Star formation along the Hubble sequence:

Star formation along the Hubble sequence:

Radial structure of the star formation of CALIFA galaxies
R. M. González Delgado Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    R. Cid Fernandes Departamento de Física, Universidade Federal de Santa Catarina, P.O. Box 476, 88040-900, Florianópolis, SC, Brazil CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    E. Pérez Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    R. García-Benito Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    R. López Fernández Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    E. A. D. Lacerda Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es Departamento de Física, Universidade Federal de Santa Catarina, P.O. Box 476, 88040-900, Florianópolis, SC, Brazil CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    C. Cortijo-Ferrero Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    A. L. de Amorim Departamento de Física, Universidade Federal de Santa Catarina, P.O. Box 476, 88040-900, Florianópolis, SC, Brazil CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    N. Vale Asari Departamento de Física, Universidade Federal de Santa Catarina, P.O. Box 476, 88040-900, Florianópolis, SC, Brazil CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    S. F. Sánchez Instituto de Astronomía,Universidad Nacional Autonóma de México, A.P. 70-264, 04510 México D.F., Mexico CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    C. J. Walcher Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    L. Wisotzki Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    D. Mast Instituto de Cosmologia, Relatividade e Astrofísica - ICRA, Centro Brasileiro de Pesquisas Físicas, Rua Dr.Xavier Sigaud 150, CEP 22290-180, Rio de Janeiro, RJ, Brazil CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    J. Alves University of Vienna, Türkenschanzstrasse 17, 1180, Vienna, Austria CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    Y. Ascasibar Depto. de Física Teórica, Universidad Autónoma de Madrid, 28049 Madrid, Spain    J. Bland-Hawthorn Sydney Institute for Astronomy, The University of Sydney, NSW 2006, Australia    L. Galbany Millennium Institute of Astrophysics and Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile    R. C. Kennicutt Jr. University of Cambridge, Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, United Kingdom    I. Márquez Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    J. Masegosa Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    M. Mollá Departamento de Investigación Básica, CIEMAT, Avda. Complutense 40, E-28040 Madrid, Spain    P. Sánchez-Blázquez Depto. de Física Teórica, Universidad Autónoma de Madrid, 28049 Madrid, Spain    J. M. Vílchez Instituto de Astrofísica de Andalucía (CSIC), P.O. Box 3004, 18080 Granada, Spain. () rosa@iaa.es CAB: ”Astro-UAM, UAM, Unidad Asociada CSIC”, 28049 Madrid, Spain    CALIFA collaboration http://califa.caha.es
Jan 2016
Key Words.:
Techniques: Integral Field Spectroscopy – galaxies: evolution – galaxies: stellar content – galaxies: structure – galaxies: fundamental parameters – galaxies: bulges – galaxies: spiral

The spatially resolved stellar population content of today’s galaxies holds important information to understand the different processes that contribute to the star formation and mass assembly histories of galaxies. The aim of this paper is to characterize the radial structure of the star formation rate (SFR) in galaxies in the nearby Universe as represented by a uniquely rich and diverse data set drawn from the CALIFA survey. The sample under study contains 416 galaxies observed with integral field spectroscopy, covering a wide range of Hubble types and stellar masses ranging from to . Spectral synthesis techniques are applied to the datacubes to derive 2D maps and radial profiles of the intensity of the star formation rate in the recent past (), as well as related properties such as the local specific star formation rate (sSFR), defined as the ratio between and the stellar mass surface density (). To emphasize the behavior of these properties for galaxies that are on and off the main sequence of star formation (MSSF) we stack the individual radial profiles in seven bins of galaxy morphology (E, S0, Sa, Sb, Sbc, Sc, and Sd), and several stellar masses. Our main results are: (a) The intensity of the star formation rate shows declining profiles that exhibit very little differences between spirals, with values at half light radius (HLR) within a factor two of Gyrpc. The dispersion in the profiles is significantly smaller in late type spirals (Sbc, Sc, Sd). This confirms that the MSSF is a sequence of galaxies with nearly constant . (b) sSFR values scale with Hubble type and increase radially outwards, with a steeper slope in the inner 1 HLR. This behavior suggests that galaxies are quenched inside-out, and that this process is faster in the central, bulge-dominated part than in the disks. (c) As a whole, and at all radii, E and S0 are off the MSSF, with SFR much smaller than spirals of the same mass. (d) Applying the volume-corrections for the CALIFA sample, we obtain a density of star formation in the local Universe of yrMpc, in agreement with independent estimates. Most of the star formation is occurring in the disks of spirals. (e) The volume averaged birthrate parameter, that measures the current SFR with respect to its lifetime average, , suggests that the present day Universe is forming stars at of its past average rate. E, S0, and the bulge of early type spirals (Sa, Sb) contribute little to the recent SFR of the Universe, which is dominated by the disks of Sbc, Sc, and Sd spirals. (f) There is a tight relation between and , defining a local MSSF relation with a logarithmic slope of 0.8, similar to the global MSSF relation between SFR and . This suggests that local processes are important in determining the star formation in disks, probably through a density dependence of the SFR law. The scatter in the local MSSF is driven by morphology-related offsets, with (the local sSFR) increasing from early to late type galaxies, indicating that the shut down of the star formation is more related with global processes, such as the formation of a spheroidal component.

1 Introduction

Nearly a century later, the simple classification scheme introduced by Hubble (1936) is still in use. The reason it remains useful is that the physical properties of galaxies correlate with the morphology in a broad context (e.g. Holmberg 1958; Roberts 1963; Roberts & Haynes 1994). In particular, the Hubble sequence can be described as a sequence in terms of recent star formation, increasing in importance from elliptical (E) to spiral (S) galaxies (e.g. Kennicutt 1983a, 1998).

Contemporary galaxy surveys have mapped this bimodal distribution implicit in the Hubble classification in terms of properties related with their structure (morphology), stellar content, and chemical composition (e.g. Blanton et al. 2003; Baldry et al. 2004; Blanton & Moustakas 2009; Kauffmann et al. 2003; Mateus et al. 2006; Ascasibar & Sánchez Almeida 2011; Casado et al. 2015). One population, located in the region of the color-magnitude diagram (CMD) known as the red sequence, is composed of galaxies with little star formation, large stellar masses (), stellar mass surface density (), and light concentration. The other major population, located in the so called blue cloud in the CMD, consists of galaxies with significant star formation, smaller and , and small concentration in light. The red sequence is the realm of early type galaxies, whereas galaxies of later Hubble types populate the blue cloud.

Other works have shown that galaxies that populate the blue cloud follow a strong correlation between and the present star formation rate (SFR) (Brinchmann et al. 2004; Salim et al. 2007; Renzini & Peng 2015; Catalán-Torrecilla et al. 2015); the main-sequence of star forming galaxies (MSSF). The correlation is tight, with only 0.2–0.3 dex dispersion in SFR for a fixed , and with a slope that is somewhat smaller than unity, implying that the relative rate at which stars form in galaxies, i.e. the specific star formation rate sSFR = SFR/, declines weakly with increasing galaxy mass (Salim et al. 2007; Schiminovich et al. 2007).

Subsequent studies have shown that the MSSF relation persists to at least (e.g. Noeske et al. 2007; Daddi et al. 2007; Elbaz et al. 2007; Peng et al. 2010; Wuyts et al. 2011). These works conclude that most of the star formation in the Universe is produced by galaxies in the main sequence, with starbursts (which deviate upwards from the MSSF) contributing with only to the total star formation rate at (Sanders & Mirabel 1996; Rodighiero et al. 2011), where the peak of the cosmic star formation rate occurs (e.g. Madau & Dickinson 2014). A recent study by Speagle et al. (2014) finds that the logarithmic slope of the MSSF relation increases with cosmic time, from at to at . This implies that the characteristic sSFR of the main sequence population evolves rapidly with redshift (Karim et al. 2011). In fact, Elbaz et al. (2011) show that star formation has decreased by a factor of 20 since , and that the corresponding sSFR declined as , where is the cosmic epoch.

There is also a substantial population of quenched galaxies that dominate the high end of the mass function, but whose sSFR is significantly lower than in star forming galaxies (Salim et al. 2007; Schiminovich et al. 2007; Chang et al. 2015). In a simple picture, galaxies evolve along the blue star forming MSSF, increasing in mass through the accretion of cold gas from the cosmic web and/or through mergers. When it approaches a critical mass the supply of gas is shut off. Star formation is thus quenched and the galaxy migrates to the red sequence, where the increase in mass and size may happen through minor mergers (e.g. Faber et al. 2007; Lilly et al. 2013). Although the quenching phase is relevant in the life of a galaxy, it is not clear at which critical mass the galaxy is quenched, and whether this is related with a change in the nature of the gas accretion, with heating of the surrounding gas by an AGN, or with the formation of an spheroidal component (Martig et al. 2009).

Evidently, this whole field relies on empirical measures of the SFR. There is no shortage of methods to estimate the SFR, each with its virtues and caveats (see Kennicutt & Evans (2012) for a review). Some gauge the SFR indirectly by quantifying how the radiative output of young stars is reprocessed by gas or dust, as H and far infra-red SFR indicators. Direct detection of recently formed stars is best done in the UV, where they outshine older populations by large factors, although dust inevitably introduces uncertainties. Because of the comparable contributions of stellar generations of all ages, the optical continuum is not the cleanest spectral range to work with if one is interested in pinning down the recent star formation history (SFH). It is, nonetheless, the very spectral range where galaxy evolution first started and matured as a research field, as illustrated by the seminal works of Tinsley (1968, 1972), Searle et al. (1973), Gallagher et al. (1984), and Sandage (1986), who first used galaxy optical colors to study how SFHs vary along the Hubble sequence and to predict the cosmic evolution of the SFR. This line of work has been revamped in the last decade or two with the confluence of advances in the spectral modeling of stellar populations (e.g. Leitherer et al. 1999; Bruzual & Charlot 2003; González Delgado et al. 2005; Maraston 2005; Vazdekis et al. 2010), the development of full spectral synthesis methods (e.g. Panter et al. 2003; Cid Fernandes et al. 2005; Ocvirk et al. 2006; Koleva et al. 2011; Sánchez et al. 2015b), and the flood of data from surveys such as the SDSS (Abazajian et al. 2003), which provided abundant observational material to explore these new tools (e.g. Panter et al. 2003; Heavens et al. 2004; Asari et al. 2007; Panter et al. 2008; Tojeiro et al. 2011). A detailed discussion of the uncertainties associated to these methods can be found in the recent reviews by Walcher et al. (2011) and Conroy (2013).

Regardless of the method employed to derive SFHs and SFRs, an important limitation of most studies to date is the lack of spatially resolved information. Galaxies are usually studied as a whole, with observations integrated over their distinct morphological components, or else with data that only partially cover them and are thus prone to aperture effects. Overcoming this limitation requires data of the kind that only recently started to become available with Integral Field Spectroscopy (IFS) surveys such as ATLAS3D (Cappellari et al. 2011), CALIFA (Sánchez et al. 2012; Husemann et al. 2013; García-Benito et al. 2015), SAMI (Bryant et al. 2015), and MaNGA (Bundy et al. 2015). These new generation surveys are a step forward to understand the star formation in galaxies, and should help us disentangling the contributions of spheroids and disks to the MSSF relation.

Because of its focus on early type galaxies (E, S0, Sa), ATLAS3D essentially avoids star forming systems, and hence does not constitute an ideal sample to study the MSSF (McDermid et al. 2015). CALIFA, on the other hand, is particularly well suited for this study. Firstly, in includes a large, homogeneous but diverse sample of galaxies covering the full Hubble sequence, from Ellipticals (E0-E7), and Lenticulars (S0-S0a), to Spirals (Sa to Sd), and a correspondingly large range of masses ( to , González Delgado et al. 2014b). Second, its large field of view (, with final spatial sampling of ) covers the full extent of the galaxies and allows us to spatially map the star formation, as well as to obtain the total integrated SFR. Third, it covers the whole rest-frame optical wavelength at intermediate spectral resolution, that allow us to apply full spectral fits to retrieve the SFHs (and thus recent SFR too). Finally, the volume-corrected distribution functions of CALIFA are fully compatible with estimates from the full SDSS when accounting for large-scale structure (Walcher et al. 2014), which allows the extrapolation of results to the overall cosmic context.

Previous papers in this series used the SFHs of –300 galaxies of the CALIFA survey to derive spatially resolved information on the mass growth of galaxies (Pérez et al. 2013), and stellar population properties like the stellar mass surface density, ages, stellar metallicity, and extinction (González Delgado et al. 2014b, a, 2015). We found that massive galaxies grow their stellar mass inside-out, where the signal of downsizing is spatially preserved, with both inner and outer regions growing faster for more massive galaxies. We confirm that more massive galaxies are more compact, older, more metal rich, and less reddened by dust. Additionally, we find that these trends are preserved spatially with the radial distance to the nucleus. Deviations from these relations appear correlated with Hubble type: earlier types are more compact, older, and more metal rich for a given , an indication that quenching is related to morphology.

Here we concentrate on the study of the ongoing star formation of CALIFA galaxies, as derived from full spectral fits of the optical stellar continuum. The goals are: 1) To characterize in detail the radial structure of the SFR and sSFR of galaxies in the local Universe; 2) to examine how SFR and sSFR relate to Hubble type; 3) to spatially resolve the MSSF relation; 4) to estimate the contribution of different types of galaxies and their sub-components to the cosmic star formation rate.

This paper is organized as follows: Section 2 describes the observations and summarizes the properties of the galaxies analyzed here. In Section 3 we summarize our method for extracting the SFH and explain how we measure the present SFR. Section 4 presents results on the MSSF relation and how our assumptions affect it. Section 5 deals with the radial structure of the intensity of the star formation rate (), and related properties such the local specific SFR. We discuss the results and their relation with the cosmic star formation of the local Universe in Section 6. Section 7 summarizes our main findings.

2 Data and sample

2.1 Observations and data reduction

The observations were carried out with the Potsdam Multi-Aperture Spectrometer PMAS (Roth et al. 2005) in the PPaK mode (Verheijen et al. 2004) at the 3.5m telescope of Calar Alto observatory. PPaK contains 382 fibers of diameter each, and a FoV (Kelz et al. 2006). Each galaxy is observed with two spectral settings, V500 and V1200, with spectral resolutions (FWHM) and 2.3 Å, respectively. The V500 grating covers from 3745 to 7300 Å, while the V1200 covers 3650–4840 Å. To reduce the effects of vignetting on the data, we combine the observations in the V1200 and V500 setups, calibrated with version 1.5 of the reduction pipeline. We refer to Sánchez et al. (2012), Husemann et al. (2013), and García-Benito et al. (2015) for details on the observational strategy and data processing.

2.2 Sample: morphological classification

The CALIFA mother sample consists of 939 galaxies selected from the SDSS survey in the redshift range –0.03, and with -band angular isophotal diameter of 45–80. It is primarily a diameter-limited sample to guarantee that the objects fill the FoV. It includes a significant number of galaxies in different bins in the CMD, and covers a wide and representative range of galaxy types. The galaxies were morphologically classified by five members of the collaboration through visual inspection of the SDSS -band images, averaging the results (after clipping outliers). The sample and its characteristics are fully described in Walcher et al. (2014).

The targets studied in this paper were selected from those observed in both V1200 and V500 setups earlier than January 2015, and excluding type 1 Seyferts and galaxies that show merger or interaction features. This leaves a final sample of 416 galaxies.

As we have done in GD15, we group the galaxies into seven morphology bins: E (57 galaxies), S0 (54, including S0 and S0a), Sa (70, including Sa and Sab), Sb (70), Sbc (76), Sc (69, including Sc and Scd), and Sd (20, including 18 Sd, 1 Sm, and 1 Irr). Fig. 1 shows the morphological distribution of our 416 galaxies (filled bars) as well as that of the mother sample (empty bars). Hubble types are labeled with a brown to blue (ellipticals to late type spirals) color palette, used throughout this paper. The similarity of the two distributions ensures that our sub-sample is a fair representation of the mother sample. This is an important aspect, as it allows us to apply the volume corrections derived by Walcher et al. (2014) to extend the statistical results presented here to those of the galaxy population as a whole.

Figure 1: Comparison of the distribution of Hubble types in the CALIFA mother sample (939 galaxies, bars) and the 416 galaxies analyzed here (filled narrow color bars). The histograms are normalized to unity, so that the two distributions are directly comparable. The number of galaxies in each morphology bin is labeled in color, with the same palette used throughout the paper.

3 Stellar population analysis: Mass and star formation rate

3.1 Method of analysis

To extract the stellar population properties from the datacubes we apply the same method than in Pérez et al. (2013), Cid Fernandes et al. (2013, 2014), and González Delgado et al. (2014b, a, 2015). Briefly, after some basic pre-processing steps like spatial masking of foreground and background sources, rest-framing, and spectral resampling, the individual spectra that have signal-to-noise ratio in a 90 Å window centered at 5635 Å (rest-frame), are coadded into Voronoi zones (Cappellari & Copin 2003). The resulting 366112 spectra (880 per galaxy, on average) are then fitted with starlight (Cid Fernandes et al. 2005) using the cluster Grid-CSIC at the Instituto de Astrofísica de Andalucía. The output is then processed through pycasso (the Python CALIFA starlight Synthesis Organizer) to produce a suite of the spatially resolved stellar population properties.

The base used in starlight’s spectral decomposition is a central ingredient in our whole analysis. The results presented here were obtained with base GMe, as defined in González Delgado et al. (2014b, a, 2015). This base comprises 235 spectra for simple stellar populations (SSP) drawn from Vazdekis et al. (2010) for populations older than Myr and from González Delgado et al. (2005) models for younger ages. The evolutionary tracks are those of Girardi et al. (2000), except for the youngest ages (1 and 3 Myr), which are based on the Geneva tracks (Schaller et al. 1992; Schaerer et al. 1993; Charbonnel et al. 1993). The Initial Mass Function (IMF) is Salpeter. The range covers the seven metallicities provided by Vazdekis et al. (2010) models: , , , , , 0, and , but SSPs younger than 63 Myr include only the four largest metallicities. The Appendix presents some comparisons with results obtained with an alternative base built from a preliminary update of the Bruzual & Charlot (2003) models.

3.2 Stellar masses

Our galaxy stellar masses () are obtained by adding the masses of each spatial zone (Cid Fernandes et al. 2013; González Delgado et al. 2015). This procedure takes into account spatial variations of the stellar population properties and stellar extinction, something which cannot be done when dealing with integrated light data (i.e., one spectrum per galaxy). Masked spaxels, due to foreground stars or other artifacts, are corrected for in pycasso using the stellar mass surface density () radial profile as explained in González Delgado et al. (2014b).

Both and Hubble type play important roles in this paper, so it is important to know how these two properties relate to each other. Table LABEL:tab:Massdistribution shows the distribution of galaxies by Hubble type in several bins of . The masses range from to (for a Salpeter IMF), and peak at . As expected, correlates with Hubble type (see also González Delgado et al. 2015, particularly their Fig. 2). E are the most massive galaxies with (average dispersion) in solar units, and the least massive galaxies are those in the Sd bin, with . The more typical CALIFA galaxy has , similar to the Milky Way’s mass (Licquia & Newman 2015).

E S0 Sa Sb Sbc Sc Sd
- - - - - 1 1
  9.1–9.6 - - - - 15 11
  9.6–10.1 - 1 2 - 5 14 5
10.1–10.6 1 3 10 14 18 28 3
10.6–10.9 7 15 10 19 29 4 0
10.9–11.2 16 18 28 22 20 6 -
11.2–11.5 19 15 20 14 4 1 -
11.5–11.8 13 2 - 1 - - -
1 - - - - - -
total (416) 57 54 70 70 76 69 20
11.3 11.0 11.0 10.9 10.7 10.1 9.6
0.3 0.3 0.4 0.3 0.3 0.5 0.4
Table 1: Number of galaxies in each Hubble type and mass interval.

3.3 Estimation of the recent SFR from the spectral synthesis

Figure 2: Average light (upper panel) and mass (bottom) fractions (defined with respect to = 5635 Å, the normalizing wavelength) due to stars in different age ranges as a function of Hubble type. Age ranges are coded by color: The youngest ones, Myr, in violet (hardly visible in the bottom panel because they carry little mass). Populations from 32 to 900 Myr are shown in green; those from 0.9 to 2 Gyr in orange, and older ones in red.

SFR is usually estimated from H, far-infrared, or UV luminosities (Kennicutt 1998; Kennicutt & Evans 2012; Catalán-Torrecilla et al. 2015), which, despite their own caveats and limitations, get the job done with conveniently simple, one-line formulae. No such straightforward recipe exists for optical continuum data, however. The reason is that stars of all ages can make comparable contributions to the optical light, and isolating the part due to those formed in the recent past is not a trivial task. It is, however, a feasible one. After all, decomposing a spectrum in terms of stellar populations of different ages is precisely what starlight does. In fact, an extended version of the code is being developed which incorporates UV, far-infrared, and/or emission line information (López Fernández et al. 2016), all of which should improve its sensitivity to young stars. In any case, as shown by Asari et al. (2007), the standard version of starlight already performs well in this respect.

This section explains our methodology to compute SFRs. The SFR values themselves are presented in later sections, while the discussion here focuses on how to handle the starlight output to produce meaningful SFR estimates, the uncertainties involved, and how to improve the results by means of criteria based on ancillary emission line information.

3.3.1 Choice of a ”recent” star formation time scale

Let us first specify what we mean by “recent past” by defining as the age of the oldest stars to be included in the computation of our recent SFR. The mean rate of star formation then follows from a simple summation over all populations younger that :

(1)

where denotes a spaxel (or Voronoi zone) and is the mass initially turned into stars which now have age at the same location. Radial profiles of SFR and galaxy wide rates are trivially obtained by averaging over the desired region. Similarly, surface densities () are obtained by dividing by the corresponding area (a spaxel, a radial ring, the whole galaxy, etc.).

The choice of is arbitrary, so let us sketch some general guidelines to choose a useful value. Naturally, the larger is the more robust the corresponding SFR becomes, since more base elements are summed over in eq. 1, thus minimizing known degeneracies in stellar population synthesis (e.g., Cid Fernandes et al. 2014). On the other hand, one would like to be much smaller than the Hubble time (otherwise SFR and become equivalent quantities). Furthermore, it would be desirable to have a of the same order of the time scale involved in some other independent SFR tracer to which we can compare ours. The natural choice of reference in our case is H, first because of the wide spread use of this tracer, but also because we lack UV or far infrared data with CALIFA-like spatial resolution for our sample. The H luminosity responds to the eV radiation field, which is completely dominated by Myr populations, so we aim at of this same order of magnitude.

After some experimentation we chose Myr111 This overly precise looking value of merely reflects the choice of which ages in our discrete grid to include in the summation in eq. (1). We chose to include up to the base element at Myr (actually 31.62 Myr). . This choice follows the same rationale (but different data) as in Asari et al. (2007), who, in a study of star-forming galaxies in the SDSS, found that a very similar time-scale (25 Myr; see their figure 6) produces the best correlation between starlight and H-based estimates of SFR. We defer a detailed discussion of this point to a future communication (Lacerda et al., in prep.). For the purposes of this paper it suffices to say that -values between and 100 Myr would lead to the same overall qualitative conclusions.

3.3.2 SFHs along the Hubble sequence: a condensed view

Fig. 2 tracks the percent contribution in light (top panels) and mass (bottom) of our recent populations ( Myr, in magenta) along the Hubble sequence, as well as those of stars in three other intervals: 32 Myr to 0.9 Gyr (green), 0.9 to 2 Gyr (orange), and 2 Gyr (red). These four intervals roughly represent populations in which the light is dominated by O, B, A–early F, and later type (lower mass) stars. This strategy of grouping stellar populations in broad age-ranges as a way of summarizing SFHs goes back to early studies based on equivalent widths and colors (Bica 1988; Bica et al. 1994; Cid Fernandes et al. 2001), but was also applied in full spectral fitting work (González Delgado et al. 2004; Cid Fernandes et al. 2004, 2005).

The top panels in Fig. 2 show a steady progression of young and intermediate age populations along the Hubble sequence. The percent light contribution (at Å) of populations younger than 32 Myr decreases from in Sd galaxies to 17.2 in Sc, 12.6 in Sbc, 5.5 in Sb, and 4.9 in Sa. Because of their low mass-to-light ratio as well as the tiny time-span compared to other bins, these populations are essentially invisible in the bottom panels, where mass fractions are plotted. Indeed, in terms of mass fractions the Myr populations account for only 0.97, 0.59, 0.36, 0.12, and 0.05% for Sd, Sc, Sbc, Sb, and Sa, respectively.

3.3.3 Star formation in early type galaxies

The contribution of young stars decreases even further towards E and S0, but it is not null, with . Naturally, the reality of populations accounting for so little light is questionable. Based on the extensive set of simulations carried out by Cid Fernandes et al. (2014) to evaluate uncertainties in the starlight results for CALIFA-like data, we estimate the level of noise-induced uncertainty in to be of the order of 3%. Given this, the small fractions identified in E and S0 should be considered noise. However, this 3% error estimate reflects the level of uncertainty expected for a single spectral fit, whereas the in the top left of Fig. 2 reflects an average over 115927 zones inside of the central 3 HLR of 111 E and S0 galaxies. Looking from this statistical angle one should perhaps take the small fractions in these systems as a sign that they may not be so quiescent after all. There is in fact evidence for some level of star formation in at least some early type galaxies (Kaviraj et al. 2007). In the context of CALIFA data, Gomes et al. (2015b) have unveiled spiral-arm like features consistent with recent star formation in three early type galaxies.

In any case, at such low -levels one also needs to worry about systematic effects, and the study by Ocvirk (2010) is specially relevant in this respect. He finds that blue horizontal branch stars can easily masquerade as massive young stars in spectral fits, creating the artificial impression of recent star formation in otherwise genuinely old populations. This same effect was in fact detected in previous starlight-based work on both globular clusters (Cid Fernandes & González Delgado 2010) and passive galaxies (Cid Fernandes et al. 2011), and ultimately reflects limitations in the modeling of stellar evolution embedded in the SSP models used in our spectral decomposition.

As will soon become clear, for the purposes of this paper the exact values of SFR or in E and S0 galaxies are not as important as the fact that their star forming properties are markedly different from those of later type galaxies, a relative behavior which is safely immune to the uncertainties discussed above.

3.3.4 The equivalent width of H as an ancillary constraint

Figure 3: Left: Point density diagram of the equivalent width of the H nebular emission, , versus the light fraction due to populations younger than 32 Myr () for 12540 radial bins of 416 galaxies. The color bar shows the density of data points in logarithm scale. White circles trace the mean relation (obtained from the mean values in -bins). The grey line shows the linear fit to all points: . Horizontal lines are drawn at = 3 (dashed) and 6 Å (dotted). Vertical lines mark (the mean for points with Å; dashed) and (the mean for points with Å; dotted). Middle: Mean radial profiles for galaxies in the seven Hubble type bins. Horizontal lines mark (dashed), and 6 Å (dotted). Right: Radial profile of in the same Hubble type groups. Horizontal lines mark (dashed) and 4.3 (dotted). The dispersion in (middle panel) and (right panel) measured at 1 HLR in Sb galaxies is shown as an error bar. (The corresponding statistical errors are much smaller.)

The above raised issue of the reliability of the recent star formation derived from our optical spectral synthesis analysis is relevant to all our galaxies, not only to early type ones. We now seek for ways to filter out or at least flag objects where starlight-based SFRs are not reliable enough.

A possible first-cut solution would be to plainly eliminate all data points where is below, say, twice its uncertainty. Adopting the typical uncertainty from the simulations of Cid Fernandes et al. (2014) would then lead to a two-sigma criterion to select reliable individual galaxy zones. We note, however, that for statistical reasons a much less restrictive cut would make more sense for the averaging in Hubble type and radial distance bins performed throughout this paper.

We chose to define a criterion based on entirely different precepts. The idea is to use the H emission equivalent width () to guide our decision on whether starlight-derived SFR is indeed tracing recent star formation reliably or not. The rationale goes as follows: (1) The recent populations we aim to trace are young enough to photoionize the surrounding gas into HII regions, and hence produce H. (2) Stellar evolution plus straightforward nebular physics predicts a floor-value of in the range of 1–3 Å, corresponding to the limit where the interstellar medium is photoionized by hot, old, low mass, evolved stars (HOLMES, as defined by Flores-Fajardo et al. 2011. Systems with Å must therefore have stopped forming stars very long ago, a regime dubbed as “retired galaxy” by Stasińska et al. (2008) and Cid Fernandes et al. (2011).

This whole scheme is based on the idea that both and trace recent star formation, a corollary of which is that they are correlated. This expectation is fully born out by our data, as seen in the left panel of Fig. 3. The plot shows a (log-scale) density map of versus for 11894 radial points where H emission could be measured. White circles trace the mean values in bins, and the grey line shows the corresponding linear fit. We point out that, although expected, this empirical correlation is in no sense tautological, since the two axis are derived from completely independent observables222Strictly speaking does depend on the starlight run, since the line flux is measured over the residual spectrum obtained after subtracting the starlight fit, but this is only a “second order” dependence.. In fact, we regard this independence as an added benefit of our approach.

Points with Å in the left panel of Fig. 3 have on average . This limit on is based both on the observed bimodal distribution of in local Universe galaxies and on long-known theoretical expectations (Cid Fernandes et al. 2011)333 The values expected for galaxies where HOLMES dominate the ionizing flux is in the 0.5–2.4 Å range (Binette et al. 1994, Cid Fernandes et al. 2011, Gomes et al. 2015a). Our Å limit adds a (small) safety cushion to this prediction. . Sánchez et al. (2015a) propose a more stringent Å cut to isolate regions ionized by young stars. The mean for populations with weaker is 4.3, very close to that obtained with the Cid Fernandes et al. (2011) criterion. Dashed and dotted lines mark and in Fig. 3, respectively. It is clear that adopting either of these cuts should not lead to significantly different results.

Before elaborating more on the effects of and -based reliability criteria, let us first examine how these two properties vary across the face of galaxies.

3.3.5 The radial profiles or and

The middle and right panels in Fig. 3 show the average radial profiles of and for the seven morphological bins. Dashed and dotted lines mark the same limits as in the left panel. As in our previous papers (e.g., González Delgado et al. 2014b), these average profiles are constructed by first expressing the radial distance for each galaxy in units of the corresponding half light radius (HLR), defined as the length of the elliptical aperture along the major axis that contains half of the total flux at 5635 Å (rest-frame) within the field of view of PPaK.

The vertical ordering of Hubble types in the middle and right panels of Fig. 3 follows the expected tendency, with late type systems being more star-forming than early type ones. Focusing on the lower part of the plots, we see that E and S0 have mean Å at all locations, confirming that the extended H emission in these systems is consistent with being produced from photoionization by old stars (Sarzi et al. 2006; Kehrig et al. 2012; Papaderos et al. 2013; Singh et al. 2013; Gomes et al. 2015a). Whatever little star formation remains in these early type galaxies it is the exception, not the rule. Furthermore, such residual star formation would be located towards the outskirts of these galaxies, as indicated by the rise in their profiles, reaching 3–5% for HLR).

Moving to Sa galaxies, we see that, on average, they have Å at all radii, although they get close to this limit in their central regions (probably reflecting a contribution from retired bulges). Also, except for the central 0.5 HLR, values are all above the 3.4% line. Beyond 1 HLR their mean oscillates around 6 Å, so a Å cut would remove significant portions of their disks. Finally, Fig. 3 shows that whichever reliability cut we chose to apply would make little difference for Sb and later type galaxies.

In what follows we shall give more emphasis to results obtained by applying a cut when computing SFR through equation 1, but results obtained with the alternative or 6 Å criteria will also be presented for completeness. In the next section we explore the impact of these three different criteria on the galaxy-wide SFR and the correlation between and SFR.

4 The global main sequence of star forming galaxies

Figure 4: Relation between SFR and stellar mass for 416 CALIFA galaxies, color coded by Hubble type. A linear fit to the points of Sc galaxies is shown as grey-blue dashed line. Different panels show the results obtained considering different selection criteria imposed upon the individual spaxels included in the computation of the galaxy’s total : Only (left), Å (middle), and Å (right).

As reviewed in the introduction, the main sequence of star forming galaxies (MSSF) is the name given to the correlation between SFR and (Noeske et al. 2007). This correlation has been found in star forming galaxies of the local Universe (Brinchmann et al. 2004), and seen to persist at least to redshift 4 (Peng et al. 2010; Wuyts et al. 2011). The logarithmic slope of the relation varies in the range from 0.4 to 1, depending on the galaxy selection criteria and on the indicator used to estimate the SFR (Speagle et al. 2014). Recently, Renzini & Peng (2015) proposed to characterize the main sequence by the ridge line of the star forming peak in a 3D SFR--Number plot obtained with the SDSS sample. Their objective definition leads to a best fit line given by .

Fig. 4 shows three versions of the SFR vs. relation obtained with our data and methods. We call this relation the ”global MSSF”, in contrast to the ”local MSSF” where SFR and values are replaced by their respective surface densities (cf. Sec. 6.3 below and Cano-Díaz et al. 2016). The total SFR is calculated for each galaxy using Eq. 1 and adding the contribution of all spaxels that verify (panel a), Å (b), or Å (c). Galaxies are color coded according to their morphology.

The dashed gray-blue lines in all panels show fits obtained for Sc galaxies. The correlation is very similar in the three panels, with a logarithmic slope and zero point of . These values are indistinguishable from those obtained by Renzini & Peng (2015) for the whole SDSS sample. This coincidence is not surprising because Sc, along with Sbc, are the galaxies that contribute the most to the local star formation rate density (Sec. 6.1), being the ones that produce the ridge line in the MSSF relation.

As is clear from Fig. 4, the spread in SFR at fixed is related to galaxy morphology. Table LABEL:tab:GlobalMSSF lists the slopes and zero points obtained for subsamples of fixed Hubble type. The slopes steepen systematically from 0.34 for Sa to 0.94 for Sd galaxies. This range is essentially the same as the 0.4–1 quote by Speagle et al. (2014) as resulting from different selection criteria. The flattening for the early types also explains why many works obtain a flattening of the MSSF relation at increasing (e.g. Brinchmann et al. 2004; Peng et al. 2010). It is clear in Fig. 4 that the bending in the main sequence, at least in our sample, is produced by the inclusion of large bulges, such as those in Sa and S0, and also E, where the star formation is already quenched or in the process of being quenched. These galaxies (Sa, S0, and E) are the most massive ones in our sample, but they contribute little to the cosmic star formation (as we will see in Sec. 6.1), as they are clearly off below the MSSF.

Fig. 4 shows that the three alternative cuts defined in the previous section produce practically identical MSSF when galaxies later than Sa are considered. The differences in SFR between the panels become significant in the high and low SFR regime typical of early type galaxies. Note that the masses are the same from panel to panel, since all spaxels contribute to . What changes is the list of spaxels entering the computation of SFR of each galaxy, hence the differences in the total rate. In practice we obtain a more extended quenched cloud in the left than in middle and right panels. This happens because the -based cuts eliminate most E and several S0 and Sa galaxies altogether, while is not as restrictive. This again suggests that our estimation of the SFR in E and S0 is uncertain, and our method only provides an upper limit to the real SFR.

morph. Sa Sb Sbc Sc Sd
logarithmic slope () 0.34 0.65 0.71 0.77 0.94
zero-point () -9.12
Table 2: Parameters of fits of the global MSSF for galaxies of different morphologies. They are obtained for panel (a) in Fig. 4. For convenience, the corresponding SFR for a galaxy is also listed (in yr). Note that the slope is significantly smaller in Sa that in later spirals because most of the Sa galaxies are off the MSSF.

5 Radial structure of the recent star formation

We now present a series of results related to spatially resolved SFR measurements of CALIFA galaxies. We focus on the radial structure of the star formation rate surface density, (also referred to as the intensity of star formation), and the local specific star formation rate, .

Using pycasso we obtain, for each galaxy, 2D maps of the recent SFR computed as in equation 1 with Myr. Each 2D map is then azimuthally averaged to obtain the radial variation of the . Only spaxels that meet the criterion of are included in the azimuthal average. Elliptical apertures 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. We express the radial distance in units of HLR to allow comparison of the profiles of individual galaxies, and to produce stacks as a function of Hubble type and/or stellar mass.

5.1 Radial profiles of and the role of morphology

Figure 5: Upper left: Radial profiles (in units of HLR) of the star formation rate surface density (), averaged in seven morphology bins. The horizontal line at 5 Gyrpc marks the average in the Milky Way (MW). Only the locations where the light fraction due to young populations is higher than 3.4% are included. Error bars show the dispersion (not the uncertainty) in for all the spirals (black) and for Sb galaxies (green). Other panels: For each Hubble type, solid, dashed, and dotted lines show the mean profiles obtained by excluding , , and , respectively. The grey-dashed lines show profiles, the SFR surface density profiles obtained assuming a constant rate of star formation throughout the Hubble time.

Fig. 5 shows azimuthally averaged radial profiles of stacked by Hubble type. The upper-left panel shows the results for all the seven morphological classes together.

All spirals show decreasing with radial distance, with a typical gradient (measured in the central 1 HLR) dex/HLR. Interestingly, the at any radius falls within a relatively tight range of values. At HLR our average is 20 Gyrpc, with a dispersion of 0.13 dex between spirals of different Hubble type. This is about one to two orders of magnitude smaller than the global measured in starbursts and local Lyman break analogs (Heckman et al. 2005), but consistent with the value obtained by Schiminovich et al. (2007) for a complete sample of GALEX star forming galaxies444They divide half of the total SFR (derived from the UV luminosity) by an area equal to HLR..

The plot also illustrates how E and S0 are clearly distinct from the spirals. Their radial profiles are flat (except for some slight increase at the center of S0). The at 1 HLR is Gyrpc, a 20-fold decrease from spirals (maybe more given that our estimates of SFR for early types are probably upper limits).

Each of the other panels in Fig. 5 shows the radial profile of for each Hubble type, now computed with each of our three reliability cuts. As already discussed, imposing (solid line), (dashed) or 6 Å (dotted) makes no difference for galaxies later than Sb, so much so that the three profiles are hardly distinguishable. The effects of the somewhat more restrictive -cuts start to be noticed in Sa galaxies, become evident in S0 (factor of difference) and grow even larger in E (where the dotted and dashed lines fall off below the plot limits). As previously discussed, though some of our E galaxies do exhibit signs of recent star formation (Gomes et al. 2015c), most can be regarded as quenched systems, which retired from forming stars long ago. We note in passing that although our estimates for E and S0 are very uncertain, the typical value of Gyrpc is consistent with the global in early type galaxies estimated by Schiminovich et al. (2007).

The individual panels of Fig. 5 present two other lines which allow for interesting comparisons. The first is the horizontal line at Gyrpc, which marks the of the Milky Way. This value is obtained by dividing the recent SFR of the Milky Way (MW), yr, by the area of a disk of radius the Galactocentric radius of the Sun, 8.33 kpc (Licquia & Newman 2015). This distance is equivalent to HLR of typical Sb-Sbc CALIFA galaxies. The results in Fig. 5 suggest that, in the inner HLR, most spirals in the main sequence have higher than the average in the Milky Way. This is not unexpected because it is known that the SFR in the MW is significantly lower than in other spirals of similar type and mass (see Kennicutt & Evans 2012, particularly the discussion around their figure 7, where the profiles of the Galaxy and NGC 6946 are compared).

The dashed-grey-black lines in Fig. 5 present another useful reference to compare our results to. They represent the the galaxy should have if it formed stars at a constant rate throughout the lifetime of the Universe. Except for the correction for returned mass (a simple scaling factor under most circumstances), these profiles reflect the stellar mass surface density profile divided by 14 Gyr.

E and S0 are clearly quenched, with dex below their . Sa and Sb galaxies, although still active in forming stars, do so at a lower rate than in the past. In contrast, spirals of later types are forming stars at a rate similar to or higher than their . In the central 0.5 HLR of Sbc, presumably their bulges, have decreased with respect to the past, although the disk (outside 1 HLR) is currently forming stars somewhat more actively than in the past. The intersection of the and curves occurs even closer to the nucleus in Sc, while in Sd the current intensity of star formation exceeds the past average at all radii.

5.2 The dependence of on stellar mass

Figure 6: Radial profiles of for different Hubble types in six galaxy stellar mass bins. From top-left to bottom-right: –9.6, 9.6–10.1, 10.1–10.6, 10.6–10.9, 10.9–11.2, 11.2–11.5. In each panel, the average profile for each Hubble type is plotted if more than five galaxies have masses in the corresponding -bin. The number of galaxies in each bin is also labeled and color coded.

As usual, it is difficult to disentangle the relative roles of morphology and , but CALIFA has grown large enough a sample to attempt to tackle this issue by plain brute force statistics.

Fig. 6 shows profiles as a function of both and morphology. Besides the seven Hubble types we now break up the sample in six mass bins: –11.2, 11.2–10.9, 10.9–10.6, 10.6–10.1, 10.1–9.6, and 9.6–9.1. In each panel (one per bin), the average profile for each Hubble type is plotted if it contains more than five galaxies. These plots allow to evaluate how changes with Hubble type for galaxies of similar mass.

An inspection of Fig. 6 shows that spirals with (top panels) have very similar profiles. When relevant, the differences occur in the inner regions. Above this mass, the profiles start to disperse, although they are still packed in a relatively small range of values. This high degree of uniformity is a remarkable result taking into consideration that the sample covers all types of spirals and two orders of magnitude in galaxy mass. In Section 6.4 we speculate that this behaviour is intimately linked to the tightness of the MSSF.

In contrast, E and S0 have profiles well below those in spirals of similar mass. This suggests that in massive galaxies with a large spheroidal component the star formation is significantly quenched in the whole galaxy. However, this effect seems to be more relevant in the centers than in the outskirts, as suggested by the flat profiles in E and S0 in comparison with the radially decreasing profile in spirals. Note that the most massive Sa galaxies in the sample show a bimodal behavior, with a smooth decrease of outwards of 1 HLR, and a relative rate in the central part that is almost flat and significantly depressed with respect to spirals of later types. Again, this points out to the relevance that the formation of a big bulge may have in quenching the star formation in galaxies.

5.3 Radial structure of the local specific star formation rate

Figure 7: As the upper-left panel of Fig. 5, but for the local specific star formation rate, . The error bar shows the dispersion in for Sb galaxies. The grey-dashed line at Gyr marks the value adopted by Peng et al. (2010) as a threshold to separate star forming galaxies from quiescent systems.

For a galaxy, the specific star formation rate is defined by . Overlooking trivial multiplicative factors (see equation 2), it gives a measure of the relative rate at which stars are forming now in a galaxy with respect to the past average rate. Because the relation between SFR and is sub-linear (e.g. Fig.  4), the sSFR declines with galaxy mass. Also, because of the tightness of the MSSF relation, star forming galaxies occupy a correspondingly tight locus in the sSFR vs.  space, but bulge dominated galaxies display a much larger spread of sSFR at a fixed galaxy mass (Schiminovich et al. 2007; Salim et al. 2007—see also Fig.  4)

In analogy with the global sSFR, CALIFA data allow us the study of the local sSFR, defined by the ratio , that measures the relative rate of ongoing star formation with respect to the past in each position in a galaxy.

Fig. 7 shows the results of stacking the profiles by Hubble type. These profiles show a clear ranking with morphology, increasing from early to late Hubble type. We obtain, at HLR, , , , , , , and for E, S0, Sa, Sb, Sbc, Sc, and Sd bins, respectively. This ordering is preserved at any given radial distance, as is also the case with other stellar population properties such as mean stellar age, metallicity, and (González Delgado et al. 2015).

Fig. 5 showed that profiles are very similar for all spirals, so the scaling of sSFR seen in Fig. 7 is a direct consequence of the variation of with Hubble type, increasing from to pc, from Sd to Sa galaxies. The opposite happens for early type galaxies, with the sSFR profiles of E and S0 galaxies running well below those of Sa, while their profiles are similar (González Delgado et al. 2015). The difference in this case comes from the much smaller levels of star formation in these systems.

All the galaxies have outwardly increasing sSFR profiles. Fig. 7 shows that in spirals sSFR grows faster with radius in the inner 1 HLR than outwards, probably signaling the bulge-disk transition. Assuming that the central 0.1 HLR is dominated by the bulge and that the disk dominates outside 1 HLR, we can compare the sSFR values in these two morphological components through a ratio like . For early type spirals (S0, Sa, Sb) this exercise results in that the sSFR of bulges is on average 0.40 dex smaller than in the disks. The difference is larger, 0.60 dex, for Sbc, while for later later types (Sc, Sd, with their small on non-existent bulges) it decreases to 0.24 dex. The sample dispersions around these values is dex.

As in the case of the global sSFR, the local one can also be expressed as a characteristic time-scale of star formation, that, independently of IMF and cosmology, tells the period of time that the system needs to build its current stellar mass forming stars at the present rate555 This standard reading of actually neglects the difference between the mass turned into stars and that which stays in stars (or remnants). Because the denominator in sSFR is the current stellar mass, a rigorous definition would require a correction for the returned mass fraction , not important for the discussion at this point. . Measured at HLR, ranges from 12.6 Gyr in Sbc to 5 Gyr in Sd galaxies. Early type spirals (Sa, Sb), S0, and E would all need more than the Hubble time to build their mass at their current SFR.

The dashed grey-black line in Fig. 7 at Gyr marks the value adopted by Peng et al. (2010) as a threshold to separate star forming galaxies from quiescent systems. This line also marks the sSFR that galaxies should have to build their mass at the present rate during a Hubble time (approximated to 10 Gyr). The comparison of 0.1 Gyr with the sSFR profiles indicates that Sd, Sc, and the disks of Sbc are very actively forming new stars, while Sa and Sb galaxies and the bulges of Sbc, although still forming stars, are evolving to quiescent systems.

Finally, E and S0 have sSFR values 10–100 times smaller than 0.1 Gyr, with a steep increase outwards. This suggests that quenching in these galaxies has progressed inside-out.

6 Discussion

The central goal of this paper, the one embodied in its very title, was fulfilled in the previous section with the results on the radial profiles of and sSFR for galaxies along the Hubble sequence (Figs. 5 to 7). In this final part we go beyond this point and examine a few related issues. First we take advantage of the volume corrections computed by Walcher et al. (2014) to extrapolate the SFR computed from our sample to a local Universe SFR density and how it breaks up into contributions from different Hubble types and radial regions (Section 6.1). Secondly we re-express our results (both the radial profiles and the local Universe average) for SFR in terms of the birthrate parameter (Section 6.2). We then turn our eyes to the spatially resolved version of the global MSSF. Like the SFR and for entire galaxies (Fig. 4), their surface densities and correlate strongly, with a morphology-related scatter (Section 6.3). Finally, we gather our results to formulate an empirical scenario which identifies the origin of the global MSSF (Section 6.4).

6.1 The SFR volume density in the local Universe

Figure 8: The star formation rate density in the present study (black star). Colored stars represent the contribution of each morphological type to the total star formation rate density (). The blue ellipse represents the contribution to of the regions outside 1 HLR; and the red-dot blue ellipse represents the contribution to of the regions inside 0.5 HLR. Other results are from recent determinations by Gunawardhana et al. (2013, 2015) (grey triangles) and their compilation (grey points), and the redshift evolution of from Hopkins & Beacom (2006) (two top grey-dotted lines are of their relation); Madau & Dickinson (2014) (middle grey-dashed line); Fardal et al. (2007) (bottom grey-dashed line); and from the fossil record method applied to SDSS data by Panter et al. (2003) (grey squares). When needed, literature values have been scaled to a Salpeter IMF.

CALIFA, as many other samples, is not volume-limited, but can be “volume-corrected” using the method (Schmidt 1968). is the volume available per galaxy, here calculated for a diameter-limited sample by assuming that the ratio between apparent and linear isophotal size of a galaxy depends only on its angular diameter distance (see Walcher et al. 2014 for details).

We use this method to extend our results to those expected for local Universe galaxies as a whole. In particular, we transform our SFR estimates into the volume density of SFR, , by adding for our galaxies and correcting the result by , the ratio of galaxies in the mother sample to those used in this paper666For this analysis we exclude NGC 4676B and NGC 5947 because they do not belong to the original CALIFA sample, and have no associated estimates.. CALIFA is a local sample, so there is no need to correct for evolution over the lookback time spanned by its redshift limits.

This process yields (random) yrMpc. Fig. 8 places our estimate (black star) in the vs.  diagram, along with other values from the literature, coming from different samples and methods. The dashed lines shows the evolution of from Madau & Dickinson (2014), Hopkins & Beacom (2006), and Fardal et al. (2007). We also include the local from the compilation of Gunawardhana et al. (2015, 2013), and the results obtained by Panter et al. (2003) from the fossil record method applied to the SDSS data. When necessary, the literature results are scaled to a Salpeter IMF. Our estimate is smaller by 0.15 dex and higher by 0.05 dex than the values at from Madau & Dickinson (2014) and Fardal et al. (2007), respectively. It is also in excellent agreement with the estimates compiled by Gunawardhana et al. (2015, 2013), which average to yrMpc.

Obviously, the above refers to integrated measurements, which in our case tantamounts to collapsing all our 11894 radial points into a single number. To better explore our data Fig. 8 also shows the contribution to the overall from the different morphological types, plotted as stars (color coded by their morphology). It is clear that Sbc, Sc, and Sd galaxies dominate the budget. Together they contribute of , despite accounting for only of the stellar mass volume density of the local Universe (, computed following the same methodology). In contrast, Sa and Sb galaxies contribute to and to , while E and S0 add less than 2% to but 43% to .

In terms of spatial origin, 53% of comes from the regions outwards of 1 HLR, 29% from HLR, and 18% from the inner 0.5 HLR. In contrast, the budget for these same regions are 40, 25 and 35%, respectively. Most of the ongoing star formation thus occurs outside the centers, in disk dominated regions, while the stellar mass is more evenly distributed with radius. If we take as reference the half mass radius (HMR), which is typically the HLR (González Delgado et al. 2015), we find that only 35 of comes from the regions inside the central 1 HMR, suggesting again that most of the star formation density comes from the disk dominated regions.

6.2 The birthrate parameter

Figure 9: Radial profiles of the birthrate parameter, , averaged in seven Hubble type bins; compares the present to the past-average SFR at radius (cf. equation 4). The dashed and solid black lines mark, respectively, our (volume-corrected) value for the local Universe, and the reference value .

It is often useful to consider the SFR in relation to some fiducial value, instead of in absolute units. A classical example is the birthrate parameter, , that measures the current SFR of a system with respect to its lifetime average, (Kennicutt 1983b; Scalo & Struck-Marcell 1986). This parameter conveniently separates galaxies with declining SFRs () from those with SFR increasing () from past to present. and sSFR are related by

(2)

where is the time over which the galaxy has formed stars777, where is the Hubble time at redshift and is the time of formation., and denotes the fraction of the mass initially turned into stars which is returned to the interstellar medium by stellar evolution. In practice, for Gyr and (1-) = 0.72 (average over our sample and the Salpeter IMF assumed in the models).

A volume-corrected value of representative of the local Universe can be obtained from

(3)

We find that (random). Put in words, the present-day Universe is forming stars at a little over 1/3 of its past average rate.

As for (Section 6.1), though useful, this one-number-summary of the star formation history of the Universe as a whole averages over the richness of information in CALIFA data. Our spatially resolved observations allows for definitions of that take into account its variation within galaxies (Cid Fernandes et al. 2013), the simplest of which is

(4)

This radial profile ) behaves exactly as the global of equation 2. There is, however, a relevant assumption implicit in this comparison of past and present as a function to radius, namely, that (statistically) stars do not move too far from their birthplaces along their lives.

Fig. 9 shows our results for for our seven Hubble types. Clear and systematic trends are identified with both radial distance and morphology. First, increases outwards, as expected from the inside-out growth of galaxies (Pérez et al. 2013; González Delgado et al. 2014b; Sánchez-Blázquez et al. 2014; Sánchez et al. 2014; González Delgado et al. 2015). Secondly, scales in amplitude with Hubble type, increasing from early to late spirals. Sd and Sc galaxies are currently forming stars faster than in the past at all radii. The disks ( HLR) of Sbc galaxies also show , but their bulges are forming stars at lower rates than in the past. Sb and earlier types have throughout their disks and bulges.

Finally, we note that spheroids (E, S0, and the inner regions of early type spirals, presumably associated to bulges) all have . Star formation has thus stopped (or been quenched) sometime ago. Most regions in Sa have , so, even though these galaxies are still forming stars, they are located in the transition between the MSSF and the quenched cloud.

6.3 The local main sequence of star formation

Figure 10: Left: The local star forming main sequence - relation, color coded by morphology. Large white circles show the mean (i.e., -binned) relation for all points; orange and blue circles show - for Sa and Sc galaxies, respectively. Only points for which are included. Diagonal dash-black lines are loci of constant sSFR = 0.01, 0.1, and 1 Gyr. Right: the same - distribution on the left panel but with points weighted with (E and S0 are excluded). Lines show the linear fits (for and ) to the points in Sa and Sc galaxies, and for all spirals (black-grey).

CALIFA is ideally suited to investigate the roles of global and local properties controlling the MSSF. In fact, using the spatially resolved H flux of more than 500 CALIFA galaxies, Cano-Díaz et al. (2016) have recently found that the H-based correlates with the stellar mass surface density, , and that the slope and dispersion of this local MSSF are similar to those of the global SFR- relation. A local MSSF relation has also been also reported by Wuyts et al. (2013) in a sample of massive star-forming galaxies at through spatially resolved H images provided by HST. Section 4 presented our version of the global MSSF (see Fig. 4). Here we use our radial profile data to investigate the local relation.

Fig. 10 plots (R) against (R) for the nearly 12 thousand radial bins in our 416 galaxies. The plot is ultimately a collection of 416 profiles where the radial coordinate is replaced by . Clearly, our starlight-based and values correlate. Dotted diagonals mark lines of constant sSFR. An eye-ball comparison of these lines with the data already hints that, like the global one, the local MSSF is sublinear.

Individual points in the left panel of Fig. 10 are color coded according to the galaxy morphology. Large white circles show the mean in 0.2 dex wide bins in . The scatter around this mean relation is visibly related to morphology, as further illustrated by the mean relations obtained for Sa and Sc galaxies, drawn as blue and orange circles, respectively. The increase in at fixed from early to late types is another manifestation of our earlier finding that the sSFR profiles scale with Hubble type (Fig. 7).

Galaxies of different morphologies thus seem to follow roughly parallel local MSSF relations of the type , with similar logarithmic slopes () but zero points () increasing steadily from early to late types. This behavior prompted us to follow a two-steps approach to estimate and . First, scale effects are removed by rescaling both and for each galaxy by their corresponding values at HLR. The value of obtained in this way is then used to derive as the average of .888Units of and are assumed throughout.

morph. All Sa Sb Sbc Sc Sd
Table 3: Parameters of fits to the local MSSF to spirals of different types.

For the whole data set we obtain and , with an rms dispersion of 0.27 dex. We have also carried out fits weighting each point by the value of its host galaxy999In these “volume-corrected fits” the weight attributed to all radial bins of the galaxy is , where the sum runs over all galaxies., which gives the slope and zero point the status of being representative of the local Universe. The parameters for this alternative fit are and . This fit is shown as a dashed black-grey line in the right panel of Fig. 10, which repeats our local MSSF, but now coloring each radial bin of each galaxy by its contribution to the total SFR cosmic density in the local Universe ().

These fits describe well the local MSSF as a whole, but completely overlook the evident role of morphology. It is thus more appropriate to fit the relation for different Hubble types, in analogy with what was done in Table LABEL:tab:GlobalMSSF for the global MSSF. Table LABEL:tab:LocalMSSF lists the and values obtained subdividing the sample in morphology. Coefficients for the -weighted fits ( and ) are also given. Dashed blue-grey and orange-grey lines in the right panel of Fig. 10 show the fitted relations for Sc and Sa galaxies, respectively.

Inspection of the results in Table LABEL:tab:LocalMSSF shows that, as anticipated by a visual assessment of the local MSSF, slopes are indeed fairly similar for all types, while increases monotonically from early to late types. In all cases we obtain . While the mixture of morphological types certainly explains part of the sub linearity of both the global and local MSSF when lumping all sources together, this result indicates that the local MSSF is sub linear even for fixed Hubble type. Our values of for Sb and for Sc galaxies bracket the slope of 0.72 derived by Cano-Díaz et al. (2016) for the H-based local MSSF relation.

Our own previous work has shown that is an effective tracer of local stellar population properties. Both mean stellar ages (González Delgado et al. 2014b) and metallicities (González Delgado et al. 2014a) correlate well with , and this work shows that also follows this pattern.

These previous studies reveal that the overall balance between local (-driven) and global (-driven) effects varies with the location within the galaxy. While in disks regulates the mean stellar ages and metallicities, it plays a minor role in spheroids (bulges and elliptical galaxies), whose chemical enrichment happened much faster and earlier than in disks. How does the local MSSF relation found in this work fit into this general scheme?

On the one hand, we have seen that the local MSSF relation is mostly a disk phenomenon. In fact, it points to a density dependence of the SFR law akin to that proposed by Schmidt (1959) and Kennicutt (1998), where the gas density sets the rate at which stars form. On the other hand, the clear role of Hubble type in defining the offset around the overall - relation suggests that some global morphology-related property modulates the local sSFR. Gas content is an obvious candidate hidden variable in this context (Roberts & Haynes 1994; Tacconi et al. 2013).

Alternatively (or complementarily), the modulation of the - relation with Hubble type may reflect the effect of a “morphological quenching”. In González Delgado et al. (2015) we have found that, for the same , early type galaxies are older than later types, both globally and in the disk, and that this ranking is maintained with radial distance. This gradual age change from spheroidals to Sa and to late spirals reflects the change of sSFR with Hubble type, and can be interpreted as a consequence of the mechanism building the bulge. The steep potential well induced by the formation of a large spheroid component stabilizes the disk, cutting the supply of the gas and preventing its local fragmentation into bound, star-forming clumps (Martig et al. 2009). This effect should thus be more significant in E and S0, and gradually decrease from Sa to Sb. Later types, Sc and Sd, where the bulge (if present) may be formed by secular processes, may not be affected by this morphological quenching.

6.4 The relation between local and global MSSFs

The results reported throughout this paper give plenty of material to explore in relation with galaxy structure and evolution studies. In this final section we develop some simple math relating the local and global MSSF relations.

The global (i.e., spatially integrated) SFR and stellar mass of a galaxy relate to the local properties through

(5)
(6)

where we have denoted HLR by for convenience, and

(7)
(8)

are shape factors of order unity. Equations 5 and 6 lead to

(9)

which predicts the global MSSF relation in terms of spatially resolved properties.101010Eq. 9 can be written more compactly as , where the left-hand-side is the global (spatially integrated) sSFR.

Direct integration of the profiles yields a ratio of typically for our spirals (average and dispersion), and a very weak () trend with mass. Relevant deviations from a linear global MSSF must therefore come from variations of with .

Fig. 7 shows that increases systematically towards later type spirals, indicating an anti correlation with stellar mass and hence a sub-linear predicted global MSSF. More quantitatively, recalling that from our local MSSF relation, and that , with (González Delgado et al. 2014b), the predicted relation goes as . For between 0.70 and 0.84 (Table LABEL:tab:LocalMSSF), and correcting for the mild trend of with mass, the predicted logarithmic slope of the global MSSF is in the 0.78–0.85 range, in good agreement with Renzini & Peng (2015) and Cano-Díaz et al. (2016).

We close by noting that it is plausible to conclude from this analysis that the sub-linearity of the local MSSF () is what causes sub-linearity of the global MSSF111111 We clarify that the sub-linearity we refer to here is not that resulting from mixing galaxies of different morphologies in a same sample, but the one found when fitting the global MSSF at fixed Hubble type (i.e., the slopes in Table LABEL:tab:GlobalMSSF). . A caveat in this tempting local global argument is that it uses to trace the local SFR density, whereas gas, not stars, is the actual fuel of star formation. We thus postpone further analysis of this issue to future work involving gas density estimates.

7 Summary and conclusions

We analyzed the stellar population properties of 416 galaxies, observed by CALIFA at the 3.5m telescope in Calar Alto, to investigate the trends of the recent star formation rate with radial distance and as a function of Hubble type. The sample includes ellipticals, S0, and spirals all the way from Sa to Sd, covering a stellar mass range from to (for a Salpeter IMF). A full spectral fitting analysis was performed using the starlight code and a combination of SSP spectra from González Delgado et al. (2005) plus Vazdekis et al. (2010). Our pycasso pipeline was used to process the spectral fitting results to produce maps of the recent star formation rate (SFR, averaged over the last 32 Myr), and the stellar mass surface density (). For each galaxy, the maps are azimuthally averaged to produce radial profiles (in units of the half light radius, HLR) of the SFR surface density, , and the corresponding local specific SFR, sSFR. Variations of the traditional birthrate parameter, , are obtained to compare the present and the past SFR at different radial positions. The radial profiles are stacked as a function of Hubble type and of galaxy mass to identify the main trends.

Our main results are:

  1. Spiral galaxies have declining profiles, with a relatively tight range of values at any given radial distance. At HLR the is typically Gyrpc, with a factor of two dispersion. Spirals with have profiles that are very similar and independent of Hubble type and galaxy mass. Above the profiles are slightly more dispersed. This is a remarkable result taking into consideration that the sample covers two orders of magnitude in and all Hubble types. Ultimately, it is the constancy of that, coupled to the - relation, makes the MSSF a tight sequence.

  2. In contrast, E and S0 galaxies have that are at all radii significantly depressed with respect to spirals, with flat Gyrpc profiles, with a large uncertainty.

  3. Expressed in units of the lifetime averaged SFR intensity at each location, the present is currently lower in E, S0, and early type spirals (Sa and Sb), but higher in later spirals (Sc and Sd). Sbc galaxies seem to be the transition type in which ”bulges” (central 1 HLR) have already suppressed/quenched their star formation activity, as in Sa and Sb, but their disks are still forming new stars at a rate similar to the past.

  4. The local shows radial profiles that increase outwards and scale with Hubble type, from Sa to Sd. This behavior is preserved at any given . This quantity, that relates locally the present and the past star formation rate, is orders of magnitude smaller in E and S0 than in spirals. The characteristic time scale of star formation given by sSFR in spirals ranges from 12.6 Gyr in Sbc to 5 Gry in Sd galaxies. Early type spirals (Sa, Sb) and spheroidals (E, S0) would need more than a Hubble time to build their current stellar mass at their recent SFR.

  5. The slope of sSFR in the inner 1 HLR is steeper than outwards. This behavior with radial distance suggests that galaxies are quenched inside-out, and that this process is faster in the central part (dominated by the bulge) that in the disk.

  6. The CALIFA sample is well suited to compute the SFR density in the local universe, with a value (random) yrMpc (for a Salpeter IMF), in excellent agreement with previous estimates from completely difference methods and data. We find the majority of the star formation at to take place in Sbc, Sc, and Sd galaxies with masses below . In terms of spatial distribution, most of the star formation is occurring outside galaxy centres, in regions that are mainly in the disks of spirals.

  7. The volume average birthrate parameter, , suggests that the present day Universe is forming stars at of its past average rate. E, S0, and the bulge of early type spirals have , thus contributing little to the present star formation rate of the Universe. The disks (regions outside 1 HLR) of Sbc, and Sc, and Sd galaxies, all with , dominate the present star formation of the Universe.

  8. Galaxy mass and morphology, in particular the formation of a spheroidal component, play a relevant role in depressing/quenching the star formation in galaxies. Galaxies dominated by the spheroidal component, E and S0 in our sample, are all quiescent. Disk dominated galaxies (Sbc, Sc, Sd) are very actively forming stars with a rate per unit mass that decreases with .

  9. There is tight relation between the local values of and , defining a local main sequence of star forming regions with slope , and a scatter strongly related to Hubble type. This relation is tighter than the global main sequence relation between SFR and

    once morphology-related offsets are accounted for. This suggests that local processes are important in determining the star formation in a galaxy, possibly due to a density dependence of the SFR law. The shut down of the star formation is more related with global processes, such as the formation of a spheroidal component. These findings agree with our previous analysis that showed that the mean stellar ages and metallicity are mainly governed by local processes (-driven) in disks, and by global processes in spheroids.

Thanks to the uniqueness of CALIFA data and the homogeneity of our analysis, we were able to, for the first time, characterize the radial structure of the star formation rate along the Hubble sequence. This octogenarian sequence, by the way, has once again demonstrated its usefulness as a way to organize galaxies in terms of their spatially resolved properties. Our previous work showed the systematic behavior of , mean stellar ages and metallicity with Hubble type, while this paper showed the same also applies to the SFR and related quantities.

The large file FoV of PPaK allows us to cover galaxies in their entire optical extent, a design feature of CALIFA which eliminates aperture-related biases in the derivation of galaxy properties. Furthermore, the well defined selection function of the survey allows for reliable volume corrections. In fact, an important “byproduct” of this study is that it exemplifies how well these corrections work, as demonstrated by the excellent agreement between our estimate for the of the local Universe and independent determinations from large galaxy surveys. This validates and reinforces the statistical approach to CALIFA followed in this, previous and future papers in this series.

Acknowledgements.
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 AYA2014-57490-P, AYA2010-15081, and Junta de Andalucía FQ1580, AYA2010-22111-C03-03, AYA2010-10904E, AYA2013-42227P, RyC-2011-09461, AYA2013-47742-C4-3-P, EU SELGIFS exchange programme FP7-PEOPLE-2013-IRSES-612701, and CONACYT-125180 and DGAPA-IA100815. We also thank the Viabilidad, Diseño, Acceso y Mejora funding program, ICTS-2009-10, for funding the data acquisition of this project. ALdA, EADL and RCF thanks the hospitality of the IAA and the support of CAPES and CNPq. RGD acknowledges the support of CNPq (Brazil) through Programa Ciência sem Fronteiras (401452/2012-3). CJW acknowledges support through the Marie Curie Career Integration Grant 303912. We thank the support of the IAA Computing group, and to the referee for useful comments.

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Appendix A Dependence of SFR on SSP models

Figure 11: Comparison of several stellar population properties as obtained with the bases GMe (x-axis) and CBe (y-axis). The average difference between the property in the y and x-axis is labeled as in each panel, and its standard deviation as . Panels (a), (b), and (d) show the galaxy mass and SFR, with galaxies colored by their Hubble type. In the other panels, the values of the property measured every 0.1 HLR are compared, and the color indicates the density of points in a logarithmic scale.

In order to evaluate to what extent our results depend on the choice of SSP models, we compare the properties derived with two bases: Base GMe, i.e., the one used in the main text and briefly described in Sec. 3.1, and base CBe, used in several earlier works by our group, and fully described in González Delgado et al. (2015). In short, this base is built out of a preliminary update of the Bruzual & Charlot (2003) models (Bruzual 2007, private communication), from which we draw = 246 elements with 41 ages (from 0.001 to 14 Gyr) and six metallicities (, , , , , and ). The evolutionary tracks are those collectively referred to as Padova 1994 by Bruzual & Charlot (2003), and the IMF is that of Chabrier (2003). Compared to GMe, base CBe differs in evolutionary tracks, IMF, and metallicity range.

We make two types of comparisons in this appendix: (i) global (galaxy wide) quantities, such as the present day and initial stellar masses, and the total SFR; and (ii) radial averages of , , , , and for up to a maximum 30 of points for each galaxy (corresponding to –3 in steps of 0.1 HLR). Fig. 11 shows the results, with base GMe values in the x-axis and CBe ones in the y-axis. Each panel shows a one-to-one line, as well as the mean () and standard deviation () of the difference property(CBe) property(GMe).

On average, GMe-based and -values are 0.26 dex higher than the corresponding CBe-based values, reflecting the different IMF used. Discounting this offset, the two values of stellar mass and mass surface density agree to within 0.06 and 0.11 dex, respectively. In terms of the initial mass that is converted into stars () there is a difference of 0.12 dex between the two bases and a dispersion of 0.06 dex. Again, the difference reflects the change of IMF between the two bases. Note that is higher than because the returned fraction also differs from one base to the other (= 0.28 and 0.48 for GMe and CBe, respectively).

Due to the IMF difference, the SFR should be lower for CBe than for GMe. This is in fact the result (Fig.11d), but the difference is only 0.07 dex, lower than what we would expect due to the change of IMF. This implies that besides the IMF, there are differences in the SFH between GMe and CBe and/or in stellar extinction. The latter explanation does not hold, since is very similar in the two sets of models, with an offset of only mag and dispersion mag. However, we note that there is an important difference between the light fraction in populations younger than 32 Myr. On average, is 0.18 dex higher with CBe than GMe. This explains why the SFR with CBe, although lower than with GMe, is not a full factor of lower, as expected due to the change of IMF.

This change in SFH, and in particular in , does not produce any significant effect in the radial distribution of the star formation rate intensity, . The two sets of values are well correlated (Fig. 11g), with a tiny difference of dex (lower in CBe than in GMe), and a dispersion dex. The offset of between the two bases is dex, reflecting mainly the offset in due to the IMF (Fig. 11b).

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