly acknowledged. We also thank the Viabilidad, Diseño, Acceso y Mejora funding program, ICTS-2009-10, for funding the data acquisition of this project. RCF thanks the hospitality of the IAA and the support of CAPES and CNPq. ALA acknowledges support from INCT-A, Brazil. BH gratefully acknowledges the support by the DFG via grant Wi 1369/29-1. AG acknowledges funding from the FP7/2007-2013 under grant agreement n. 267251 (AstroFIt). R.A. Marino was also funded by the Spanish programme of International Campus of Excellence Moncloa (CEI). RGD acknowledges the support of CNPq (Brazil) through Programa Ciência sem Fronteiras (401452/2012-3). We also thank the referee for her/his suggestions and comments.

References

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