© ESO, 2012

1. Introduction

For more than fifty years, nebular emission lines from bright-individual H ii regions have been the main tool at our disposal for the direct measurement of the gas-phase abundance at discrete spatial positions in galaxies. A good observational understanding of the distribution of element abundances across the surface of nearby galaxies is necessary to place constrains on theories of galactic chemical evolution. The same information is crucial to derive accurate star formation histories of and obtain information on the stellar nucleosynthesis in normal spiral galaxies.

Several factors dictate the chemical evolution in a galaxy, including the primordial composition, the content and distribution of molecular and neutral gas, the star formation history (SFH), feedback, the transport and mixing of gas, the initial mass function (IMF), etc. (e.g. López-Sánchez 2010; López-Sánchez & Esteban 2010, and references therein). All these ingredients contribute through a complex process to the evolutionary histories of the stars and the galaxies in general. Accurate measurements of the present chemical abundance constrain the different possible evolutionary scenarios, and thus the importance of determining the elemental composition in a global approach, among different galaxy types.

Previous spectroscopic studies have unveiled some aspects of the complex processes at play between the chemical abundances of galaxies and their physical properties. Although these studies have been successful in determining important relationships, scaling laws and systematic patterns (e.g. luminosity − metallicity, mass − metallicity, and surface brightness vs. metallicity relations: Lequeux et al. 1979; Skillman 1989; Vila-Costas & Edmunds 1992; Zaritsky et al. 1994; Tremonti et al. 2004; effective yield vs. luminosity and circular velocity relations: Garnett 2002; abundance gradients and the effective radius of disks: Diaz 1989; systematic differences in the gas-phase abundance gradients between normal and barred spirals: Zaritsky et al. 1994; Martin & Roy 1994; characteristic vs. integrated abundances: Moustakas & Kennicutt 2006; etc.), they have been limited by statistics, either in the number of observed H ii regions or in the coverage of these regions across the galaxy surface.

Hitherto, most studies devoted to the chemical abundance of extragalactic nebulae have only been able to measure the first two moments of the abundance distribution: the mean metal abundances of discs and their radial gradients. Indeed, most of the observations targeting nebular emission have been made with single-aperture or long-slit spectrographs, resulting in a small number of galaxies studied in detail, a small number of H ii regions studied per galaxy, and a limited coverage of these regions within the galaxy surface. The advent of multi-object spectrometers and Integral Field Spectroscopy (IFS) instruments with large fields of view now offers us the opportunity to undertake a new generation of emission-line surveys, based on samples of scores to hundreds of H ii regions and full two-dimensional (2D) coverage of the discs of nearby spiral galaxies.

Two years ago, we started a major observational program to understand the statistical properties of H ii regions, and to unveil the nature of the reported physical relations, using IFS. This program was initiated with the PINGS survey (Rosales-Ortega et al. 2010), which acquired IFS mosaic data of a number of normal nearby galaxies. In Sánchez et al. (2011) and Rosales-Ortega et al. (2011), we studied in detail the ionized gas and H ii regions of the largest galaxy in the sample (NGC 628). We then continued the acquisition of IFS data for a larger sample of visually classified face-on spiral galaxies (Mármol-Queraltó et al. 2011, hereafter Paper I), as part of the feasibility studies for the CALIFA survey (Sánchez et al. 2012). The spatially resolved properties of a typical galaxy in this sample, UGC 9837, was presented by Viironen et al. (2012). Face-on galaxies are more suitable to study the spatial distribution of the properties of H ii regions: (i) they are identified and segregated more easily; (ii) their spatial distribution is less prompt to the errors induced by inclination effects; (iii) they are less affected by dust extinction along the line of sight within the galaxy and (iv) it is more easy to identify their association with a particular spiral arm.

Here we focus on the study of the properties of H ii regions for the face-on spiral galaxies observed so far. In Sect. 2 we summarize the main properties of the analysed galaxies. In Sect. 3 we present the automatic algorithm developed to detect, segregate and extract the integrated spectra of the different H ii regions within a datacube; a comparison between the results derived with this method and those provided with other published ones is shown in Sect. 4. In Sect. 5 we describe an analytical method to define the presence and location of spiral arms within a galaxy. The method has been tested and used to associate the detected H ii regions to different spiral arms and/or to the intra-arm region. The main spectroscopic properties of the catalogued H ii regions and the morphological structure of each galaxy are described in Sects. 6.1.1 and 6.1.2. The main results of our analysis are included in Sect. 7, where we describe the statistical properties of the H ii regions (Sect. 7.1), and their radial gradients (Sect. 7.2). Our conclusions are presented in Sect. 8. In the Appendix, the publicly accessible catalogues of the properties derived for the analysed H ii regions are described in Sect. A, and an empirical method to correct [N ii] emission for non-star forming sources on narrow-band Hα images is proposed in Sect. B.

2. Sample of galaxies

Table 1 lists the sample of galaxies analysed in the current study, including for each object, its name, central coordinates, morphological classification, redshift, and some additional information that we will describe later. The sample of galaxies has been selected from two available datasets: (1) the IFS survey of nearby galaxies described in Paper I, which comprises ~85% of the galaxies analysed here; and (2) galaxies selected from the PINGS survey (Rosales-Ortega et al. 2010), accounting for the remaining ~15% of the galaxies. In both cases we selected visually classified face-on galaxies, with a relatively unperturbed spiral structure.

The sample is dominated by late-type spirals (31 out of 38), according to the classification criteria by Laurikainen et al. (2010), shown in Table 1. Therefore, we lack the statistics required to analyse possible differences in the properties of H ii regions between late/early-type spirals. About 40% of the galaxies show evidence of a bar (based on its visual classification listed in Table 1), although this feature clearly dominates the morphology of the galaxy in only a few cases (e.g. UGC 5100). Regarding the structure of their spiral arms, the sample includes a mix of grand-design spirals (e.g. NGC 628), or clearly flocculent ones (e.g., UGC 9837, Viironen et al. 2012). Although it is by no means a statistically well defined sample, we consider that it is representative of the average population of spiral galaxies in the local Universe.

Both sub-samples of galaxies were observed using similar techniques (IFS), using the same instrument (PMAS in the PPAK configuration, Roth et al. 2005; Kelz et al. 2006), covering a similar wavelength range (~3700 − 6900 Å), with similar resolutions and integration times. The data reduction was performed using the same procedure (R3D, Sánchez 2006), as described in Paper I and Rosales-Ortega et al. (2010). The main difference is that for the first sample a single pointing strategy using a dithering scheme was applied, while for the largest galaxies of the PINGS survey, a mosaic comprising different pointings was required. This is due to the differences in projected size, considering the different redshift range of both samples: for the first one corresponds to ~0.01−0.025, while the second one corresponds to ~0.001−0.003. Therefore, in both survey samples, the data extent corresponds to about ~2 effective radii for all galaxies (the effective radius is classically defined as the radius at which one half of the total light of the system is emitted).

The observational setups allowed us to cover the optical wavelength range, sampling many of the most important emission lines for H ii regions, from [O ii] λ3727 to [S ii] λ6731. Details on the observing strategy, setups, reduction and main characteristics of the dataset are described in Paper I and Rosales-Ortega et al. (2010). The final dataset comprises 38 individual datacubes, one per galaxy, with a final spatial sampling of 1″/pixel for most of the galaxies. The datacubes were created using the interpolation scheme described in Sánchez et al. (2012), developed for the CALIFA survey. Despite of the original fiber size (2.7″/fiber), the three pointing dithering scheme allows to increase slightly the final resolution. The selected offsets, with values corresponding to a fraction of the fiber-size, allows to cover the gaps between adjacent fibers too. In average natural seeing conditions of ~1″ (Sánchez et al. 2007a), this technique allows to provide a final spatial resolution of FWHM ~ 2″ for this instrument (Sánchez et al. 2007b). The size of the spaxel was selected as the largest convenient pixel to the sample this resolution element, 2 pixels per FWHM, i.e., 1″/pixel. Due to the large size of the IFS mosaics of NGC 628 and NGC 3184, the two largest galaxies observed with PINGS, and the fact that they were not observed using a dithering scheme for all the pointings, we set the spatial sampling to 2″/pixels. In this case, the final resolution is larger than the original size of the fiber, due to the interpolation kernel. A rough estimation indicates that the final spatial resolution is FWHM ~ 3.5−4″.

On average the physical spatial sampling ranges between a few hundreds of parsecs (for the nearest galaxies) to almost 1 kpc (for the more distant ones). To derive this physical scale it is required to adopt a certain distance modulus. Consistently with values reported in Table 1, we adopted the distance modulus provided by Hyperleda, mod, defined as mod = 5log (D_L) + 25 and D_L is the luminosity distance in Mpc¹. The derived scale can be compared to the physical diameter of a well-known H ii region in our Galaxy, i.e. the Orion nebula (D ~ 8 pc), or to the extent of those which are considered prototypes of extragalactic giant H ii regions, such as 30 Doradus (D ~ 200 pc), NGC 604 (D ~ 460 pc) or NGC 5471 (D ~ 1 kpc) as reported by Oey et al. (2003) and García-Benito et al. (2011). Thus, given the undersampling in the physical size of the H ii regions in our data, we cannot use it to derive direct estimates of the optical extension of these regions. In other aspects, like the depth, covered extension of the galaxy, projected resolution and wavelength coverage, the data provided by both samples are very similar.

3. Extraction of the H ii regions

The segregation of H ii regions and the extraction of the corresponding spectra is performed using a semi-automatic procedure, named HIIexplorer². The procedure is based on some basic assumptions: (a) H ii regions are peaky/isolated structures with a strong ionized gas emission, clearly above the continuum emission and the average ionized gas emission across the galaxy; (b) H ii regions have a typical physical size of about a hundred or a few hundreds of parsecs (e.g. Gonzalez Delgado & Perez 1997; Lopez et al. 2011; Oey et al. 2003), which corresponds to a typical projected size at the distance of the galaxies of a few arcsec.

The algorithm requires a set of input parameters: (i) a line emission map, with the same world-coordinate system (WCS) and resolution as the input datacube (preferentially an Hα emission line map); (ii) a flux intensity threshold for the peak emission of each H ii region; (iii) a maximum distance to the peak location for a pixel associated with each H ii region; (iv) a relative threshold with respect to this peak emission of the minimum intensity of each H ii region; (v) an absolute threshold of the minimum intensity corresponding to each H ii region. All these parameters can be derived from either a visual inspection and/or a statistical analysis of the Hα emission line map. The algorithm produces as an output a segmentation FITS file describing the pixels associated to each H ii region, designated with a running index starting with 1 (e.g. the primary H ii region ID in this article), with the zero reserved to areas not associated with any H ii region (i.e. regions free of emission or below the absolute threshold described above).

The segregation algorithm is based on a simple iterative procedure, summarized in the flow chart shown in Fig. 1. As a first step the algorithm looks for the brightest pixel within the emission line map. Its location is stored as the peak/central coordinate of a new H ii region, associated with a certain running index (ID number). After this, the adjacent pixels are aggregated to this H ii region if all of the following criteria are fulfilled: (i) the distance to the central/peak pixel is below the selected limit; (ii) the flux at the pixel is above the relative threshold with respect to the peak emission; (iii) the flux at the pixel is above the absolute flux threshold described before. Whenever any of these criteria are not fulfilled the aggregation procedure stops, the ID number is increased by one, all the aggregated pixels are masked-off, and the peak-identification procedure is repeated. The overall procedure stops whenever no new peak is detected above the selected peak-intensity threshold.

The outcome of the procedure is illustrated in Fig. 2 where we show: (i) the input emission line map, in this case the Hα map corresponding to a set of galaxies and (ii) the corresponding derived segmentation map. Despite the simplicity of the described algorithm it is clearly seen that (1) it is able to detect all the H ii regions that can be identified by eye; and (2) it produces a reliable segmentation map. The black segmented areas indicate those regions with good quality spectra, while the grey ones indicate those with poor extracted spectra. The actual procedure to detect and reject those ones is described later. In addition, the procedure provides with a mask where all the H ii regions are flagged out. This mask is important to define the areas where it is possible to study the diffuse gas emission.

There are other publicly accessible packages for the automatic selection/segregation of H ii regions in the literature (e.g. HIIphot, Thilker et al. 2000; Region, Fathi et al. 2007), that in principle could be adapted for the main purpose of the current study. However, these packages are strongly focused on the analysis of narrow-band images, of much higher spatial resolution, where the H ii regions are clearly resolved. In some cases the procedure requires a detailed knowledge of the observational procedure (number of frames co-added, ADU of the CCD, etc.). For example, HIIphot uses object recognition techniques to make a first guess at the shapes of all sources and then allows for departure from such idealized seeds through an iterative growing procedure. In essence, this algorithm is similar to the one used by SExtractor (Bertin & Arnouts 1996), for the detection and segregation of galaxies in crowed fields. We experimented with these packages before developing our own code, but we did not get any optimal solution. The main reasons were that (1) our data have a much coarser resolution than the one provided by narrow-band imaging (even from ground-based telescopes); (2) reconstructed IFU map have a strong cross-correlated noise among nearby interpolated pixels and (3) none of the preceding codes provide a final segmentation map usable to extract the integrated spectra of the H ii regions from the datacubes in a convenient way.

We experimented with the use of HIIexplorer on a Hα narrow-band image provided by the SINGS legacy survey for NGC 628 (Kennicutt et al. 2003). A visual inspection of the selected regions with those shown by Thilker et al. (2000), indicates that although we detect similar regions, HIIexplorer tends to define regions of mostly equal size. This is expected, since for the spatial resolution the maximum size allowed for each region is reached before that imposed by the ratio of local to peak intensity. Our code was never meant to provide a particularly reliable measure of the projected size, as in our data this parameter is ill-defined. Specifically, H ii regions can be significantly smaller than the resolution element size. In Sect. 4 we present a quantitative comparison with methods available in the literature.

Once tested the procedure, we applied it to our IFS data. First, we create a Hα intensity map for each object by co-adding the flux intensity within a square-shaped simulated filter centered at the wavelength of Hα (6563 Å), with a width of 60 Å. The adjacent continuum for each pixel was derived by averaging the flux intensity within two similar bands red- and blue-shifted 100 Å from the center of the initial one. This continuum intensity is then subtracted from the Hα intensity to derive a continuum-subtracted emission line map. The central wavelength of all these bands has been shifted to the observed frame taking into account the redshift of the object. The separations between the filters and the filter widths are large enough to avoid any possible error in the derivation of the Hα intensity map due to kinematic shifts.

However, this Hα intensity map is contaminated with the adjacent [N ii] emission lines, and it is not corrected for the emission of the underlying stellar population (see Appendix B for a discussion on the topic). A cleaner Hα emission map can be derived using emission-line/stellar population decoupling procedures (e.g., Rosales-Ortega et al. 2010; Sánchez et al. 2011; Mármol-Queraltó et al. 2011; Sánchez et al. 2012). This allow us to recover much fainter emission line regions on top of underlying strong absorption features. However, in most cases these emission line regions do not correspond with classical H ii regions and are associated with other ionization processes (e.g. Kehrig et al. 2012, and references there in). On the other hand, the adopted procedure resembles as much as possible the classical procedure used to detect H ii regions, which will allow us to make a better comparison with previous results.

As the main goal of the current study is to extract the spectroscopic properties of the H ii regions, we applied HIIexplorer adopting the following input parameters for all the galaxies: (i) a minimum flux density for the peak intensity of an H ii region of 2 × 10^-17 erg s^-1 cm^-2 arcsec^-1; (ii) a minimum relative flux to the peak intensity for associated pixels corresponding to the same H ii region of 10% and (iii) a maximum distance to the location of the peak of 3.5″ (7″ for NGC 628 and NGC 3184). The maximum distance was selected using and iterative process, maximizing the number of detections when compared with a visual inspection, and do not allow to segment clearly single H ii regions. Then, we extracted a single spectrum for each region by co-adding all the spectra in the original cubes with the same identification index (ID) in the the derived segmentation map. The final spectra are stored in the so-called row-stacked spectra (RSS) format Sánchez et al. (2004), which comprises a 2D spectral image, with the spectrum corresponding to each H ii region order by rows (each one corresponding to the considered ID), and an associated position table which records the barycenter of each H ii region (based on the Hα intensity). This format allows us to visualize individual spectra of H ii regions and their spatial distribution using standard techniques (e.g., E3D, Sánchez et al. 2004). The ID is a unique identification index that will be used to identify the H ii regions hereafter (including the tables, figures and on-line material).

Table 2 summarizes the results from this analysis. It shows, for each galaxy, the number of H ii regions detected, the number of regions with good quality extracted spectra, the median Hα flux intensity as directly measured from the IFS-based narrow-band image, and its standard deviation. Due to the different redshift range, there is a wide variance in the median flux intensity of the Hα emission, much larger than the absolute luminosity as we will describe later. Since we are selecting H ii regions which physical size is slightly smaller than our typical resolution element, this implies that we are actually not aggregating a large number of real H ii regions in each detected complex. Our comparisons with higher resolution narrow-band images confirms this suspicion. Finally, we have included in the table the median radius of the regions, defined as $\mathit{R}\mathrm{=}\sqrt{\mathit{A}\mathit{/}\mathit{\pi }}$, where A is the area within a region (Rosales-Ortega et al. 2011). We should state clearly here that the physical scale is an ill-defined parameter in our survey, due to two reasons: 1) the coarse spatial sampling compared to the expected size of H ii regions, these can be significantly smaller than the resolution element size and 2) the adopted procedure to detect and segregate the regions, namely the introduction of an angular upper size limit to the continuous emission region. Only for the galaxies at lower redshift, the sizes of the H ii regions are of the order of the expected one, i.e. ~100 pc.

In practice, our segregated H ii regions may comprise several classical ones, in particular for the more distant galaxies. Detailed simulations on the effect of resolution loss have shown us that on average each selected region at z ~ 0.02 may comprise 1 − 3 H ii regions from the ones selected from low redshift galaxies, z ~ 0.002 (Mast et al., in prep.). Following Lopez et al. (2011), the considered H ii regions would have a size of a few to several hundreds of parsecs, based on their Hα luminosity, detailed in Sect. 7.1, Table 7. Thererefore, the results from the simulations are expected, due to the typical size of an extragalactic H ii region and the lose of physical resolution at the higher redshifts. I.e. we are selecting H ii-regions and/or H ii aggregations (note that throughout this paper we will refer indistinctively to these segmented regions as H ii regions). Therefore, our results are not useful to analyse additive/integrated properties on individual H ii regions, like the Hα luminosity function, but are perfectly suited for the study of line ratios, chemical abundances and ionization conditions.

In total, we have detected 3107 H ii regions, 2573 of them with good spectroscopic information. To our knowledge this is by far the largest 2-dimensional, nearby spectroscopic H ii region survey ever accomplished.

4. Comparisons with previous selection methods to detect H ii regions

In order to assess quantitatively the degree of segmentation provided by HIIexplorer with respect to other traditional H ii region catalogues generators, we performed a comparison between the H ii region catalogues of NGC 628, NGC 3184 and NGC 5474 obtained with HIIexplorer and those reported in the literature.

For NGC 628 we used the Hα image extracted from the IFS data with a resolution of 2 arcsec/pixel and a FoV of ~6 arcmin, and the one produced by the Region software in Fathi et al. (2007; hereafter Fa07), obtained from a narrow-band Hα image with a resolution of 0.33 arcsec/pixel and a FoV of ~11 arcmin. Similar comparisons could be performed with any other package created to segregate H ii regions (e.g. HIIPhot, Thilker et al. 2000). We selected this one because Fa07 provided publicly accessible catalogues.

The full Fa07 catalogue has 376 regions of which 299 are within the FoV of our IFS data. However, the public Fa07 catalogue reports only the position and the full-width at half maximum (FWHM) of each H ii region, not the actual shape obtained by the software, and this leads to significant overlaps when the Region catalogue is plotted over the galaxy image. Taking this into account and considering the difference in resolution between the two Hα images, we created a modified version of the Fa07 catalogue in order to make a fair comparison. The modified Fa07 catalogue was obtained in an iterative way. First we took the first region of the catalogue and calculated its distance from the rest of the regions. Those regions for which the distance was less or equal to the sum of their radii were considered as a single region. In this case, the involved regions are removed from the original catalogue and a new entry is added with coordinates and size corresponding to the luminosity weighted mean of the merged regions, the process is repeated for the rest of the catalogue entries in an iterative manner. We obtain 180 regions in the modified Fa07 catalogue of NGC 628.

Figure 3 shows the comparison between the modified Fa07 catalogue and the HIIexplorer segmentation map. The blue circles correspond to the modified Fa07 catalogue, while the grey contours to the 286 segmented regions obtained by HIIexplorer for NGC 628 based on the IFS data. We note that, a) HIIexplorer detects and segments more regions than Fa07, except for those cases in which the difference in spatial resolution (0.33 vs. 2 arcsec/pixel) prevents further segmentation; b) there is a nearly 1:1 correspondence of regions detected in Fa07 with respect to HIIexplorer, the incompleteness of Fa07 with respect to HIIexplorer is 5%; c) 19% of the regions in HIIexplorer have 2 or more regions of the modified Fa07 catalogue, which is simply due to the difference in resolution. We have checked visually the extracted spectra of the additional H ii regions detected by our algorithm, and inspected the original narrow band image and they seem to be real H ii regions, clearly distingued from the low surface brightness diffuse gas. The performance of HIIexplorer compared with Region is remarkable, considering both that the narrow-band Hα image used to generate the Fa07 catalogue is deeper than the image extracted from the IFS data, and that HIIexplorer runs in a completely automated way.

The H ii regions of NGC 3184 and NGC 5474 were studied by Bradley et al. (2006) using REGION (hereafter B06). For NGC 3184, the catalogue obtained by B06 contains 576 H ii regions of which 209 are within the FoV of our IFS data. Like the Fathi et al. (2007) case for NGC 628, the B06 catalogues report only the offset from the galaxy centre and the total area of the region, not the actual shape obtained by the software, which leads to significant overlaps when the REGION B06 catalogue is plotted over a RA vs. Dec plane using an effective radius derived from the B06 catalogue. Therefore, we applied the same methodology for a fair comparison obtaining a modified B06 catalogue for this galaxy, imposing a Hα luminosity threshold of log  (L_Hα) > 37.96 erg s^-1 (the minimum luminosity detected by HIIexplorer at this redshift). The level of completeness is 73%, i.e. regions detected by HIIexplorer with respect to B06 (note that in the majority of cases there is a 1:1 correspondence); in 15 cases 2 or more B06 regions are found within 1 segmented area by HIIexplorer. However, in 5 cases 2 H ii regions by HIIexplorer correspond to 1 region found by B06, while 13 regions detected by HIIexplorer are not present in the B06 catalogue.

In the case of NGC 5474, the original B06 catalogue contains 165 H ii regions, of which 98 are within the FoV of the IFS data. For this galaxy, we worked directly with the published catalogue without further modifications for a better visual comparison. There was no need to apply a luminosity threshold since all the regions were above the minimum luminosity observed by the regions segmented by HIIexplorer, log  (L_Hα) ~ 36.6 erg s^-1. We note that HIIexplorer detects and segments more regions than B06, except for those cases in which the difference in spatial resolution prevents further segmentation. The level of completeness (regions detected by HIIexplorer compared to the B06 catalogue) is of 90% (including 1:1 correspondence and multiple B06 HII regions within one HIIexplorer segmentation), but interestingly 31 regions detected by HIIexplorer are not found in the B06 catalogue, which is surprising given the that the Hα image used to generate the B06 catalogue is deeper than the Hα map extracted from the IFS data.

This exercise shows that HIIexplorer is capable of performing an excellent H ii region extraction for the resolution of our IFS data, and that the generated catalogues are comparable (and even more efficient) than those generated in a traditional way based on narrow-band Hα imaging.

5. Analytical characterization of the spiral arms

A fundamental question regarding the star-forming regions in galaxies is whether their distribution and properties depend on their association (or not) with a particular spiral arm. Two main questions are directly connected with this one: (i) whether there are azimuthal variations within the spectroscopic properties of the H ii regions, which would possibly reflect non-radial differences in the galaxies evolution, maybe induced by non secular processes, and (ii) whether the properties of the inter-arm H ii regions are different than those of the H ii intra-arms ones, which will reflect a possible differential evolution associated with ram pressure in the spiral arms. The lack of a sample with a statistically large number of H ii regions, with homogeneously derived spectroscopic properties, and with a good characterization of the structure of the spiral arms has not allowed to give a conclusive answer to these questions so far.

In the following we attempt to give a good description of the structure (number, shape, radial path) of the spiral arms and to define a procedure to associate H ii regions with each spiral arm and/or classify them as inter-arm ones. We adopt the prescription proposed by Ringermacher & Mead (2009) to describe the general shape of the spiral arms. This formalism describes the radial path of any spiral arm using the formula: $\mathit{r}\mathrm{\left(}\mathit{\theta }\mathrm{\right)}\mathrm{=}\frac{\mathit{A}}{\log \left(\mathit{B}\tan \mathrm{(}\mathit{\theta }\mathit{/}\mathrm{2}\mathit{C}\mathrm{)}\right)}$(1)this function intrinsically generates a bar in a continuous, fixed relationship relative to an arm of arbitrary winding sweep. A is simply a scale parameter while B, together with C, determines the spiral pitch. Roughly, larger C results in tighter winding. Greater B results in larger arm sweep and smaller bar/bulge, while smaller B fits larger bar/bulge with a sharper bar/arm junction. Thus B controls the “bar/bulge-to-arm” size, while C controls the tightness much like the Hubble scheme. Special shapes such as ring galaxies with inward and outward arms are also described by the analytic continuation of the same formula, which is particularly useful to analyse the diversity of spiral structures within our sample.

The previous formula describes the radial path in the physical plane of the disk for each spiral arm. To describe the full observed spiral structure, for a galaxy with N_A arms, it is required to project it at the observed plane (taking into account the inclination and position angle), and to add N_A copies of the considered arm, rotated by an angle of 360/N_A degrees with respect to the precedent one.

The optimal parameters that describe the current spiral structure (N_A, A, B and C) have been derived using an interactive fitting algorithm that is based on two simple assumptions: (1) the spiral arms trace the location of the stronger Hα emission and continuum emission. i.e., the integrated intensity along the arm should be maximized; and (2) the H ii regions are more frequently clustered around the spiral arms. i.e., the distance from each region to the nearest spiral arm should be minimized. The analytical parameters of the spiral arms are then derived based on these assumptions and using as inputs (i) a broad band image of the galaxy. The SDSS g-band image in most of the cases (extracted from the SDSS imaging survey, York et al. 2000, and Paper I), and when not feasible the V-band one, from our own observations (Paper I), or literature data (Rosales-Ortega et al. 2010); (ii) the spatial distribution of H ii regions derived by HIIexplorer; and (iii) a few simple assumptions of the number of arms and the scale-length of the possible bar and/or the initial ring, based on the visual inspection of the images. In general, we selected the spiral structure with the smallest possible number of spiral arms that fulfill the criteria.

We are aware that the formalism adopted here to describe the analytical structure of the spiral arms is clearly not the most mathematically exact one. However it is useful for the ultimate goal of our study, i.e. to determine how many spiral arms are in a considered galaxy and if a certain H ii region belongs to an arm or not. A more analytical description of the spiral arms is clearly out of the scope of the current study.

Table 3 lists the results of this analysis, including, for each galaxy, its name, the number of derived spiral arms, a flag indicating the reliability of the results, and the parameters of the radial path for each arm, according to the described formula: A, B and C. The quality flag is 1 for those galaxies with a clearly distinguised spiral structure and a well defined set of parameters to describe them, and for those galaxies without a well defined spiral structure (flocculent). Figure 4 shows four examples of the derived spiral structure for the galaxies in our sample, including two cases with well defined spiral structure (NGC 628 and UGC 1081), one without a clear defined spiral structure (NGC 1637) and a clear flocculent case (UGC 9837).

We associated H ii regions to the nearest spiral arm by computing the minimum distance between the centroid of the H ii region and the radial distribution of the considered arm. The mean of these distances is then used as a scale-length to separate between H ii regions clearly associated with an arm, and possible inter-arm ones. A final flag is included in the corresponding catalogue table describing the coordinates of the detected H ii regions, indicating the nearest arm and the relative distance with respect to the median one. Table 4 illustrates the result of this analysis. It shows, for one single galaxy (UGC 9837), the absolute, relative, polar and deprojected coordinates of the 10 brightest H ii regions, together with identification of the nearest spiral arm, the Cartesian and angular distance to this arm and the spiralcentric distance (i.e. the distance to the center along the spiral arm). In this context brightness means the peak intensity within a certain H ii, as considered by HIIexplorer. In addition, we included in this table the systemic velocity and absolute luminosity of Hα for each H ii, derived on basis of the emission line fitting described in Sect. 6.1.1. Similar parameters are derived for all the H ii regions in the different galaxies, as indicated in Appendix A. To our knowledge, this is the first attempt to perform an analytical association of H ii regions to a particular arm and/or to an inter-arm area in a survey mode.

6. Deriving the main spectroscopic properties of the H ii regions

6.1. Decoupling the emission lines from the underlying stellar population

To extract the nebular physical information of each individual H ii region, the underlying continuum must be decoupled from the emission lines for each of the analysed spectra. Several different tools have been developed to model the underlying stellar population, effectively decoupling it from the emission lines (e.g., Cappellari & Emsellem 2004; Cid Fernandes et al. 2005; Ocvirk et al. 2006; Sarzi et al. 2006; Sánchez et al. 2007a; Koleva et al. 2009; MacArthur et al. 2009; Walcher et al. 2011; Sánchez et al. 2011). Most of these tools are based on the same principles, i.e., they assume that the stellar emission is the result of the combination of different (or a single) simple stellar populations (SSP), and/or the result of a particular star-formation history, whose emission is redshifted due to a certain systemic velocity, broadened and smoothed due a certain velocity dispersion and attenuated due to a certain dust content.

For the particular case of the H ii regions, the main purpose of this analysis is to provide a reliable subtraction of the underlying stellar population. For doing so, we performed a simple but robust modeling of the continuum emission. We use the routines described in Sánchez et al. (2011) and Rosales-Ortega et al. (2010), which provided us with certain parameters describing the physical components of the stellar populations (e.g., luminosity-weighted ages, metallicities and dust attenuation, together with the systemic velocity and velocity dispersion) and a set of parameters describing each of the analysed emission lines (intensity, velocity and velocity dispersion). A simple SSP template grid was adopted, consisting of three ages (0.09, 1.00 and 17.78 Gyr) and two metallicities (0.0004 and 0.03). The models were extracted from the SSP template library provided by the MILES project (Vazdekis et al. 2010). The two considered metallicities are the most metal poor and most metal rich with the largest coverage range in ages, within the considered library. The oldest stellar population was selected to reproduce the reddest possible underlying stellar population, mostly due to larger metallicities than the one considered in our simplified model, although it is clearly older than the accepted cosmological time of the Universe. Our youngest stellar population is the 2nd youngest in the MILES library with both extreme metallicities. No appreciable difference was found between using this one or the youngest one (~80 Myr). Finally, we selected an average stellar population, of ~1 Gyr, required to reproduce the intermediate-to-blue stellar populations, and to produce more reliable corrections of the underlying stellar absorptions (Paper I). This library is clearly insufficient to describe in detail the nature of all the stellar populations and star formation histories. However, it covers the parameter space of possible stellar populations well enough to describe them at to 1st order, providing a clean residual information of the ionized gas. Evenmore, with a combination of the considered templates it is possible to reconstruct any of the SSP of the full MILES library within an accuracy similar to our photometric uncertainty (~10%, Paper I). Therefore, to include any other template is redundant for the main purpose of this analysis.

Figure 5 illustrates the results of the fitting procedure for three H ii regions (the brightest, the average and the faintest one, in terms of Hα luminosity) extracted from two typical galaxies (NGC 628 and UGC 1081). The figure shows for each H ii region the extracted spectrum (black line), together with the best multi-SSP model for the stellar population (red line), and the pure nebular emission spectrum (blue line).

6.1.1. Deriving the main properties of the emission lines

To derive the properties of the stronger emission lines detected in the stellar-population subtracted spectra, each line was fitted with a single Gaussian, coupled with the systemic velocity and velocity dispersion of different emission lines when needed (e.g., for doublets and triplets). This procedure provide us with the intensity, systemic velocity and velocity dispersion for each emission line. Note that by subtracting a stellar continuum model derived with a set of SSP templates, we are already taking into account (and correcting for, to a first order) the contribution of underlying absorption, which is particularly important in the Hα and Hβ lines.

As discussed in Paper I, there are different issues that may affect the final quality of the individual spectra in the datacubes (uncleaned cosmic rays, trace problems, low transmission fibers, spectra near to the edge of the FoV and vignetting). These quality issues, that affect a reduced number of spaxels, propagate along the segregation, extraction and “stellar continuum” cleaning processes, and therefore they may affect the final quality of the “pure emission” spectra of the H ii regions. In order to minimize the impact of these issues on the final sample of H ii spectra, we have performed an automatic quality check. Only those “pure emission” spectra fulfilling the following criteria are flagged as good quality data:

• 1.

  The derived intensity for Hα is above zero or below three times that of the brightest H ii region based on the narrow-band image intensity. The contrary may happen in case of problems with the fitting procedure, or problems with one or a few spectra of those that were co-added to derive the integrated spectrum (like a cosmic rays).

• 2.

  The fraction of spectral pixels with negative values in the original spectra, i.e. prior to the subtraction of the underlying stellar continuum, is lower than 10%. The contrary may happen in the outer regions of the galaxies, if there is any problem with the sky subtraction.

• 3.

  The fraction of spectral pixels in the “pure emission” spectra of the H ii region with a value below the median flux 1σ within the wavelength range between 3900 and 6500 Å, is at maximum three times lower than the median of this fraction for all the H ii regions in the same galaxy. This criterion is used to remove spectra strongly affected by the vignetting effect, which affects only ~ 30% of the data (Paper I).

• 4.

  The derived intensity for Hα is more than five times above the background noise (σ_back), estimated as σ_back = σ_{6300 − 6500} FWHM_line, where (i) σ_{6300 − 6500} is the standard deviation of the continuum intensity once subtracted the underlying stellar component for the wavelength range between 6300 and 6500 Å (i.e., a continuum adjacent to Hα); and (ii) FWHM_line is the full width at half maximum derived for the emission line, as described before.

The remaining regions are flagged out, masked, and the corresponding spectra are set to zero. The criteria were based on iterative experiments on the data, and visual inspections of hundreds of spectra, before and after subtracting the underlying continuum. Although the fraction of flagged-out/rejected spectra change from object to object, on average this final cleaning affects ~15% of the H ii regions, as can be seen in Table 2. Finally, only those H ii regions with measured Hβ emission line detected at >3σ significance were considered for further analysis (e.g. Marino et al. 2012), although they were not masked out and their spectra were not set to zero. This criteria was included to consider only those regions with good line diagnostic ratios and well defined Balmer ratio, both required in further analysis. It further reduces the number of selected H ii regions by ~5% on average, although is some cases the fraction is much larger (see Table 2). Due to thesize of our original sample and the pseudo-random selection of H ii-regions that are affected by these issues, we consider that this last cleaning process will have little effect in the overall statistical significance of our survey.

Once derived the emission line intensities, we estimate their corresponding equivalent width for each H ii region and line. For doing so, instead of using the classical procedure (i.e., measuring the flux within a narrow-band wavelength range centred in the line and in two adjacent ones corresponding to the continuum), we make use of the results from our fitting analysis. We derive the equivalent width by dividing the emission line integrated intensities by the underlysing continuum flux density. We estimated the continuum as the median intensity in a band-width of 100 Å, centred in the line, using the gas-subtracted spectra provided by our fitting procedure. With this method we can estimate the equivalent width of nearby lines, which contaminate the measurements of this parameter using the classical method.

Table 5 illustrates the result of this analysis. It shows, for a sub-set of H ii regions in a particular galaxy (UGC 9837) the Hβ line intensity and relative flux of some of the most prominent emission lines. Table 6 reports the equivalent widths for the corresponding emission lines and regions. The same parameters are derived for all the H ii regions in the different galaxies, as indicated in Appendix A.

6.1.2. Structural parameters of the galaxies

To understand the fundamental properties of the H ii regions and their relation with the overall evolution of galaxies, it is required to characterize the main structural parameters of these galaxies. We have collected the available information in public collections like NED (http://ned.ipac.caltech.edu/) and Hyperleda (http://leda.univ-lyon1.fr/). Table 1 already contains the most relevant parameters for the current study, including the morphological type, the redshift, the integrated B-band magnitude and the B − V colour. All the galaxies in the sample are spirals by selection, but different kinds of spiral galaxies are covered, including galaxies with and without bars, galaxies showing rings, etc. The observed B-band magnitude is ~14 mag, in average. However, the galaxies selected from the PINGS sample are in general brighter (B ~ 11 mag). As expected, galaxies have blue colours (B − V ~ 0.8 mag), although with a considerable dispersion. The covered absolute magnitudes range from M_V ~ −23 mag to ~−18 mag. In summary, the sample covers typical members of the so-called blue cloud, from typical standard spiral galaxies to almost dwarfs.

The listed information was complemented with additional parameters, like the maximum rotation velocity, the inclination, the position angle and the effective radius (defined as the radius at which one half of the total light of the system is emitted), derived from the analysis of the data presented here. The first three parameters were derived from the modeling of the gas velocity pattern extracted from the the Hα emission line fitting for the H ii regions, described in previous sections. The wide spatial coverage and high S/N of the Hα emission line in the integrated spectra for each region guarantee a good determination of the velocity pattern. The rotation curve was fitted using a simple arctan model (Staveley-Smith et al. 1990), $\mathit{v}\mathrm{\left(}\mathit{r}\mathrm{\right)}\mathrm{=}{\mathit{v}}_{\mathrm{sys}}\mathrm{+}\frac{\mathrm{2} {\mathit{v}}_{\mathrm{rot}}}{\mathit{\pi }}\arctan \mathrm{(}\mathit{s}\mathrm{·}\mathit{r}\mathrm{-}\mathit{c}\mathrm{)}$(2)where v_sys is the systemic velocity of the gas and v_rot is the asymptotic rotation speed of the disc, s characterizes the slope of v(r) in the inner part of the galaxy, r is the distance to the rotational center, and c is the parameter that characterizes any offset in the rotation axis of the galaxy. A model of the velocity map was created by re-projecting the best fitting arctan function, taking into account the position angle and inclination of the galaxy. We fitted to the data following a similar procedure as the one described in Sánchez et al. (2012), using a χ²-minimization algorithm included in FIT3D (Sánchez et al. 2006).

As an initial guess for the fitting, the position angle and inclination were derived from the isophotal analysis described later in this section, and the maximum rotational velocity was set to half of the maximum difference in velocity from receding to approaching velocities. For all the galaxies the rotational center is fixed to the location of the peak intensity in the V-band image created from the datacubes. The parameter c is fixed to zero (i.e., it is assumed that there is no offset between the rotation and photometric centers). The v_sys is fixed to the median value of the gas velocities for those H ii regions located in the inner regions (r < 0.5r_max, where r_max is the maximum distance to the center for all the H ii regions).

Finally v_rot and s are fitted, together with the position angle and inclination of the galaxies, v_rot is fitted within a range between ~0.3 and 6 times the maximum velocity difference among the H ii regions, and s is fitted between 0.1 and 10 arcsec^-1. Figure 6 illustrates a typical result of this analysis, showing, for a particular galaxy (UGC 9837) the Hα velocity map, the best fit model, and the residual. Despite the low inclination of the galaxies, in most of the cases it is possible to obtain a good model. In most of the cases the residual velocities ranges between ± 15 km s^-1, ~15% of the maximum rotational velocity. This is expected due to random motions in the galaxies, compare e.g. Andersen et al. (2008); Neumayer et al. (2011).

The effective radius was derived based on an analysis of the azimuthal surface brightness (SB) profile, derived based on elliptical isophotal fitting of the ancillary g-band images collected for the galaxies (extracted from the SDSS imaging survey, York et al. 2000, and Paper I). When these ancillary images were not available we used the B-band (Paper I). In order to homogenize the dataset, both sets of SBs were transformed to the B-band using the average g − B colour for each galaxy. When both band images where available a comparison between the directly derived and the estimated surface brightness profile was performed, finding no significant differences in the average gradient. We note here that the observed B and g-bands sample a range of wavelengths between ~4150−4750 Å and ~4450−5210 Å, respectively, due to the redshift range of the sample. Therefore, there is an inherent imprecision in the intrinsic wavelength range in this analysis.

The surface brightness profile was then fitted using a pure exponential profile, following the classical formula, $\mathit{I}\mathrm{=}{\mathit{I}}_{\mathrm{0}}\exp \left[\mathrm{-}\mathrm{(}\mathit{r}\mathit{/}{\mathit{r}}_{\mathrm{d}}\mathrm{)}\right]$(3)where I₀ is the central intensity, and r_d is the disk scale-length (Freeman 1970), using a simple polynomial regression fitting. Prior to this analysis, a visual inspection is performed to remove the inner-most values of the SB profile, strongly affected by seeing effect, and/or not following a linear relation due to the presence of other components like the bulge and/or bars.

The scale-length is used to derive the effective radius, defined as the radius at which the integrated flux is half of the total one, by integrating the previous formula, and deriving the relation: ${\mathit{r}}_{\mathrm{e}}\mathrm{=}\mathrm{1.67835}{\mathit{r}}_{\mathrm{d}}\mathit{.}$(4)The results of these analyses are included in Table 1. In average, the derived inclination agrees with the visual selection of the galaxies as face-on spirals. The average inclination is ~33°, and only two galaxies have an inclination larger than 60° (NGC 7570 and UGC 5100). This confirms our visual classification as face-on galaxies. The average maximum rotational velocity is ~100 km s^-1, with a wide range of values, between ~ 50 km s^-1 and ~300 km s^-1 (values which are typical for spiral galaxies, e.g., Persic et al. 1996). Note that the effective radius ranges between ~1.5 and ~5.5 kpc.

7. Analysis and results

In this section we analyse both the mean statistical properties of the H ii regions and explore the possible regular patterns in their radial variations.

7.1. Statistical properties of the H ii regions

Despite the many different spectroscopic studies in extragalactic H ii regions, we still do not have the understanding of which are the statistical spectroscopic properties of these common star-forming regions. This is a fundamental problem that it is mostly due to the lack of big statistical samples, and the reduced number of coherent compilations. The lack of a well defined set of normal values for the most frequent parameters, like the diagnostic line ratios (e.g., [O iii]/Hβ and/or [N ii]/Hα), ionization strength, dust attenuation and/or electron density is a clear limitation to understand if a particular set of H ii regions is different from the average, and if different at which significance level. To address this question a statistically significant, large sample of H ii regions is required, with well derived spectroscopic parameters, over a large sample of star-forming galaxies of different types. An additional requirement is good spatial coverage, not biased towards the outer (bright) H ii regions, which is a common bias in this kind of studies. Despite the large number of H ii regions catalogued in this work, the current sample is still incomplete to address this fundamental question. We will require a sample as the one that will be provided by a survey like CALIFA (Sánchez et al. 2012), without selection effects by galaxy types. However, the current catalogue of H ii regions is good enough to derive the statistical properties of these regions for a sub-set of galaxies: quiescent/non highly disturbed, field, average luminosity spiral galaxies.

Among the several different spectroscopic parameters describing H ii regions, we have analysed a set of them based on the strongest detected emission lines: (i) EW_Hα, the equivalent width of the Hα emission line. This parameter is directly related to the fraction of very young stars (~10 Myr), and can be used to estimate the aging process of the ionizing population; (ii) A_V, the dust attenuation derived from the Hα/Hβ Balmer decrement. To derive it the extinction law by Cardelli et al. (1989) was assumed, with R_V = 3.1, and the theoretical value for the unobscured line ratio for case B recombination of Hα/Hβ = 2.86, for T_e = 10 000 K and n_e = 100 cm^-3 (Osterbrock 1989); (iii) two typical diagnostic line ratios, [O iii] λ5007/Hβ and [N ii] λ6583/Hα, that define the nature of the ionization source; (iv) the ionization parameter, estimated as log ₁₀U = −3.02 − 0.80log ₁₀( [O ii] / [O iii] ), a measurement of the strength of the ionization radiation (Díaz et al. 2000); (v) the oxygen abundance, 12 + log (O/H), derived using the O3N2 indicator defined by Pettini & Pagel (2004), that estimates the gas enrichment; (vi) r_HII, the Strömgren radius of the H ii regions (Osterbrock 1989), i.e., a hint of the size of the H ii regions based on pressure equilibrium considerations, and (vii) n_e, the electron density derived from the [S ii] doublet line ratio, i.e., a proxy to the density of the ionized gas (e.g., Osterbrock 1989).

Table 7 shows the mean values and standard deviations of the considered parameters for the H ii regions of each galaxy, together with the mean value for all the galaxies. Based on this analysis, it is possible to describe two kind of behaviors: on one hand, some of the parameters have a large variation object by object (e.g., EW[H_α], r_HII), reflecting the different physical conditions of H ii regions in individual galaxies. On the other hand, there are parameters with a well defined mean value and little variation object-by-object, and even region by region (e.g., the dust attenuation, the ionization parameter and the oxygen abundance), i.e., despite of the many differences between the considered galaxies (luminosity, morphology, colour), and the physical conditions in each H ii region, it is possible to define a statistically meaningful standard mean value for certain spectroscopic parameters.

Due to the particular sample of galaxies studied here, and the large number of H ii regions explored, we consider that these values define the average physical conditions of H ii regions for spiral galaxies in the Local Universe. They can either be used to determine whether a particular (spiral) galaxy deviates from the average population (i.e., it is metal rich or poor and/or it is more or less dusty), or as the anchor point of chemical evolution of ionized gas along cosmological times. The H ii regions discussed here have a range of Hα luminosities between 10³⁷ and 10⁴¹ erg s^-1, with a well defined bell-like shape centred at 10^39.5±0.6 erg s^-1. Therefore, most of our regions correspond to intermediate/luminous ones, as indicated in Sect. 2. These H ii regions are expected to have a typical size of few to several hundreds of parsecs, at the edge of our spatial resolution or below.

For some parameters the mean value is well defined (i.e., it shows a dispersion around the mean value of the order of the estimated error). Thus it is a good characterization of the considered property of the ionized gas. However, it is important to remember that the variations within the considered distributions reflect changes in the physical conditions of the ionized nebulae, either within each galaxy, or galaxy by galaxy. To illustrate this effect we present in Fig. 7 three panels showing the classical [O iii]/Hβ vs. [N ii]/Hα (Baldwin et al. 1981) diagnostic diagram, hereafter BTP-diagram, for (i) the average values shown in Table 7; (ii) all the emission line regions detected using the procedure described in previous sections; and (iii) those emission line regions located at the center of the galaxies (r < 0.5r_e). In each panel, we include the Kauffmann et al. (2003) and Kewley et al. (2001) demarcation curves. These curves are usually invoked to distinguish between star-forming regions, and other sources of ionization, like AGN/Shocks/post-AGBs. The location within both curves is normally assigned to a mix origin for the ionization and/or contamination by different sources of ionization. Since our sample is dominated by H ii regions, most of the regions lie in the demarcation region corresponding to star-forming areas, although a few of them are located in the so-called intermediate region. There are clear differences galaxy by galaxy, reflecting changes in the average oxygen abundance and ionization strength. On the other hand, it is clear that for the regions located in the center of the galaxies the fraction of emission line regions lying in the intermediate region is larger. This is expected since these are the regions more likely to be contaminated by other ionization sources than star-formation: e.g., central low-intensity AGNs, Shocks, post-AGB stars. It is beyond the scope of this article to determine the real nature of this ionization in the central regions. This will require a more detail analysis and the use of other more suitable diagnostic diagrams like [NII]/Hα vs. [SII]/Hα and/or [NII]/Hα vs. [SII]6717, 6731/Hα, to distinguish between HII regions, SNR and PNe. We just want to emphasize that if there is any possible contamination, this will more likely affect only the central regions. This clearly indicates a change in the ionization conditions galaxy by galaxy and across the optical extension of each galaxy. One may wonder whether the described differences are induced by the errors in the represented parameters. However, most probably this is not the case. The typical error is represented as an error-bar in the central panel of the figure, showing that it is smaller than the dispersion of values found (in particular for the range of [N ii]/Hα values sampled).

Another possible explanation is that the large range of redshifts/distance has an effect in variation of some properties due to our coarse resolution. This could be the case for the differences found for the Stömgren radius or the luminosity of Hα for some galaxies, like NGC 628, at a distance of ~9 Mpc and Mrk 1477, at a distance of ~90 Mpc. However, this cannot be the only explanation, since there are other galaxies with large difference in both parameters at lower relative cosmological distance, like UGC 6410 (at ~80 Mpc), and NGC 4109 (at ~100 Mpc).

In summary, although the mean values listed in Table 7 are somehow representative of the average ionization conditions in each galaxy, they do not show the complete picture, since there are clear/expected variations of the ionizing condition across the optical extension of the galaxies.

7.1.1. Strong-line calibrators of the oxygen abundance

One of the fundamental parameters that can be derived from the spectroscopic analysis of H ii regions is the oxygen abundance. Oxygen is one of the easiest elements to measure in H ii regions, due to the strength of its emission lines in the optical wavelength range. This is fortunate, since O is an α-process element made directly in short-lived massive stars (dominant in H ii regions). It is a good proxy of all heavy elements, comprising ~50% of all the metals by mass in all the Universe. Therefore, it is a fundamental parameter to understand the evolution of the stellar populations galaxy-by-galaxy and at different locations within the same galaxy.

Accurate abundance measurements for the ionized gas in galaxies require the determination of the electron temperature (T_e) in this gas which is usually obtained from the ratio of auroral to nebular line intensities, such as [O iii] λ4363/[O iii] λλ4959, 5007 (Osterbrock 1989). It is well known that this procedure is difficult to carry out for metal-rich galaxies since, as the metallicity increases, the electron temperature decreases (as the cooling is via metal lines) and the auroral lines eventually become too faint to measure. Therefore, calibrators based on strong emission lines are used. Lopez-Sanchez et al. (2012) has recently presented a revision on the different methods, showing their main problems, and illustrating in which range/conditions then can be applied. In particular they describe the most widely used methods in large galaxy surveys, that rely on the measurement of different strong emission lines (and line ratios) in the H ii region spectrum and empirical calibrations with regions of well-known oxygen abundance.

One of the first strong emission line methods was proposed by Pagel et al. (1979). It relies upon the ratio of [O ii] λ3727 and [O iii] λλ4959, 5007 with respect to Hβ, the so-called R₂₃ ratio: ${\mathit{R}}_{\mathrm{23}}\mathrm{=}\frac{\mathit{I}\mathrm{\left(}\mathrm{\right[}\mathrm{O}\hspace{0.17em}{ii}\mathrm{]} \mathit{\lambda }{\mathrm{3727}}^{\mathrm{)}}\mathrm{+}\mathit{I}\left(\mathrm{\left[}\mathrm{O}\hspace{0.17em}{iii}\mathrm{\right]} \mathit{\lambda \lambda }\mathrm{4959}\mathit{,}\mathrm{5007}\right)}{\mathit{I}\mathrm{\left(}\mathrm{H}\mathit{\beta }\mathrm{\right)}}$(5)however, this index is double valued, with two different calibrations for low metallicity (12 + log (O/H) < 8.1) and high metallicity (12 + log (O/H) > 8.4) H ii regions. There is an ill-defined regime where regions with the same R₂₃ (>0.7) value have oxygen abundances that differ by almost and order of magnitude (e.g., see Fig. A.1 in López-Sánchez & Esteban 2010). Ratios such as O3N2 (Alloin et al. 1979; Pettini & Pagel 2004), N2O2 (van Zee et al. 1998; Dopita et al. 2000), N2 (van Zee et al. 1998; Pettini & Pagel 2004; Denicoló et al. 2002), and many others, were introduced in an attempt to solve this ambiguity in the derived abundances: $\begin{array}{ccc}\mathrm{O}\mathrm{3}\mathrm{N}\mathrm{2}& \mathrm{=}& \frac{\mathit{I}\mathrm{\left(}\mathrm{\right[}\mathrm{O}\hspace{0.17em}{iii}\mathrm{\left]} \mathit{\lambda }\mathrm{5007}\mathrm{\right)}\mathit{/}\mathit{I}\mathrm{\left(}\mathrm{H}\mathit{\beta }\mathrm{\right)}}{\mathit{I}\mathrm{\left(}\mathrm{\right[}\mathrm{N}\hspace{0.17em}{ii}\mathrm{\left]} \mathit{\lambda }\mathrm{6584}\mathrm{\right)}\mathit{/}\mathit{I}\mathrm{\left(}\mathrm{H}\mathit{\alpha }\mathrm{\right)}}\\ \mathrm{N}\mathrm{2}\mathrm{O}\mathrm{2}& \mathrm{=}& \frac{\mathit{I}\mathrm{\left(}\mathrm{\right[}\mathrm{N}\hspace{0.17em}{ii}\mathrm{\left]} \mathit{\lambda }\mathrm{6584}\mathrm{\right)}}{\mathit{I}\mathrm{\left(}\mathrm{\right[}\mathrm{O}\hspace{0.17em}{ii}\mathrm{\left]} \mathit{\lambda }\mathrm{3727}\mathrm{\right)}}\\ \mathrm{N}\mathrm{2}& \mathrm{=}& \frac{\mathit{I}\mathrm{\left(}\mathrm{\right[}\mathrm{N}\hspace{0.17em}{ii}\mathrm{\left]} \mathit{\lambda }\mathrm{6584}\mathrm{\right)}}{\mathit{I}\mathrm{\left(}\mathrm{H}\mathit{\alpha }\mathrm{\right)}}\end{array}$some of these indicators are strongly affected by the dust attenuation, like N2O2 and R₂₃, and should be determined after correcting it. Others are less sensitive to dust attenuation. Furthermore, empirical calibrations based on direct estimates of the electron temperature of the ionized gas systematically provide oxygen abundances which are systematically 0.2−0.4 dex lower than those derived using calibrations based on photoionization models (e.g. Lopez-Sanchez et al. 2012).

To derive the main statistical properties of the oxygen abundance, we adopted the O3N2 ratio. This ratio is less dependent on the adopted correction for the dust attenuation, and uses emission lines covered by our wavelength range for all the galaxies in the current sample. Like the N2O2 indicator, it relies on the use of the intensity of [N ii]. In the high metallicity regime − 12 + log  (O/H) ≳ 8.3 – nitrogen is produced by both massive and intermediate-mass stars (e.g. Pilyugin et al. 2003) and hence nitrogen is essentially a secondary element in this metallicity regime. The [N ii]/Hα ratio will therefore become stronger with on-going star formation and evolution of galaxies, until very high metallicities are reached, i.e. 12 + log (O/H) > 9.0, where [N ii] starts to become weaker due to the very low electron temperature caused from strong cooling by metal ions. However, N2 is an indirect estimator that may depend on the ionization strength.

We should remember here that for ~50% of our targets [O ii] λ3727 was not covered by the observed wavelength range, and therefore, the fraction of H ii regions with R₂₃ and N2O2 line ratios is just half of the total number of regions, since both rely on this emission line. The direct estimate based on the electron temperature is of less use. The fraction of H ii regions with reliable measurements of the the auroral [O iii] λ4363 is just ~10%. This line is either too faint or is blended and/or strongly affected by the Hg I 4348 atmospheric light pollution emission line, and even Hγ, in most of the cases. Due to that we consider O3N2 the best estimator for the purpose of the current study. In general it is considered that this estimator is valid for the range between −1 < log O3N2 < 1.9 (e.g. Yin et al. 2007). However it becomes less reliable for metallicities lower than 12 + log (O/H) < 8.3 (e.g. Yin et al. 2007; Lopez-Sanchez et al. 2012).

It is beyond the scope of the current study to make a detailed comparison of the oxygen abundances derived using the different proposed methods, in a similar way as it was presented by Kewley & Ellison (2008); Lopez-Sanchez et al. (2012). However, it is a good sanity check to compare between some of the most frequently used ones. This comparison will help us to understand (1) if the H ii regions described here are in the valid range for the adopted metallicity indicator; (2) which are the real differences in using one indicator or another; and (3) how accurate is the adopted correction for the dust attenuation, since we can compare indicators with different degree of dependency on the adopted correction.

Figure 8, shows the comparison between O3N2, N2O2 and N2 indicators, all of them using the [N ii] λ6584 line, with respect to the solely oxygen-based R₂₃ ratio. Only the H ii regions with detected [O ii] λ3727 emission line have been included in this plot (1142 individual regions). In each panel it is shown the image and contours of the density distribution of both parameters. The red-dashed lines show the best fits found using a 2nd-order polynomial function between the two considered parameters. The light-blue solid-circles indicate the median values of both parameters, with their corresponding standard deviations represented as error bars, for consecutive equally spaced bins of 0.10 dex of the parameters shown. In all cases the distributions are similar to the ones previously described in the literature between the considered estimators and/or their derived abundance (e.g. van Zee et al. 1998; Yin et al. 2007; Rosales-Ortega et al. 2011). However, in none of the precedent studies the distributions are shown with such a large statistical sample.

In the three cases there is a clear correlation between the median/high dense distribution of both parameters. The correlation is stronger for N2O2 vs. R₂₃ and for N2 vs. O3N2 than for the remaining one. The first of this relations is well described by a 2rd order polynomial function: $\begin{array}{ccc}\log \mathrm{N}\mathrm{2}\mathrm{O}\mathrm{2}\mathrm{=}\mathrm{0.15}\mathrm{-}\mathrm{0.97}\log {\mathit{R}}_{\mathrm{23}}\mathrm{-}\mathrm{0.39}{\left[\log {\mathit{R}}_{\mathrm{23}}\right]}^{\mathrm{2}}\mathit{.}& & \end{array}$(9)The dispersions of each parameter around the best fit curve are σ_N2O2 ~ 0.11 and σ_R23 ~ 0.17, respectively. The dispersion in the y-axis is very similar to the typical (mean) errors of the corresponding line ratio, e_N2O2 ~ 0.07. This indicate that most of the dispersion is due to the errors in the derived line ratios, and not in a physical dependence with a third parameter.

The second relation is also well described by a 2nd order polynomical function: $\begin{array}{ccc}\log \mathrm{N}\mathrm{2}\mathrm{=}\mathrm{0.46}\mathrm{-}\mathrm{0.12}\log \mathrm{O}\mathrm{3}\mathrm{N}\mathrm{2}\mathrm{-}\mathrm{0.19}\mathrm{[}\log \mathrm{O}\mathrm{3}\mathrm{N}\mathrm{2}{\mathrm{]}}^{\mathrm{2}}\mathit{.}& & \end{array}$(10)For this distribution, the dispersions of each parameter around the best fit curve are σ_N2 ~ 0.10 and σ_O3N2 ~ 0.32, respectively. Once more, the dispersion in the y-axis is very similar to the typical (mean) errors of the corresponding line ratio, e_N2 ~ 0.17. Again, this indicates that most of the dispersion is due to the errors in the measured line ratios, rather than a unknown relation with a third parameter.

Finally, the correlation is less tight for the the O3N2 and R₂₃ parameters, with a broader dispersion and a tail for R₂₃ > 0.7. In this case a 2nd order polynomial function describe will enough $\begin{array}{ccc}\log \mathrm{O}\mathrm{3}\mathrm{N}\mathrm{2}\mathrm{=}\mathrm{0.18}\mathrm{-}\mathrm{3.76}\log {\mathit{R}}_{\mathrm{23}}\mathrm{+}\mathrm{5.88}{\left[\log {\mathit{R}}_{\mathrm{23}}\right]}^{\mathrm{2}}& & \end{array}$(11)however, the dispersion around the best curve is larger for the O3N2 parameter, σ_O3N2 ~ 0.62, but similar for the R₂₃ one, σ_R23 ~ 0.17. This dispersion cannot be explained only by the larger typical (mean) error of the represented line ratios (e_O3N2 ~ 0.2 and e_R23 ~ 0.3, respectively), and most probably indicates a real difference and/or a dependence with a third parameter (like the ionization strength).

Tremonti et al. (2004) proposed a non linear fit of the oxygen abundance for the R₂₃ indicator that is nowadays widely used. Assuming that this calibration derives a similar oxygen abundance than the one proposed by Pettini & Pagel (2004) is is possible to derive the following relation between both parameters: $\begin{array}{ccc}\mathit{y}\mathrm{=}\mathrm{-}\mathrm{1.406}\mathrm{+}\mathrm{0.987}\mathit{x}\mathrm{+}\mathrm{0.825}{\mathit{x}}^{\mathrm{2}}\mathrm{+}\mathrm{1.396}{\mathit{x}}^{\mathrm{3}}& & \end{array}$(12)where y = log O3N2 and x = log R₂₃. This relation has a similar shape than the one described before for the range of values corresponding to 0.5 < R₂₃ < 1, however it is offset by ~0.15 dex in R₂₃ and ~−0.5 dex in O3N2. The oxygen abundance derived using both indicators agrees if it is assumed that the Tremonti et al. (2004) relation overestimate the abundance by ~30%. The difference is due to the photoionization models adopted by Tremonti et al. (2004), as discussed in Lopez-Sanchez et al. (2012). Correcting for that difference, the derived relation between O3N2 and R₂₃ agrees with the one found with our dataset (blue dashed-dotted line in Fig. 8). Therefore, the oxygen abundance derived using the Pettini & Pagel (2004) and Tremonti et al. (2004) calibrators do not provide consistent results, as already pointed out in previous studies (e.g. Lopez-Sanchez et al. 2012). However, the discrepancy is in the zero-point of the adopted calibration, rather than in the actual values for the indicators. The dispersion is tighter for R₂₃ < 0.7, i.e., the parameter range for which the oxygen abundance is not double valued. For values of R₂₃ larger than 0.7 we found that the discrepancy with the derived relation shows a trend with the ionization parameter, being larger at lower values of U.

Kewley & Ellison (2008) performed a comparison between the oxygen abundance derived using different strong line indicators, based on analysis of large sample of SDSS spectra of star-forming galaxies. They derived a set of transformation for the different analysed indicators, including R₂₃ and O3N2. These transformation are consistent with the ones presented here, for the range of abundance for which their are valid (see Table 3 in Kewley & Ellison 2008).

In summary, it seems that (i) N2O2 and R₂₃ indicators provide statistically similar empirical information on the oxygen abundance, i.e. measuring one or the other in the considered range of parameters will yield a similar estimation of the oxygen abundance, when a consistent calibration is used. On the other hand, O3N2 provides different information than the other two indicators, when dealing with individual regions, even when consistent calibrators are used; (ii) the range of values covered by the O3N2 indicator for the H ii regions of our sample is within the values where this indicator is reliable (as indicated before); and (iii) the lack of outliers in the N2O2 vs. R₂₃ distribution indicates that we have adopted a good correction for the dust attenuation.

7.1.2. Mass–metallicity relation

Stellar mass and metallicity are two of the most fundamental physical properties of galaxies. Both are metrics of the galaxy evolution process, the former reflecting the amount of gas locked up into stars, and the later reflecting the gas reprocessed by stars and any exchange of gas between the galaxy and its environment. Understanding how these quantities evolve with time and in relation to one another is central to understanding the physical processes that govern the efficiency and timing of star formation in galaxies.

Tremonti et al. (2004) found a tight correlation between stellar mass and gas-phase metallicity (MZR) spanning over 3 orders of magnitude in stellar mass and a factor of 10 in metallicity. This correlation has been interpreted as a direct evidence of the anticorrelation between metal loss with baryonic mass, and the ubiquity of galactic winds and their efficiency in removing metals from low-mass galaxies. Additional interpretations consider that the observed mass − metallicity relation is due to a more general relation between stellar, gas-phase metallicity and star formation rate (Lara-López et al. 2010; Mannucci et al. 2010).

Despite the strength of the considered correlation and how it matches with our current understanding on galaxy evolution, there are a few caveats on how the MZR is derived: (i) the oxygen abundance used by Tremonti et al. (2004) was derived assuming a Bayesian approach based on simultaneous fits to all the most prominent lines assuming the results provided by photoionization models. However, as explained before these methods systematically overestimate by 0.2−0.4 dex the oxygen abundances derived using the Te-based calibrations (Lopez-Sanchez et al. 2012); (ii) the calibrator was derived for H ii regions, but applied to integrated apertures in galaxies. Although it is widely used, it is is not firmly tested if this procedure is valid; (iii) the apertures of the considered spectra cover a different optical extent for each galaxy, due to the fixed aperture of the SDSS fiber spectra (3″).

So far, there has been no major effort to test the reported relation using spatially resolved spectroscopic information, like the one provided by the current analysis. The number/statistics of our analysis, galaxy-by-galaxy, is reduced, and we can only test if our results are consistent with the derived relation. However, it will be a first step towards a stronger statistical result, that could be provided with the large sample currently under observation by the CALIFA survey (Sánchez et al. 2011).

We derive the luminosity mass of the considered galaxies using the integrated B-band magnitudes, B − V colours and the average mass − luminosity ratio (M/L) described in Bell & de Jong (2001). This derivation is less accurate than the one described in Tremonti et al. (2004). However, it should be enough for the purpose of this analysis, considering that the derived M/L has an expected scatter of ~0.15 dex (Bell & de Jong 2001). As an additional cross-check we also derived the dynamical mass. We use the effective radius (r_e), the maximum rotational velocity (v_rot) listed in Table 1, and the classical formula³: ${\mathit{M}}_{\mathrm{dyn}}\mathrm{=}\frac{{\mathit{r}}_{\mathrm{e}}{{\mathit{v}}_{\mathrm{rot}}}^{\mathrm{2}}}{\mathit{G}}\mathrm{·}$(13) We note here that this mass is indeed the dynamical mass at a particular radius (roughly twice the effective one), and therefore, the derived values should be taken with caution for any further interpretation. As expected the dynamical mass is slightly larger than the stellar mass, since the first considers the total mass of the galaxy. However, both masses agree within ±0.2 dex for ~90% of the objects. Similar results have been recently reported for the same sort of galaxies, using more sophisticated derivations of the stellar masses (Gerssen et al. 2012). This consistent result strengthens the validity of our derived masses.

Figure 9 shows the distribution of the oxygen abundance at the center of the galaxies vs. the stellar masses described before. The oxygen abundance has been derived extrapolating the radial gradients found for each galaxy (see Sect. 7.2), to the center. For comparison, we estimate the central abundance using the average of the metallicity values within 0.2r_e, using the O3N2 calibrator, for those galaxies with H ii regions at this distance (20 out of 38). Both values agree within the errors. We prefer to use the extrapolation of the derived gradient, since they have lower dispersion, and they can be derived for more galaxies (i.e., all but MRK 1477). We include in Fig. 9 the relation between both quantities derived by Tremonti et al. (2004), corrected for the mismatch between their calibrator and the currently used here (i.e., 0.15 dex). The derived central abundance and stellar masses for the galaxies analysed here are consistent with this relation, showing a similar distribution: about 75% of the galaxies are located at less than ~1σ of the scaled relation.

7.2. Radial gradients

It is well known that different spectroscopic properties of H ii regions show strong variations across the area of disk galaxies. In particular, some of these parameters (e.g., oxygen abundance, EW[Hα], etc.), show a strong radial gradient, that in average indicates that more evolved, metal rich, stellar populations are located in the center of galaxies, and less evolved, metal poor ones are in the outer ones (e.g. Zaritsky et al. 1994; Rosales-Ortega et al. 2011, and references therein). This observational result is consistent with the our current understanding of the formation and evolution of spiral galaxies (e.g. Tsujimoto et al. 2010, and references therein). Gas accretion brings gas into the inner region, where it first reaches the required density to ignite star formation. Thus the inner regions are populated by older stars, and they have suffered a faster gas reprocessing, and galaxies experience an inside-out mass growth (e.g. Matteucci & Francois 1989; Boissier & Prantzos 1999). Both the extinction-corrected colour gradients in nearby galaxies, Muñoz-Mateos et al. (2007), and weak dependence of the mass-size relation with redshift (Trujillo et al. 2004; Barden et al. 2005; Trujillo et al. 2006) support an inside-out scenario for the evolution of disks.

Pure inside-out growth is affected by internal and external events, like bars and/or galaxy interaction and mergers, which induce radial migration. In principle, radial migration affects the stellar populations more strongly, since they are dynamically more susceptible to the effects that produce migration (interactions, bars, etc.). The overall result is a change in the slope of the surface brightness profile and colours of these galaxies (e.g. Bakos et al. 2008). However, gas clumps, like H ii regions, may also be affected (e.g. Minchev et al. 2012). The net effect of these processes is a possible flattening of the radial gradient and/or a truncation at outer regions, where some of these properties (e.g. oxygen abundance) show values that are expected at more inner regions. This change in the slope of the radial gradient of oxygen abundance has been reported by several authors (e.g. Bresolin et al. 2009; Marino et al. 2012; Bresolin et al. 2012). If true, migration is an efficient mechanism to intermix the gas and stellar population properties of galaxies, and even to enrich the intergalactic medium (Sánchez-Blázquez et al. 2009, for a different explanation to the surface-brightness truncation).

Despite of the several different studies describing these observational events, there is a large degree of discrepancy between the actual derived parameters describing the gradients: (i) slope of the gradient; (ii) average value and dispersion of the zero-point and (iii) scale-length of the truncation. In general, this is mostly due to different observational biases and historical methods to perform the analysis: (i) most of the studies lack a proper statistical number of analysed H ii regions per galaxy; (ii) in many cases the samples cover mostly the outer regions (R > R_e), with a lack of H ii regions in the inner ones; (iii) there is no uniform method to analyse the gradients. In some cases the physical scales of the galaxies (i.e., the radii in kpc) are used, (e.g. Marino et al. 2012). In others the scale-length are normalized to the R₂₅ radii, i.e., the radii at which the surface brightness in the B-band reach the value of 25 mag/arcsec² (e.g. Rosales-Ortega et al. 2011). Finally, a much more reduced number of studies tries to normalize the scale-length based on the effective radii (described in Sect. 6.1.2). Diaz (1989), in one of the earliest compilations of H ii regions already showed that the effective radius is the best one to normalize the abundance gradients. This is somehow expected since it is directly related with the mass concentration and reflects how fast the gas is recycled in different galaxies. Despite its benefits, it is the least used one, which has produced an ill-defined set of definitions for these gradients. It is important to remember here that both the physical scale of the radial distance and/or the normalized one to an absolute parameter like the R₂₅ radius, although they are widely used, could not produce useful gradients to compare galaxy to galaxy, since in both cases the derived gradient is correlated with either the scale-length of the galaxy of its absolute intensity.

7.3. Analysis of gradients galaxy by galaxy

We used our catalogue of H ii regions to characterize the radial gradients of the physical properties of the H ii regions. For each galaxy we derive the correlation coefficient, and the slope and zero-point of a linear regression; for the radial distribution we derived each of the parameters discussed in the previous section. The radial distance is normalized to the effective radius of each galaxy, listed in Table 4. Only those galaxies with a good sampling of the radial distribution of H ii regions have been considered. To do so, we adopted two criteria: (i) the galaxy should comprises more than 30 individual H ii regions, and (ii) there should be equally distributed along the sampled region (~2.5 R_e).

Table 8 summarizes the result of this analysis. It includes, for each of the considered parameters, the actual number of galaxies considered (N_gal), the median of the correlation coefficients (r_cor), with its standard deviation (σ_r), the median zero-point (med_a), with its standard deviation (σ_a), and the mean error of each individual zero-point (err_a), together with the median slope (med_b), its standard deviation (σ_b), and the mean error of each individual derived slope (err_b). In addition to the physical parameters of the H ii regions discussed in the previous section we have included, for comparison purposes two properties of the underlying stellar population, that are well known to correlate with the radial distance: the B-band surface brightness (μ_B), and the B − V colour. The table is ordered by the strength of the correlation for the physical parameters of the H ii regions.

The overall analysis is illustrated is Fig. 10, where we show the distribution of the correlation coefficients, zero-points, and slopes for each individual galaxy, for three particular parameters: (i) the surface brightness, as an example of a strongly correlated parameter; (ii) the oxygen abundance, i.e., the strongest correlated parameter for the ionized gas; and (iii) the dust extinction, a parameter with no gradient in most of the cases. For highly correlated parameters the mean value, shown in Table 7 is not enough to characterize their behavior.

There are parameters that show a statistically significant correlation with the radial distance (r_cor > 0.5, and σ_cor < 0.3). These parameters are the Strömgren radii, the oxygen abundance, the equivalent width of Hα and the classical ionization diagnostic line rations ([O iii]/Hβ and [N ii]/Hα). The first correlation may indicate that the H ii regions are larger towards the center. However, we have to be cautious about this statement, since we do not have a direct estimate of the actual size of the H ii regions, and the Strömgren radii are based on particular radiation equilibrium conditions (Osterbrock 1989). We need to recall here that since many of our so-called H ii regions, are indeed, H ii aggregates, this radius should be considered as an effective radius. The next two correlations show that the more metal rich and evolved stellar populations are located in the inner regions, in agreement with expectations. The remaining two gradients indicates that in general the strength of the ionization is larger in the outer than in the inner regions. Finally, the ionization parameter shows a weaker trend, in the way that less powerful H ii regions are located in the central areas, while the stronger ones are located in the outer regions. However, this result has to be taken with care, since the correlations are weak and the ionization parameter depends both on the electron density and the number of ionizing photons, which may present also radial gradients.

Finally, there are parameters with little dependence with the radial distance, like the dust attenuation and the electron density. If the radial gradient of the parameters discussed before (e.g., oxygen abundance and/or equivalent width of Hα) is a consequence of the time evolution of the H ii regions (aging, enrichment, lose of strength and expansion), those later ones are not strongly affected by this overall evolution.

7.4. Universal gradients

For those properties showing a strong correlation, it is equally important to understand if the gradient is universal, within our range of explored parameters. Inspecting the histograms shown in Fig. 10 and the values for the slopes listed in Table 8, we can conclude that all the parameters showing either a clear correlation or a trend show well defined slopes, taking into account the considered errors for the measured parameters. For the equivalent width of Hα and the oxygen abundance a Lilliefors-test indicates that the histogram of the slopes of the gradients are consistent with a Gaussian distribution (Lilliefors 1967). This implies that we can define a characteristic value for the slope and that we do not find a population of galaxies with slopes inconsistent with the normal distribution. To illustrate this result we show in Fig. 11 the radial distribution of two of the parameters with stronger correlation: (i) the equivalent width of Hα and (ii) the oxygen abundance. We include all the H ii regions in our catalogue (~2600). For doing so, a global offset has been applied galaxy by galaxy to normalize the equivalent width and the abundance at effective radius. This offset was derived by subtracting the value derived by the individual regression to the median value listed in Table 8. A new regression is estimated for all the dataset of H ii regions. Both the average regression listed in Table 8 (red dashed-line), and the regression for the full sample (black solid-line), has been included. It is clear that both correlations are very similar, which support our claim that there is a universal slope for the gradient of either the equivalent width and the oxygen abundance when the radial scale is normalized by the effective radius.

Figure 11 shows that the scatter around the described correlation, ~0.6 dex, is much larger than the average error of each individual measurement, ~0.15 dex, for the case of the equivalent width of Hα. However, in the case of the oxygen abundances both values are very similar, ~0.2 dex. If we interpret this scatter as a typical coherent scale-length, we can conclude that stellar populations with similar star-formation histories are distributed at a wider radial ranges than the corresponding ionized gas with similar oxygen abundance. Thus, the possible intermix due to radial migrations (or similar effects) affects strongly the stars than the ionized gas, as expected. A larger relative scatter in the properties of the stellar population compared with the oxygen abundance ones was reported even in our Galaxy (e.g. Friel 1995).

For the particular case of the oxygen abundance, the same caveats expressed in Sect. 7.1.1 have to be taken into account here. We derive the abundance using the O3N2 empirical estimator (Pettini & Pagel 2004), calibration which has a certain range of validity. Due to that we included the corresponding scale of O3N2 values to illustrate that we are in the range where this calibrator provides reliable results. We repeated the analysis using the R₂₃ calibrator, deriving similar results for the radial gradient. However, there is a larger scatter in this distribution, mostly due to the larger error bar of our derivation of oxygen abundance based on this later method, and the lower number of H ii regions with measured [O ii] λ3727 emission line (~50% of the total sample).

Despite these caveats, the main result are valid: i.e., there seems to be a universal radial gradient for oxygen abundance when normalized with the effective radii of the galaxies. This result apparently contradicts previous ones, in which the slope of the radial gradients show a trend on certain morphological characteristics of the galaxies. Vila-Costas & Edmunds (1992) shows that barred spirals have a shallower gradient than non-barred ones. However, we must recall here that this statements are based, in general, in gradients on physical scales (i.e. dex kpc^-1), not in normalized ones. A slight decrease in the scatter between the different slopes is appreciated by Vila-Costas & Edmunds (1992) and Diaz (1989), when the scale-length is normalized by the disk-scale, which agrees with our results. We conjecture that both results would come into agreement if the size-luminosity/morphological type relation was considered.

In order to make an independent cross-check we analysed the distribution of gradients among our galaxies for barred (10 galaxies) and un-barred ones (28 galaxies). No significant difference is found between the distributions, or between any of them and the one comprising the full sample of galaxies; on the basis of a t-test analysis, the probability of being different was 63.1% in the worst case. In addition to this test we repeated the comparison for those galaxies with and without well defined spiral arms (see Table 3). The nature of flocculent spirals is still unclear, although the star formation in these galaxies (and therefore, the H ii regions) may not be connected with density waves, but rather with differentially rotating galactic disks (e.g. Efremov et al. 1989). They could be produced also due to gravitational instabilities in the stars due to interactions (e.g. Toomre 1964). We found no differences among the distributions of slopes for both kind of galaxies.

Finally, for the Grand Design galaxies (i.e., those galaxies with two clearly defined spiral arms listed in Table 3), we repeated the analysis of the gradients for the H ii regions located at each spiral arm. Despite of the lower number statistics, we found not significant difference between the gradients for each spiral arm.

Figure 11 shows that for the spatial scale which is well sampled by our catalogue of H ii regions (r < 2r_e), the mean value of the analysed properties follow the described distribution. For radii larger than ~2 effective radii, the mean abundance and Hα equivalent width seem to be slightly offset, with values compatible with more inner regions (~1 r_e). Although this seem to agree with previous results reporting a flattening on the oxygen abundance, and even with the migration as a possible explanation, we have to take this result with a lot of caution. There is just a hand-full of H ii regions sampled by our catalogue in this spatial regime (less than a 1%), and therefore the result is not significant. On the other hand, it seems that there is a decrease of mean oxygen abundance in the inner regions of the galaxies (<0.3 r_e), compared with the expected value extrapolating the reported correlation. This decrease is not due to the abundance indicator used, since we detect it using either O3N2 or R₂₃ one. Indeed, this decrease was already detected in individual galaxies, like in NGC 628 (Sánchez et al. 2011; Rosales-Ortega et al. 2011).

We explored the possibility of a statistical origin of this effect, by analysing the distribution of oxygen abundance galaxy by galaxy. However, we found that this decrease is present in 20 of the 28 galaxies with H ii regions detected in the central region. A lower slope in the abundance gradient may induce this effect. However, we found no significant difference in their gradients, with respect to the average values.

Finally, we have explored which would be the actual location of the solar neighborhood in the proposed abundance gradient shown in Fig. 11. For the distance of the Sun to the center of the Milky way we adopted the value deduced by Eisenhauer et al. (2003), of 7.94 ± 0.42 kpc. The value of the disk scale-length, and therefore the effective radius, is still controversial, with large discrepancies between different results. The more likely value is ~4.5 kpc (i.e., r_e ~ 7.6 kpc), although a dispersion larger than 1 kpc is expected (van der Kruit & Freeman 2011). Therefore the Sun would be at ~1.1 effective radius of the Galactic center. We note that the abundance in the solar neighborhood is also under debate (Asplund 2007). The current convention is that it is around ~8.7, with a dispersion of ~0.2 dex (Asplund et al. 2006). Adopting this scale-length and abundance the actual location of the solar neighborhood would be just at the average location from our derive radial gradient (orange square in Fig. 11). Considering that the oxygen abundance has been scaled to the average value at the effective radius, it is interesting to note that our galaxy behaves as the average for typical spiral galaxies.

8. Summary and conclusions

In this article we have analysed the H ii regions of a sample of 38 nearby galaxies. The sample has been constructed selecting the almost face-on spiral galaxies presented in Paper I, and similar ones extracted from the PINGS survey Rosales-Ortega et al. (2010). In both cases, the galaxies have been observed using IFS, using the same instrument and sampling similar wavelength ranges with similar resolutions. The IFS data cover most of the optical extension of these galaxies, up to ~2−2.5 effective radii, with enough S/N for the purpose of this study.

We presented HIIexlorer, an automatic method to detect and segregate H ii regions/aggregations based on the contrast of the Hα intensity maps extracted from IFS datacubes. Once detected, the procedure provides us with a segmentation map that is used to extract the integrated spectra of each individual H ii region. The method has been compared successfully with other codes available in the literature for NGC 628, the largest galaxy (in projected size) included in the sample.

In total, we have detected 3107 H ii regions, 2573 all of them with good spectroscopic information (i.e. ~60 H ii regions per galaxy). This is by far the largest nearby, 2-dimensional spectroscopic survey presented for this kind of regions up-to-date. Even more, our selection criteria and dataset guarantee that we cover the galaxies in an unbiased way, regarding the spatial sampling. Therefore, the final sample is well suited to understand the spatial variation of the spectroscopic properties of H ii regions in this kind of galaxies.

A well-tested automatic decoupling procedure has been applied to remove the underlying stellar population, and to derive the main properties (intensity, dispersion and velocity) of the strongest emission lines in the considering wavelength range (covering from [O ii] λ3727 to [S ii] λ6731). A final catalogue of the spectroscopic properties of these regions has been created for each galaxy. Additional information regarding the morphology, spiral structure, gas kinematics, and surface brightness of the underlying stellar population has been added to each catalogue. In particular, a detailed analysis of the number and structure of the spiral arms has been presented, associating each H ii region to the nearest spiral arm, and classifying them among inter-arms and intra-arms ones. This analysis is highly experimental, and its main aim is to understand asymmetries in the spiral distribution of H ii regions. To our knowledge this is the first time that an H ii region catalogue is provided with two dimensional information and linked to the spiral structure and intra-arm association. The full capabilities of the derived catalogues will be presented in subsequent articles.

In the current study we focused on the understanding of the average properties of the H ii regions and their radial distributions. Among the analysed properties we include: (1) the equivalent width of Hα, (2) the amount of dust attenuation (A_V), (3) the most widely used diagnostic line ratios ($\frac{\mathrm{\left[}\mathrm{O}\hspace{0.17em}{iii}\mathrm{\right]}}{\mathrm{H}\mathit{\beta }}$ and $\frac{\mathrm{\left[}\mathrm{N}\hspace{0.17em}{ii}\mathrm{\right]}}{\mathrm{H}\mathit{\alpha }}$), (4) the ionizing parameter (U), (5) the oxygen abundance (O/H), (6) the effective Strömgren radius and (7) the electron density.

We derive the following results:

• 1.

  There is statistically significant change in the ion-ization conditions across the field of view. The fractionof H ii regionsaffected either by AGNs, shocks or post-AGB stars is much larger for the central regions(r < 0.25r_e), than in the outer ones.

• 2.

  The average abundances for the central regions are comparable with the mass − metallicity relation derived by Tremonti et al. (2004). This is particularly important considering that both the technique to derive the stellar masses and the central metallicities (including the adopted calibrator) are different. The fully independent confirmation of the proposed relation through integral field spectroscopy is particularly important as aperture biases can be virtually eliminated.

• 3.

  The oxygen abundance and the equivalent width of Hα present a radial gradient that, statistically, has the same slope for all the galaxies in our sample, when normalized to the effective radius. The derived slopes for each galaxy are compatible with a Gaussian random distribution and are independent of the morphology of the analysed galaxies (barred/non-barred, grand-design/flocculent).

• 4.

  Other properties show no gradient but seem to vary across each galaxy, and galaxy by galaxy (like the electron density), without a clear characteristic value, or they are well described by the average value either galaxy by galaxy or among the different galaxies (like the dust attenuation).

The H ii regions catalogues of this analysis will be made publicly available for a better use on the astronomical community (see Appendix A and ftp://ftp.caha.es/CALIFA/early_studies/HII/tables/).

Online material

Appendix A: Catalogues of the H ii regions

The results of the overall analysis on the properties of the H ii regions is compiled in three different catalogues per galaxy, each of them comprising different information. The nomenclature of each catalogue is table.HII.TYPE.GALNAME.csv (for the coma separated version) or table.HII.TYPE.GALNAME.txt (for the space separated ones), where TYPE correspond to each of the following types: coords (coordinates of the H ii regions), flux (fluxes of the stronger emission lines) or EW (equivalent width of the stronger emission lines). GALNAME corresponds to the galaxy name as listed in Table 1.

The catalogues are stored in the CALIFA public ftp server:

ftp://ftp.caha.es/CALIFA/early_studies/HII/tables/ The content of each table is described in the following sections.

A.1. coords tables

They include all the information regarding the location of each H ii region within the galaxy, and additional information regarding their relation with the galaxy morphology, kinematics and the Hα luminosity. The tables have the following columns:

• 1.

  ID, unique identifier of theH ii region, including the nameof the galaxy (NAME) and a running index (NN), in the form:NAME-NNN.

• 2.

  RA, the right ascension of the H ii region.

• 3.

  DEC, the declination of the H ii region.

• 4.

  Xobs, the relative distance in right ascension to the center of the galaxy, in arcsec.

• 5.

  Yobs, the relative distance in declination to the center of the galaxy, in arcsec.

• 6.

  Xres, the deprojected and derotated distance in the X-axis from the center, in kpc.

• 7.

  Yres, the deprojected and derotated distance in the Y-axis from the center, in kpc.

• 8.

  R, the deprojected and derotated distance to the center, in kpc.

• 9.

  Theta, the deprojected position angle of the H ii region, in degrees.

• 10.

  N_Arm, the ID of the nearest spiral arm.

• 11.

  Inter_Arm, a flag indicating if the H ii region is most probably associated to a particular arm, 1, or most likely an inter-arm region, 0.

• 12.

  D_min−Arm, the minimum distance in arcsec to the nearest spiral arm.

• 13.

  D_Arm, the spiralcentric distance, i.e., the distance in arcsec along the nearest spiral arm.

• 14.

  Theta_Arm, the angular distance in degree to the nearest spiral arm.

• 15.

  vel_Hα, the Hα rotational velocity, in km s^-1.

• 16.

  e_vel_Hα, error of the Hα rotational velocity, in km s^-1.

• 17.

  log10(L_Hα), decimal logarithm of the dust corrected luminosity of Hα, in using of Erg s^-1.

• 18.

  e_log10(L_Hα), error of the decimal logarithm of the dust corrected luminosity of Hα, in using of Erg s^-1.

A.2. flux tables

They comprise the fluxes and ratios of the stronger emission lines detected in each H ii region, as derived from the analysis described in Sect. 6.1. They include the following columns:

• 1.

  ID, unique identifier of theH ii region, described in theprevious section.

• 2.

  Flux_Hβ, observed flux of Hβ, in units of 10^-16 erg s^-1 cm^-2.

• 3.

  e_Flux_Hβ, error of the observed flux of Hβ, in units of 10^-16 erg s^-1 cm^-2.

• 4.

  rat_OII_Hb , [O ii] λ3727/Hβ line ratio.

• 5.

  e_rat_OII_Hb, error of the [O ii] λ3727/Hβ line ratio.

• 6.

  rat_OIII_Hb, [O iii] λ5007/Hβ line ratio.

• 7.

  e_rat_OIII_Hb, error of the [O iii] λ5007/Hβ line ratio error.

• 8.

  rat_OI_Hb, [O i] λ6300/Hβ line ratio.

• 9.

  e_rat_OI_Hb, error of the [O i] λ6300/Hβ line ratio.

• 10.

  rat_Ha_Hb, Hα/Hβ line ratio.

• 11.

  e_rat_Ha_Hb, error of the Hα/Hβ line ratio.

• 12.

  rat_NII_Hb, [N ii] λ6583/Hβ line ratio.

• 13.

  e_rat_NII_Hb, error of the [N ii] λ6583/Hβ line ratio.

• 14.

  rat_He_Hb, HeI 6678/Hβ line ratio.

• 15.

  e_rat_He_Hb, error of the HeI 6678/Hβ line ratio.

• 16.

  rat_SII 6717_Hb, [S ii] λ6717/Hβ line ratio.

• 17.

  e_rat_SII 6717_Hb, error of the [S ii] λ6717/Hβ line ratio.

• 18.

  rat_SII 6731_Hb, [S ii] λ6731/Hβ line ratio.

• 19.

  e_rat_SII 6731_Hb, error of the [S ii] λ6731/Hβ line ratio.

• 20.

  BPT_type, flag indicating the location of the ionized gas region in the classical BPT [O iii]/Hβ vs. [N ii]/Hα diagnostic diagram shown in Fig. 7, with the following values: (0) location undetermined, due to the lack of any of the required line ratios with sufficient S/N for this analysis; (1) region located below the Kauffmann et al. (2003) demarcation line, i.e., corresponding to a classical star-forming H ii region; (2) region located in the intermediate area within the Kauffmann et al. (2003) and the Kewley et al. (2001) demarcation lines, i.e.; (3) region located above the Kewley et al. (2001) demarcation line, i.e., corresponding to the area expected from being ionized by an AGN and/or a shock.

A.3. EW tables

They comprise the equivalent width, in Angstroms, of the stronger emission lines detected in each H ii region, as derived from the analysis described in Sect. 6.1. They include the following columns:

• 1.

  ID, unique identifier of theH ii region, described in theprevious section.

• 2.

  EW_OII, equivalent width of [O ii] λ3727.

• 3.

  e_EW_OII, error of the equivalent width of [O ii] λ3727.

• 4.

  EW_Hbeta, equivalent width of the Hβ emission line.

• 5.

  e_EW_Hbeta, error of the equivalent width of Hβ.

• 6.

  EW_OIII, equivalent width of [O iii] λ5007.

• 7.

  e_EW_OIII, error of the equivalent width of [O iii] λ5007.

• 8.

  EW_OI, equivalent width of [O i] λ6300.

• 9.

  e_EW_OI, error of the equivalent width of [O i] λ6300.

• 10.

  EW_Halpha, equivalent width of Hα.

• 11.

  e_EW_Halpha, error of the equivalent width of Hα.

• 12.

  EW_NII, equivalent width of [N ii] λ6583.

• 13.

  e_EW_NII, error of the equivalent width of [N ii] λ6583.

• 14.

  EW_SII, equivalent width of the [S ii] λλ6717, 6731 doublet.

• 15.

  e_EW_SII, error of the equivalent width of the [S ii] λλ6717, 6731 doublet.

An example of the use of the parameters listed in these tables is shown in Fig. 6, and in the analysis performed in Sect. 6.1.2. Figure A.1 shows an example of the two dimensional distribution of the properties included in the described catalogues, which makes use of the many different properties studied for the H ii regions.

Appendix B: Empirical correction of the [N ii] contamination in Hα narrow band images

The Hα luminosity observed in spiral and irregular galaxies is believed to be a direct tracer of the ionization of the inter-stellar medium (ISM) by the ultraviolet (UV) radiation which is produced by young high-mass OB stars. Since only high-mass, short-lived, stars contribute significantly to the integrated ionizing flux, this luminosity is a direct tracer of the star formation rate (SFR), independent of the previous star formation history. This is why dust-corrected Hα luminosity is one of the most widely used observables to derive SFR in galaxies.

Among the several methods used to derive the Hα luminosity and its distribution across the optical extension of the galaxies, narrow-band image is by far the cheapest one in terms of telescope time and complexity. Thus, it is the most frequently used too (e.g., James et al. 2004; Pérez-González et al. 2003). The technique is rather simple: (i) the galaxy is observed using both a narrow-band filter centered at the wavelength of Hα and a broader filter covering a wider range around the same wavelength range; (ii) The broad-band image is used to correct for the underlying continuum and provide a relative flux calibration of the continuum subtracted narrow-band image; (iii) by performing a flux calibration of the broad-band image it is possible to have an accurate calibration of the decontaminated Hα emission map.

One of the major limitations of narrow-band Hα imaging is contamination by the [N ii] line doublet, which can hardly be derived from a single narrow-band imaging (e.g. James et al. 2005). Most frequently used narrow-band filters have a width of ~50−80 Å, and in most of the cases the emission from the [N ii] λλ6548, 6583 contaminate the derived Hα emission map, and therefore, the derived Hα luminosity and SFR. Despite of the fact that the [N ii]/Hα line ratio present a strong variation across the field for star-forming galaxies (e.g. Sánchez et al. 2011, and Fig. 7), it is generally assumed an average correction.

The most commonly used corrections for entire galaxies are those derived by Kennicutt (1983) and Kennicutt & Kent (1983). Spectrophotometric [N ii]/Hα ratios of individual extragalactic H ii regions from the literature (see Kennicutt & Kent 1983, and references therein) were compiled from 14 spiral galaxies (mostly of type Sc) and 7 irregular galaxies. The average Hα/(Hα + [N ii]) ratio was found to be fairly constant, spanning the ranges 0.75 ± 0.12 for the spirals, and 0.93 ± 0.05 for the irregulars (Kennicutt 1983). In terms of the ratio [N ii]-total/Hα this corresponds to a median value of 0.33 for spirals and 0.08 for irregulars. These values were calculated by finding the [N ii]-total/Hα ratio of the brightest H ii regions, averaging for each galaxy and then determining the mean value for spiral and irregular types. This implicitly assumes that all H ii regions have the same proportion of [N ii]-total to Hα emission as those regions measured. We have already illustrated that this may not be the case in general, e.g., Fig. 7. However, recent results show that the total integrated spectra of galaxies may have a stronger [N ii] emission than the one reported before, with a large variation line ratios for different galaxy types Kennicutt (1992).

Jansen (2000) already showed that there is a trend of the average [N ii]/Hα ratio with galaxy luminosity. In their study, the lines ratios for galaxies brighter than M_B = −19.5 are in agreement with the values found by Kennicutt (1992), but fainter than this a striking trend is seen towards much lower values of this ratio. A similar trend is found by Gavazzi et al. (2004).

To our knowledge the only attempt to make a correction across the optical extension of each galaxy is the one introduced by James et al. (2004). In this study they used the spatial distribution of the [N ii]/Hα line ratio, instead of an average correction for all the entire galaxy. However, their estimations of the distribution of the line ratio are based on physical principles rather than in direct measurements.

Making use of our extensive catalogue of individual emission line regions, we have explored possible empirical corrections that allow us to perform spatially resolved corrections across the optical extension of each individual galaxy. For doing so we correlated the measured [N ii]/Hα line ratios for each individual region with different parameters easy to address using broad-band photometry, like the Hα intensity, B and V-band magnitudes, B − V colours and radial distance relative to the effective radius.

Among the different explored linear relations, the one with stronger correlation coefficient (r ~ 0.5), and better defined zero-point and slope, was the one with the B − V colour: ${\log }_{\mathrm{10}}\mathrm{(}\left[\mathrm{N}\hspace{0.17em}{ii}\right]\mathit{/}\mathrm{H}{\mathit{\alpha }}^{\mathrm{)}}\mathrm{=}\mathrm{-}{\mathrm{0.64}}_{\mathrm{\pm }\mathrm{0.20}}\mathrm{+}{\mathrm{0.36}}_{\mathrm{\pm }\mathrm{0.18}}\mathrm{(}\mathit{B}\mathrm{-}\mathit{V}\mathrm{)}\mathit{.}$(B.1)Figure B.1, left panel, shows the distribution of [N ii]/Hα line ratios along the B − V colour for all the detected H ii regions. The image and contours show the density distribution in this space of parameters, together with a solid line showing the best fitted linear regression described before. This relation can be used as a simple proxy of the [N ii]/Hα line ratio, and used to decontaminate the described Hα narrow-band images.

We applied the proposed correction to the Hα narrow-band images described in Sect. 3, to demonstrate its improvement over a classical single correction over the entire galaxy. We derive for each detected H ii region the corresponding flux in the Hα narrow-band images, using the segmentation maps provided by HIIexplorer (Hα^img). Then, we obtain the relative difference between this contaminated flux and the real Hα flux measured using the fitting procedure describe in Sect. 6.1. The mean value of this difference is ~0.28 ± 0.19, which is consistent with the typical average correction found in the literature (e.g., Kennicutt 1983). Figure B.1, right panel, shows a solid-blue histogram of the relative difference between the Hα flux derived from the narrow-band images, and the ones derived using the emission line fitting procedure after applying this average correction.

The derived correction is then applied on the same data using a iterative processes. In each iteration the B − V colour is used to guess the [N ii]/Hα line ratio. This ratio, together with the decontaminated Hα flux derived from in the previous iteration, is used to derive the [N ii] intensity. Finally, this intensity is subtracted to the original contaminated Hα^img intensity to derive a new decontaminated flux. For the first iteration it is assumed that the intensity decontaminated by the average correction is a good starting estimation of the Hα flux. After three iterations the decontaminated Hα flux converge with a few percent. Figure B.1, right panel, shows a hashed-red histogram of the relative difference between the the Hα flux derived from the narrow-band images, and the ones derived using the emission line fitting procedure after applying the proposed correction. It is clear that the new histogram has a lower dispersion that the previous one, with a standard deviation of ~0.15. The proposed correction improves the accuracy of the derived Hα intensity by a a ~60%, in average.

The effect of this correction is stronger when analysing the spatial distribution of the Hα emission and/or the relative strength of the SFR. As we already indicated the [N ii]/Hα ratio tends to decrease with the radius. Therefore, an average correction would overestimate the Hα emission and the SFR in the inner regions, and underestimate it in the outer ones. Indeed, some authors have corrected the image-based Hα fluxes for [N ii] contamination using available spectroscopical data of selected H ii regions within the galaxy (e.g. López-Sánchez & Esteban 2008).

So far, we did pay no attention to the possible physical connections between the explored parameters. The described relation may indicate a physical connection between the conditions of the ionized gas and the ionizing stellar population, or between both of them and a third parameter not considered here. A possible origin of this connection could be a co-evolution of both components of the H ii regions. The study of this connection, that we will address in future works, is beyond the scope of the current analysis.

---

Acknowledgments

We thank the referee for the detailed and helpful comments that have improved considerably the quality of this article. We thank the director of CEFCA, Dr. M. Moles, for his sincere support to this project. We thank the Viabilidad, Diseño, Acceso y Mejora funding program, ICTS-2009-10, for funding the data acquisition of this project. S.F.S., F.F.R.O. and D. Mast thank the Plan Nacional de Investigación y Desarrollo funding programs, AYA2010-22111-C03-03 and AYA2010-10904E, of the Spanish Ministerio de Ciencia e Innovacion, for the support given to this project. S.F.S. wants to note that the project continues despite of the lack of support of the same program during the 2012 period. F.F.R.O. acknowledges the Mexican National Council for Science and Technology (CONACYT) for financial support under the programme Estancias Posdoctorales y Sabáticas al Extranjero para la Consolidación de Grupos de Investigación, 2010–2011 J.M. and J.P. acknowledge financial support from the Spanish grant AYA2010-15169 and Junta de Andalucía TIC114 and Excellence Project P08-TIC-03531. D.M. and A.M.-I. are supported by the Spanish Research Council within the program JAE-Doc, Junta para la Ampliación de Estudios, co-funded by the FSE. R.A. Marino was also funded by the spanish programme of International Campus of Excellence Moncloa (CEI). J.I.-P., J.M.V., A.M.-I. and C.K. have been partially funded by the projects AYA2010-21887 from the Spanish PNAYA, CSD2006-00070 “1st Science with GTC” from the CONSOLIDER 2010 programme of the Spanish MICINN, and TIC114 Galaxias y Cosmología of the Junta de Andalucía (Spain). This paper makes use of the Sloan Digital Sky Survey data. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

References

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