Aperture effects on the oxygen abundance determinations from CALIFA data
J. Iglesias-Páramo, J.M. Vílchez, F.F. Rosales-Ortega, S.F. Sánchez, S. Duarte Puertas, V. Petropoulou, A. Gil de Paz, L. Galbany, M. Mollá, C. Catalán-Torrecilla, A. Castillo Morales, D. Mast, B. Husemann, R. García-Benito, M.A. Mendoza, C. Kehrig, E. Pérez-Montero, P. Papaderos, J.M. Gomes, C.J. Walcher, R.M. González Delgado, R.A. Marino, Á. R. López-Sánchez, B. Ziegler, H. Flores, J. Alves
aa r X i v : . [ a s t r o - ph . GA ] M a y Not to appear in Nonlearned J., 45.
Aperture effects on the oxygen abundance determinations from CALIFA data
J. Iglesias-P´aramo , , J.M. V´ılchez , F.F. Rosales-Ortega , S.F. S´anchez , S. Duarte Puertas , V.Petropoulou , A. Gil de Paz , L. Galbany , , M. Moll´a , C. Catal´an-Torrecilla , A. CastilloMorales , D. Mast , , B. Husemann , R. Garc´ıa-Benito , M.A. Mendoza , C. Kehrig , E.P´erez-Montero , P. Papaderos , J.M. Gomes , C.J. Walcher , R.M. Gonz´alez Delgado , R.A.Marino , , ´A. R. L´opez-S´anchez , , B. Ziegler , H. Flores andJ. Alves [email protected] Instituto de Astrof´ısica de Andaluc´ıa - CSIC, Glorieta de la Astronom´ıa s.n., 18008 Granada, Spain Estaci´on Experimental de Zonas ´Aridas - CSIC, Ctra. de Sacramento s.n., La Ca˜nada, Almer´ıa, Spain Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica, Luis E. Erro 1, 72840 Tonantzintla, Puebla, Mexico Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´ejico, A.P. 70-264, 04510 M´exico, D.F., Mexico INAF-OA Brera, via Brera 28, 20121 Milano, Italy Departamento de Astrof´ısica y CC. de la Atm´osfera, Universidad Complutense de Madrid, E-28040, Madrid,Spain Millennium Institute of Astrophysics, Chile Departamento de Astronom´ıa, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile Departamento de Investigaci´on B´asica, CIEMAT, Avda. Complutense 40, 28040 Madrid, Spain Observatorio Astron´omico, Laprida 854, X5000BGR, C´ordoba, Argentina Consejo de Investigaciones Cient´ıficas y T´ecnicas de la Rep´ublica Argentina, Avda. Rivadavia 1917, C1033AAJ,CABA, Argentina European Southern Observatory (ESO), Karl-Schwarzschild-Str.2, D-85748 Garching b. M¨unchen, Germany Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Universidade do Porto, CAUP, Rua das Estrelas, P-4150-762 Porto,Portugal Leibniz-Institude f¨ur Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany Department of Physics, Institute for Astronomy, ETH Z¨urich, CH-8093 Z¨urich, Switzerland Australian Astronomical Observatory, PO Box 915, North Ryde, NSW 1670, Australia Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia University of Vienna, T¨urkenschanzstrasse 17, 1180 Vienna, Austria GEPI, Observatoire de Paris, CNRS, 5 Place Jules Janssen, Meudon F-92195, France
ABSTRACT
This paper aims at providing aperture corrections for emission lines ina sample of spiral galaxies from the Calar Alto Legacy Integral Field AreaSurvey (CALIFA) database. In particular, we explore the behavior of thelog([O
III ] λ β )/([N II ] λ α ) (O3N2) and log[N II ] λ α (N2) fluxratios since they are closely connected to different empirical calibrations of the oxygenabundances in star forming galaxies.We compute median growth curves of H α , H α /H β , O3N2 and N2 up to 2.5 R and1.5 disk R eff . These distances cover most of the optical spatial extent of the CALIFAgalaxies. The growth curves simulate the effect of observing galaxies through aperturesof varying radii. We split these growth curves by morphological types and stellar massesto check if there is any dependence on these properties.The median growth curve of the H α flux shows a monotonous increase with radiuswith no strong dependence on galaxy inclination, morphological type and stellar mass.The median growth curve of the H α /H β ratio monotonically decreases from the centertowards larger radii, showing for small apertures a maximum value of ≈
10% largerthan the integrated one. It does not show any dependence on inclination, morpholog-ical type and stellar mass. The median growth curve of N2 shows a similar behavior,decreasing from the center towards larger radii. No strong dependence is seen with theinclination, morphological type and stellar mass. Finally, the median growth curve ofO3N2 increases monotonically with radius, and it does not show dependence with theinclination. However, at small radii it shows systematically higher values for galaxiesof earlier morphological types and for high stellar mass galaxies.Applying our aperture corrections to a sample of galaxies from the SDSS surveyat 0 . ≤ z ≤ . ≈ R eff ) giventhe high dispersion shown around the median growth curves. Thus, the application ofthese median aperture corrections to derive abundances for individual galaxies is notrecommended when their fluxes come from radii much smaller than either R or R eff . Subject headings: galaxies: general — galaxies: abundances — galaxies: ISM 3 –
1. Introduction
Bidimensional spectroscopy is gaining more and more importance as a powerful observationaltechnique capable to provide new results on the properties of galaxies. Many instruments (com-monly known as Integral Field Spectrographs, IFS) have been developed in the last years to producebidimensional spectroscopy, most of them based on arrays of fibers that collect light from the skyarea of interest and drive it through a dispersor. The main limitation of these fiber-fed spectrograpsis their limited field-of-view, which makes impossible the blind observation of large areas of the skyto observe large amounts of galaxies as it is the case of the large scale surveys like SDSS (York etal. 2000), 2dFGRS (Colless et al. 2001), VVDS (Le F`evre et al. 2005), z-COSMOS (Lilly et al.2007) and DEEP/DEEP2 (Davis et al. 2003).The best option for IFS surveys is thus to focus on selected individual objects, but this isvery time consuming and prevents the study of large samples of galaxies. So far, there are onlya few surveys employing IFS, from which we highlight: SAURON (Bacon et al. 2001), ATLAS-3D (Cappellari et al. 2011), PINGS (Rosales-Ortega et al. 2010), VENGA (Blanc et al. 2010),VIXENS (Heiderman et al. 2011) and CALIFA (S´anchez et al. 2012a).The CALIFA Survey (S´anchez et al. 2012a) is observing a statistically well-defined sample of600 galaxies in the local Universe with the Potsdam Multi Aperture Spectrograph in the PPAKmode (Roth et al. 2005) at the 3.5m telescope at Calar Alto Observatory. The survey benefitsfrom the wide field-of-view of PPAK (about 1 arcmin ) compared to similar instruments at othertelescopes. Thus, CALIFA galaxies are mapped over most of their optical spatial extent, and so farit has allowed up to date complete bidimensional studies of galaxy properties like the star formationhistories (Cid Fernandes et al. 2013, Gonz´alez-Delgado et al. 2014), the properties of the ionizedgas in early-type galaxies (Kehrig et al. 2012, Papaderos et al. 2013, Singh et al. 2013, Gomes etal. 2015a), the properties of large samples of H II regions (S´anchez et al. 2013,2014), or the effectsof the spatial resolution at different redshifts (Mast et al. 2014) among others.In addition to this, the CALIFA database allows the study of the biases introduced when galax-ies are observed through small and size-limited apertures, which usually are single-fiber spectro-graphs. Several studies have already notices the existence of such aperture effects in the propertiesof early and late-type galaxies (e.g. Kehrig et al. 2013, Gomes et al. 2015b). Aperture effects ongalaxy properties have been previously addressed by following different approaches (e.g. Hopkinset al. 2003, Brinchmann et al. 2004, Ellis et al. 2005, Kewley et al. 2005, Salim et al. 2007,Gerssen et al. 2012, Zahid et al. 2013). On top of that, a recent study by Richards et al. (2015)based on part of the SAMI Galaxy Survey (Allen et al. 2015; Bryant et al. 2015; Sharp et al. 2015)concludes that biases in the estimation of the total instantaneous star formation rate of a galaxyarise when the aperture correction is built only from spectra of the nuclear region of galaxies.A preliminary study of the aperture effects based on CALIFA data was presented in Iglesias-P´aramo et al. (2013, IP13) and was devoted to the H α and H β emission line fluxes. In the presentwork we extend their analysis using a much larger sample of galaxies which allows us to perform 4 –a more detailed study. We try to go beyond and focus on observational parameters related tothe derivation of the oxygen abundances, like the (widely used in the literature) N2 and O3N2parameters.This is a crucial point since spiral galaxies are known to show radial abundance gradients, whichmeans that observing them through a reduced aperture must not necessarily provide a completeinformation on the spatial abundance distribution. Regarding this point, it has been reportedin the literature that the oxygen abundance derived for the integrated fluxes of emission lines ofspiral galaxies equals the corresponding abundance of their H ii regions at a typical galactocentricdistance of 0 . × R opt (Pilyugin et al. 2004, Moustakas et al. 2006). This result linking theabundances of H ii regions at a fixed galactocentric radius and the abundance obtained for theintegrated emission line flux ratios from the whole disk of spiral galaxies, give some support toadopting a reference characteristic value for the abundance of a spiral galaxy. Nonetheless, weshould bear in mind that the integrated emission of the spiral disks represents in fact a compositespectrum, including different H ii regions (plus diffuse ionized ISM) with varying physical conditionsand chemical compositions.Although there is a classical method to derive oxygen abundances of bright star forming regionsbased on atomic data and the fluxes of emision lines ([O ii ] λ iii ] λ iii ] λ ii ] λ α ) and O3N2 (log([O iii ] λ β )/([N ii ] λ α )), that have been widelyused in the literature to estimate oxygen abundanes of star formation galaxies (e.g. Pettini & Pagel2004, P´erez-Montero & Contini 2009, Marino et al. 2013). The applicability intervals of theseindicators are − . < N2 < − . <
2. Marino et al. (2013) found dispersions of σ ≈ . / H = 8 .
743 + 0 . × N2 (1)and 12 + log O / H = 8 . − . × O3N2 (2)Our study is performed for these two observational quantities, so the effect of the aperture onthe abundances depends on the choice of the calibration based on any of these observed quantities. 5 –A further advantage of this larger sample, compared to the one used in IP13, is that it allows usto study the effect of parameters like inclination, morphological type and stellar masses, on thederived average aperture corrections.The paper is organized as follows: Section 2 explains the selection of the sample. The mainresults from our analysis are detailed in Section 3. Section 4 contains a discussion on the implicationsof the aperture effects on the abundance determination and an example to illustrate this interestingpoint. Finally, the conclusions of the paper are enumerated in Section 5.
2. Sample selection
The sample of galaxies used for this work has been selected from the CALIFA database updatedto December 2013, reduced with the v1.4 version of the pipeline (Garc´ıa-Benito et al. 2015). Detailson the instrumental setup and properties of the spectra can be found in S´anchez et al. (2012a),where the survey is presented. We started with an initial sample of 402 galaxies, the ones observedup to December 2013, out of the 937 galaxies comprising the total CALIFA mother sample (Walcheret al. 2014). Then we removed the elliptical and lenticular galaxies (E, S0, S0a) in order to keeponly spiral galaxies. As we are interested in covering the galaxy disks as much as possible withinthe CALIFA aperture ( ≈ ′′ radius), we have to choose a proper scale related to the spatial extentof the galaxies. For this, two possibilities, related to different structural component of the galaxies,arise as the most interesting: • The Petrosian radius in the SDSS- r ′ band within a circular aperture containing 50% of thetotal Petrosian flux (SDSS petroR r , and hereafter R ): this scale takes into accountthe stellar emission from both the bulge and the disk inside this circular aperture. Thus,this spatial scale is sensitive to light coming from stars of different ages, and has the greatadvantage of its availability for a huge number of galaxies, in particular the whole CALIFAsample. • The effective radius encompasing 50% of the light coming from the disk component (hereafter R eff ): this scale is computed after a morphological decomposition bulge/disk of the galaxySDSS g’-band surface brightness profile, removing the light coming from the bulge and as-suming that the disk has an exponential profile of the form I ( r ) = I e − . r/R eff . Detailsabout the procedure can be found in S´anchez et al. (2014).Figure 1 shows the comparison of R and R eff with the optical radii , which correspond tothe major semi-axis of the elliptical aperture at µ B = 25 mag arcsec − isophote (hereafter R op )of the CALIFA spirals. As the figure shows, for most spiral galaxies 2 R ≤ R op ≤ R , with From LEDA database (Makarov et al. 2014) R op seems to be lower than 4 R . Thisdifferential behavior is likely due to the fact that Sa-Sab galaxies present promiment bulges thatresult in reduced values of R . In addition, it is shown that R eff ≤ R op ≤ R eff , and this relationholds in the same way for all morphological types. In this case, all the morphological types behavesimilarly because R eff is estimated by using only the light from the disk.In the subsequent analysis we will present the results of the growth curves (as a function of R and R eff ) of several observable fluxes or flux ratios based on a selected set of emission lines.They will be used as indicators of the bias induced when estimating galaxy properties from fluxesmeasured within reduced apertures instead of taking the integrated values of these fluxes. Hereafterwe will refer to the median growth curves of the H α flux, and the H α /H β , N2 and O3N2 ratios as afunction of R as x ( α ), x ( αβ ), x (N2 ) and x (O3N2 ) respectively. These curves representthe value of the parameter measured within a circular aperture of a given radius normalized to thevalue of the parameter measured within 36”, which is the radius of the largest circular apertureconsidered. This way, the value of all parameters within a circular aperture of radius 36” will betaken as the integrated value of this property. In the case of N2 and O3N2, the growth curves arelogarithmic. Thus, x ( α ) r = f (H α ) r / f (H α ) ′′ , x ( αβ ) r = ( f (H α ) r / f (H β ) r )/( f (H α ) ′′ / f (H β ) ′′ ), x (N2 ) r = log[ f ([N ii ]6583)/ f (H α )] r − log[ f ([N ii ]6583)/ f (H α )] ′′ ,and x (O3N2 ) r = log[( f ([O iii ]5007)/ f (H β ))/( f ([N ii ]6583)/ f (H α ))] r −− log[( f ([O iii ]5007)/ f (H β ))/( f ([N ii ]6583)/ f (H α ))] ′′ .Correspondingly, we will refer to the growth curves of the H α flux, and the H α /H β , N2 andO3N2 ratios as a function of R eff as x ( α eff ), x ( αβ eff ), x (N2 eff ) and x (O3N2 eff ) respectively.The procedure followed to produce the growth curves is similar to the one described in IP13.For each galaxy, unidimensional spectra are constructed by adding all the pixels within circularapertures of radii varying from 3” to 36”, in steps of 3”. In order to obtain the pure emission linespectra, we use a single stellar population (SSP) fitting to remove the contribution of the underlyingcontinuum of the stellar population. We apply a linear combination of two SSP synthesis modelsof Vazdekis et al. (2010) based on the MILES stellar library (S´anchez-Bl´azquez et al. 2006) and aKroupa IMF (Kroupa 2001). The ages of the SSPs used range from 0.10 to 0.79 Gyr for the case ofthe young stellar population and from 2.00 to 14.13 Gyr for the old stellar population. Five differentmetallicities are considered for each age ([M/H] values equal to 0.00, 0.20, -0.40, -0.71 and -1.31 dexoffset from the solar value). Once the underlying stellar continuum is removed, the fluxes of theemission lines were obtained from gaussian fits to the residual spectra. The procedure followed toget the fits is as follows: first we fit the triplet H α +[N ii ] assuming a common recession velocity and 7 –FWHM for the three lines, and the usual line ratio f (6548)/ f (6583)=0.333. No broad componentsin H α were considered because we have removed AGNs from our samples and thus only narrowemission lines are expected. Then we produced individual fits for H β and [O iii ] leaving free therecession velocity and the FWHM but using as first guess the values obtained for H α +[N ii ]. Afterthat, for each galaxy we have 12-element vectors containing the fluxes of the emission lines containedwithin each of the circular apertures. The median growth curves as a function of R or R eff wherethen produced by combining the properly interpolated vectors.In addition to this, given that we focus on star-forming galaxies, for the subsequent analysiswe remove those CALIFA galaxies classified as AGN, according to the prescriptions of Best et al.(2012), Kewley et al. (2001, 2006) and Cid Fernandes et al. (2011), and to the NED database.In order to keep only galaxies with good quality data we will remove those galaxies for which f (H α ) > σ (H α )/ f (H α ) ≤ .
333 in all the circular apertures. We note that the results ofthis study are the same if we apply a 2- σ cut in signal-to-noise, resulting in a significantly largersample, instead of the 3- σ applied in what follows.As a first step we investigate the distribution of the H α emission in the CALIFA galaxies.Figure 2 shows x ( α ) and x ( α eff ) for the spirals covered in the CALIFA aperture up to 4 R and2.2 R eff respectively. These limits were imposed with the compromise of covering as much as possiblethe disks of the CALIFA galaxies, but keeping samples with reasonable numbers of galaxies. Inboth cases, x ( α ) and x ( α eff ) seem to saturate at 4 R and 2.2 R eff respectively, suggesting thatthe bulk of the H α emission of spiral galaxies is contained within these apertures. But the numbersof galaxies available for this test are very low for a detailed study of the aperture effects includingthe role of the stellar mass and morphological type. For this reason, we chose two less conservativelimits, namely 2.5 R and 1.5 R eff , that contain on average 85% and 90% of the total H α emissionin spiral galaxies (see figure 2).After imposing this last condition, we end up with 165 galaxies covered up to 2.5 R and133 galaxies covered up to 1.5 R eff , which is the case for galaxies with R ≤ ′′ and R eff ≤ ′′ , respectively . These two subsamples ( S and S eff ) will be the basis of our statistical studyof aperture effects, taking into account that S galaxies will be studied up to ≈ . R , whichcontains on average 85% of their H α emission, and that S eff galaxies will be be studied up to ≈ . R eff , which contains on average 90% of their H α emission. Table 2 shows the number ofgalaxies of each subsample after imposing each of the filters previously mentioned. Also, Table 3 http://ned.ipac.caltech.edu/ This value is slightly lower than the one, 90%, reported in IP13. Given that the current sample is larger, we aremore confident about the value reported in this paper. Further restrictions must be imposed to the subsamples when analyzing the H α /H β , N2 and O3N2 growthcurves, namely f (H β ) > σ (H β )/ f (H β ) ≤ . f ([N II ]) > σ ([N II ])/ f ([N II ]) ≤ . f ([O III ]) >
0, and σ ([O III ])/ f ([O III ]) ≤ . S to 159, 106 and 104 galaxies,and S eff to 129, 92 and 90 galaxies respectively.
3. Results3.1. Corrections for fixed angular apertures α growth curves We start discussing the behavior of the growth curves of x ( α ) and x ( α eff ) of our galaxies.For this we first compare x ( α ) of IP13 with that obtained in this work. As in IP13, we producemedian growth curves and a confidence interval equivalent to 1 σ , consistent in that one containing68.2% of the individual growth curves at each radius. Table 1 lists the values of x ( α ) of IP13 andthe one produced with the present sample. As it can be seen from Table 1, both curves are consistentwithin 1 σ along the probed range. The increased number of galaxies in our current sample willmake possible a more detailed analysis of the aperture corrections split by morphological types orstellar masses.Figures 3 to 5 show the H α growth curves split by galaxy inclination, morphological type andstellar mass. Inclination is defined as the ratio of SDSS isob r/isoa r and we consider face-ongalaxies those with inclination larger than 0.4, the rest being edge-on galaxies. Concerning themorphological types, two bins were defined as follows: Sa to Sbc, and Sc to Sdm. This splits oursample into early spirals and late spirals. Finally, the stellar mass was also split in two ranges,separated at log M ∗ /M ⊙ = 10 .
3. This limit was imposed since after removing E-S0 galaxies andAGNs, it splits the sample in two subsamples of similar numbers of galaxies. As it is clear from thefigures, the H α growth curves do not seem to show any dependence on inclination, morphologicaltype and stellar mass. The only exception, for which a slight dependence is seen, is x ( α eff ) whendifferent inclinations are taken into account. In this case, the growth curves for edge-on and face-ongalaxies look different, although still consistent with each other within the 1 σ limits shown in thefigure. α /H β growth curves Figure 6 shows x ( αβ ) and x ( αβ eff ) for different inclinations. Both curves are almostcoincident irrespective of the inclination of the galaxies. It is remarkable that both x ( αβ ) and x ( αβ eff ) show a very mild decline from the central regions to the outskirts, with a maximum valueof ≈ .
1, which corresponds to an increase of 0.20 dex in c (H β ) or 0.43 mag in A V at the center ofthe galaxies. This means that observing galaxies through a small aperture results in values of theextinction larger than those obtained with the integrated values of the H α and H β fluxes. Figure 7shows x ( αβ ) and x ( αβ eff ) for different morphological types. x ( αβ ) is slightly higher for Sa-Sbcthan for Sc-Sm galaxies, reaching values of ≈ .
15 at the center of the galaxies in the first case. This 9 –difference is not observed for x ( αβ eff ). Figure 8 shows x ( αβ ) and x ( αβ eff ) for different stellarmasses. As in the previous case, x ( αβ ) is slightly higher for galaxies with log M ∗ /M ⊙ > . M ∗ /M ⊙ ≤ . x ( αβ eff ). However, the differences observed in the median growth curves for galaxies of differentmorphological types and stellar masses are always lower than the dispersions around these mediangrowth curves, which as the figures show, increase as the radii of the apertures decrease.This slight increase in the H α /H β growth curve observed for small apertures with respect tothe integrated values can be compared with the variation in this Balmer line ratio as a functionof electron temperature. Assuming case B recombination and low-density limit, a substantialchange, from 20000 K to 5000 K, in electron temperature should be present to see a 10% change inH α /H β . This change in electronic temperature is not observed in typical H ii regions in the disksof spirals (P´erez-Montero & Contini 2009). For this reason, a radial gradient on the dust contentof star forming regions, likely related to the abundance gradient measured in spiral galaxies, wouldexplain this aperture effect. Figure 9 shows x (N2 ) and x (N2 eff ) for different inclinations. x (N2 ) and x (N2 eff ) behavein a similar way as x ( αβ ) and x ( αβ eff ), that is, they show a mild decline from the inner parts ofthe galaxies and do not show clear differences related to the inclination of galaxies. x (N2 ) and x (N2 eff ) show central values reach maxima of ≈ . − . x (N2 ) and x (N2 eff ) for different morphological types.The behavior of x (N2 ) and x (N2 eff ) is similar to the one previously described. Figure 11 shows x (N2 ) and x (N2 eff ) for different stellar masses which shows a marginal difference for smallapertures with more massive galaxies showing larger values of x (N2 ) and x (N2 eff ) than lessmassive ones. However, again this difference is much smalles than the dispersions around themedian values of x (N2 ) and x (N2 eff ). As we will show in the next section, the radial change ofthe N2 growth curves reflects in a radial change in the oxygen abundances. Figure 12 shows x (O3N2 ) and x (O3N2 eff ) for different inclinations. Following this figure, x (O3N2 ) and x (O3N2 eff ) show an almost linear increasing trend from the inner regions to theoutskirts of the galaxies, and no difference with the inclination of the galaxy is apparent. Thismeans that observing galaxies through small apertures results in values of O3N2 smaller thanthose obtained with the integrated values. Figure 13 shows x (O3N2 ) and x (O3N2 eff ) for dif- 10 –ferent morphological types. In this case, Sa-Sbc galaxies show larger values of x (O3N2 ) and x (O3N2 eff ) for apertures with R/R ≤ . R/R eff ≤ . x (O3N2 ) and x (O3N2 eff ) for different stellar masses. Similarly to the previous case,galaxies with log M ∗ /M ⊙ > . x (O3N2 ) and x (O3N2 eff ) for aper-tures with R/R ≤ . R/R eff ≤ . M ∗ /M ⊙ ≤ .
3, butas commented above, this difference is smalles than the dispersions around the median values of x (O3N2 ) and x (O3N2 eff ). In this case also the radial change of the O3N2 growth curves can beinterpreted in terms of a radial change of the oxygen abundanes.Tables 4 to 19 show the numerical values of the median growth curves and the 1 σ confidenceintervals corresponding to the growth curves previously shown. These tables also contain the fitsto all spiral galaxies considered in this work.As a summary of the present section we show in Table 20 the coefficients of the fits to 5thorder polynomials of the aperture corrections previously discussed. The large field-of-view covered by the CALIFA data allows us to predict the fraction of fluxenclosed within a given angular aperture with respect to the flux enclosed within a fixed physicalaperture at different redshifts. In our case, we have focused on the SDSS and SAMI fields-of-view.As the median value of R eff of our sample (spirals from Sa to Sdm excluding AGNs) is ≈ .
68 kpc,and based on x ( α eff ) shown in figure 2, we will estimate the quantities of interest within twocircular apertures, one containing most of the flux of the galaxy (10 kpc radius, containing onaverage 90% of the total H α flux) and another one enclosing the flux in the central region (3.3 kpcradius, containing on average 30% of the total H α flux). Then for each of the CALIFA spirals wemeasure each of the relevant quantities within the circular aperture subtended by the SDSS fiberif the galaxy was placed at different redshifts. Figure 15 gives the median values of the aperturecorrections with respect to an aperture of 10 kpc radius for the f (H α ), f (H α )/ f (H β ), N2 andO3N2. The SDSS fiber covers an aperture of ≈
10 kpc at a redshift of z ≈ .
6. The trends withredshift shown by the aperture corrections are similar to the ones obtained in previous sections asa function of R and R eff . Figure 16 also provides corrections for a physical aperture of 3.3 kpcradius. In this case, the SDSS fiber covers this aperture at a redshift of z ≈ . z ≈ .
07 and 0.02 respectively.Tables 21 to 24 list the median values and 1- σ dispersions of the aperture corrections for fixed 11 –apertures of 10 kpc and 3.3 kpc diameter, focused on the cases of the SDSS and SAMI surveys.
4. Discussion
In previous sections we have shown the growth curves of some emission line fluxes and lineratios, relevant for the estimation of Star Formation Rates (SFRs), extinction and characteristicoxygen abundances of spiral galaxies. These growth curves provide with aperture corrections forthese quantities that should be considered in a statistical sense, i.e. applicable to large statisticalsamples of spiral galaxies. The effect of the aperture on H α luminosity, H α /H β ratio, N2 and O3N2is found to be statistically uncorrelated to the inclination, morphological type and stellar mass ofgalaxies, except for some marginal differences always below the typical dispersions of the mediangrowth curves for small apertures.It is interesting noting that the aperture effect found for N2 and O3N2 can be interpreted asan aperture effect in the oxygen abundances. As a first step to illustrate the aperture effect onthe oxygen abundances we show in Fig. 19 the median growth curves of the logarithmic oxygenabundance as a function of R , x (OH ) , derived using the calibrations by Marino et al. (2013,M13), Pettini & Pagel (2004, PP04) and P´erez-Montero & Contini (2009, PMC09), for N2 and O3N2respectively. As it can be seen, the effect of the aperture marginally depends on the calibrationused both for N2 and O3N2 showing a maximum difference of ≈ . − .
03 dex, which correspondsto 5-7.5%. Although the dispersions around the median values are not shown in the figures (forclarity), they are much lower than this difference.Figures 20 to 23 show x (OH ) and x (OH eff ) estimated from N2 and O3N2 using the M13calibrations. As shown in the figures, the effect of the aperture for both indicators is maximal forsmall apertures and only marginal differences (maximum values of ≈ .
04 dex) with morphologicaltype and stellar mass are seeing, much lower than the typical dispersions around the medianvalues. However, what is more relevant is the dispersions around the median values, than can reachmaximal values of up to +25% for small apertures when deriving oxygen abundances of early-typeand/or high mass spirals using N2. We keep in mind that using other calibrations for the oxygenabundances could result in even larger dispersions around the median values. In particular, asshown in figure 19, using for example the PMC09 calibrations would result in dispersions ≈ Given that the oxygen abundance is usually given as a logarithmic quantity, the definition of x (OH ) and x (OH eff ) at a given radius r is, as in the case of N2 and O3N2, log(O/H) r − log(O/H) int , where log(O/H) int corresponds to the value of the logarithmic oxygen abundance measured within the largest aperture considered, 36”,assumed to be the integrated value.
12 –samples of galaxies and interpreted in a statistical sense. . ≤ z ≤ . R and split in two bins of stellar masses, since these two parameters are available for allthe SDSS galaxies.The sample of galaxies is the MPA-JHU sample (Kauffmann et al. 2003, Brinchmann etal. 2004, Tremonti et al. 2004, and Salim et al. 2007), that provides stellar masses and usesspectroscopy from SDSS-DR7 (Abazajian et al. 2009), and photometry complemented from SDSS-DR12 (Alam et al. 2015), satisfying the following criteria: • Redshift in the range 0 . ≤ z ≤ . • Signal-to-noise ratio of the emission lines H α , H β , [N II ] λ III ] λ • Stellar mass in the range 8 . ≤ log M ∗ /M ⊙ ≤ . • Signal-to-noise ratio of the half-light Petrosian radius in the r ′ band ( R ) larger than 3.Next we remove those galaxies classified as QSO by SDSS. We also remove those galaxies notclassified as star-forming according to the BPT diagram (Baldwin et al. 1981) of Kauffmann et al.(2003) and the condition EW(H α ) ≥ . ≤ . ′′ /R ≤ .
5, as it is the rangeof applicability of the corrections as indicated in IP13. Figure 24 shows the BPT diagram of theSDSS sample.In order to be as much realistic as possible, we want to take into account the large dispersionobserved around the median values of the growth curves for small apertures. For this, we first con-struct approximate cumulative distribution functions (CDFs) of the distribution of the individualO/H growth curves at each radius for the two stellar mass bins previously considered in Figs. 21and 23. Figures 25 and 26 show the CDFs at three different radii normalized to R . As it can beseen, the larger the radius normalized with respect to R , the closer the distribution remains tozero, as it was observed in the previous section. Several Monte Carlo tests were produced to verifythat the random distributions following these CDFs are consistent with being drawn from the sameparental distribution as the original distributions from the CALIFA galaxies.Then we are ready to quantify the aperture effect with a sample of galaxies from SDSS forwhich the stellar mass, R , and the fluxes of the required emission lines are well known. To each of 13 –the galaxies we will apply a value of the correction corresponding to its stellar mass and coverage ofthe SDSS fiber (normalized to R ) taken at random from the corresponding CDF. The differencebetween the oxygen abundances estimated from the flux of the SDSS fiber and that obtained usingthe aperture correction as described above was computed for each galaxy using the two indicatorsN2 and O3N2. Then, the median value of these differences was computed for five stellar mass bins:log M ∗ /M ⊙ ∈ [8.5,9.1], [9.1,9.7], [9.7,10.3], [10.3,10.9] and [10.9,11.5]. We repeated this processa total of 25 times, and computed the average value of the median of the differences for eachof these four mass bins. Table 25 shows the results of this simulation split in six redshift bins: z ∈ [0.02,0.05], [0.05,0.10], [0.10,0.15], [0.15,0.20], [0.20,0.25] and [0.25,0.30].In this study the aperture effect depends on two different aspects: on the one side, the fractionof galaxy covered by the SDSS fiber is partly driven by the redshift of the galaxies. On the otherhand, the aperture effect depends on the stellar mass of the galaxy. Thus, table 25 must show acombination of these effects. The first thing we note is that the maximum average aperture effectmeasured with these two calibrations at the redshifts and stellar mass ranges probed is of the orderof ≈ .
047 dex ( ≈ . < log M ∗ /M ⊙ < . . × R opt (Pilyuginet al. 2004; Moustakas et al. 2006). Although this relation links these two quantities, still furtherinformation is required in order to get information about the chemical evolution of spiral galaxies.
5. Conclusions
This paper presents the growth curves taken through circular apertures of several emission linefluxes for a sample of spiral galaxies from the CALIFA project. These curves allow to study theeffect of estimating galactic properties from the light of a circular aperture covering only partiallythe spatial extent of a galaxy instead of using the integrated light. The main conclusions arisingfrom this work are the following: • Whereas the median H α growth curves are insensitive to inclination, morphology and total 14 –stellar mass of the studied galaxies, our analysis documents a strong dependence of theregistered H α luminosity on the aperture size (consequently, also on redshift). • The median H α /H β growth curves are insensitive to the inclination, morphological types andstellar masses of the galaxies, and shows a mild trend with a maximum for small aperturessmoothly decreasing towards large apertures, which means that the extinction is overesti-mated on average when observing galaxies through small apertures. • The median N2 growth curves are also insensitive to the inclinations, morphological typesand stellar masses of the galaxies, showing a decreasing trend towards large apertures. Thismeans that the oxygen abundance is overestimated when observing through small apertures. • The median O3N2 growth curves are insensitive to the inclinations, and show higher values forgalaxies of earlier morphological types and log M ∗ /M ⊙ > . • When applying our aperture corrections to a sample of SDSS galaxies with 0 . ≤ z ≤ . ≈
11% with respect to the fiber-based ones.This work has shown that although the median aperture corrections for oxygen abundance arealways small, the dispersions around these median values become very large for small apertures,thus preventing the use of aperture corrections for studies of individual galaxies unless a very largeuncertainty is assumed. A more detailed study on the aperture effects on some individual emissionline ratios will be presented in a forthcoming paper.This study made use of the data provided by the Calar Alto Legacy Integral Field Area(CALIFA) survey ( http://califa.caha.es/ ). The CALIFA collaboration would like to thankthe IAA-CSIC and MPIA-MPG as major partners of the observatory, and CAHA itself, for theunique access to telescope time and support in manpower and infrastructures. The CALIFA col-laboration also thanks the CAHA staff for the dedication to this project. Based on observationscollected at the Centro Astron´omico Hispano Alem´an (CAHA) at Calar Alto, operated jointly bythe Max-Planck-Institut f¨ur Astronomie and the Instituto de Astrof´ısica de Andaluc´ıa (CSIC).We thank the Viabilidad, Dise˜no, Acceso y Mejora funding program ICTS-2009-10, for support-ing the initial developement of this project. JIP, JVM, CK, EPM and SDP acknowledge finan-cial support from the Spanish MINECO under grant AYA2010-21887-C04-01, and from Juntade Andaluc´ıa Excellence Project PEX2011-FQM7058. CCT and ACM also thank the supportfrom the Plan Nacional de Investigaci´on y Desarrollo funding program AYA2013-46724-P. JMGacknowledges support by Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT) through the Fellow-ship SFRH/BPD/66958/2009 and POPH/FSE (EC) by FEDER funding through the programPrograma Operacional de Factores de Competitividade (COMPETE). PP is supported by FCT 15 –through the Investigador FCT Contract No. IF/01220/2013 and POPH/FSE (EC) by FEDERfunding through the program COMPETE. JMG&PP also acknowledge support by FCT underproject FCOMP-01-0124-FEDER-029170 (Reference FCT PTDC/FIS-AST/3214/2012), funded byFCT-MEC (PIDDAC) and FEDER (COMPETE). They also acknowledge support by the exchangeprogramme Study of Emission-Line Galaxies with Integral-Field Spectroscopy (SELGIFS, FP7-PEOPLE-2013-IRSES-612701), funded by the EU through the IRSES scheme. FFRO acknowl-edges the exchange programme Study of Emission-Line Galaxies with Integral-Field Spectroscopy(SELGIFS, FP7-PEOPLE-2013-IRSES-612701), funded by the EU through the IRSES scheme.Support for LG is provided by the Ministry of Economy, Development, and Tourism’s MillenniumScience Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics,MAS. LG acknowledges support by CONICYT through FONDECYT grant 3140566. This re-search has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by theJet Propulsion Laboratory, California Institute of Technology, under contract with the NationalAeronautics and Space Administration. We acknowledge the usage of the HyperLeda database( http://leda.univ-lyon1.fr ). Funding for SDSS-III has been provided by the Alfred P. SloanFoundation, the Participating Institutions, the National Science Foundation, and the U.S. Depart-ment of Energy Office of Science. SDSS-III is managed by the Astrophysical Research Consortiumfor the Participating Institutions of the SDSS-III Collaboration including the University of Arizona,the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University,University of Florida, the French Participation Group, the German Participation Group, HarvardUniversity, the Instituto de Astrof´ısica de Canarias, the Michigan State/Notre Dame/JINA Par-ticipation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max PlanckInstitute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico StateUniversity, New York University, Ohio State University, Pennsylvania State University, Universityof Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, Uni-versity of Utah, Vanderbilt University, University of Virginia, University of Washington, and YaleUniversity. The SDSS-III web site is . REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
19 –Fig. 1.—
Left: R op vs. R for the spiral galaxies of the CALIFA sample. Solid, dashed anddot-dashed lines correspond to R op = R , R op = 2 × R and R op = 4 × R respectively. Right: R op vs. R eff for the spiral galaxies of the CALIFA sample. Solid, dashed and dot-dashed linescorrespond to R op = R eff , R op = 2 × R eff and R op = 3 × R eff respectively.Fig. 2.— Left: x ( α ) for CALIFA spiral galaxies with R <
9” normalized to 4 R . Solidlines correspond to median values. Dashed lines contain 68.2% of the values. Right: x ( α eff ) forCALIFA spiral galaxies with R eff < .
4” normalized to 2.2 R eff . 20 –Fig. 3.— x ( α ) (left) and x ( α eff ) (right) for galaxies with different inclination. Solid lines corre-spond to median values. Dashed lines contain 68.2% of the distribution. Face (blue) and edge (red)galaxies have b/a > . b/a ≤ . x ( α ) (left) and x ( α eff ) (right) for galaxies with different morphological types. Solid linescorrespond to median values. Dashed lines contain 68.2% of the distribution. Sa-Sbc and Sc-Smgalaxies are represented in blue and red respectively. The numbers within the plot box indicatethe sizes of the samples. 21 –Fig. 5.— x ( α ) (left) and x ( α eff ) (right) for galaxies with different stellar masses. Solid linescorrespond to median values. Dashed lines contain 68.2% of the distribution. Galaxies withlog M ∗ /M ⊙ ≤ . M ∗ /M ⊙ > . x ( αβ ) (left) and x ( αβ eff ) (right) for galaxies with different inclination. Solid linescorrespond to median values. Dashed lines contain 68.2% of the distribution. Face (blue) and edge(red) galaxies have b/a > . b/a ≤ . x ( αβ ) (left) and x ( αβ eff ) (right) for galaxies with different morphological types. Solidlines correspond to median values. Dashed lines contain 68.2% of the distribution. Sa-Sbc andSc-Sm galaxies are represented in blue and red respectively. The numbers within the plot boxindicate the sizes of the samples. 23 –Fig. 8.— x ( αβ ) (left) and x ( αβ eff ) (right) for galaxies with different stellar masses. Solid linescorrespond to median values. Dashed lines contain 68.2% of the distribution. Galaxies withlog M ∗ /M ⊙ ≤ . M ∗ /M ⊙ > . x (N2 ) (left) and x (N2 eff ) (right) for galaxies with different inclination. Solid linescorrespond to median values. Dashed lines contain 68.2% of the distribution. Face (blue) and edge(red) galaxies have b/a > . b/a ≤ . x (N2 ) (left) and x (N2 eff ) (right) for galaxies with different morphological types. Solidlines correspond to median values. Dashed lines contain 68.2% of the distribution. Sa-Sbc andSc-Sm galaxies are represented in blue and red respectively. The numbers within the plot boxindicate the sizes of the samples. 25 –Fig. 11.— x (N2 ) (left) and x (N2 eff ) (right) for galaxies with different stellar masses. Solidlines correspond to median values. Dashed lines contain 68.2% of the distribution. Galaxies withlog M ∗ /M ⊙ ≤ . M ∗ /M ⊙ > . x (O3N2 ) (left) and x (O3N2 eff ) (right) for galaxies with different inclination. Solidlines correspond to median values. Dashed lines contain 68.2% of the distribution. Face (blue) andedge (red) galaxies have b/a > . b/a ≤ . x (O3N2 ) (left) and x (O3N2 eff ) (right) for galaxies with different morphological types.Solid lines correspond to median values. Dashed lines contain 68.2% of the distribution. Sa-Sbcand Sc-Sm galaxies are represented in blue and red respectively. The numbers within the plot boxindicate the sizes of the samples. 27 –Fig. 14.— x (O3N2 ) (left) and x (O3N2 eff ) (right) for galaxies with different stellar masses. Solidlines correspond to median values. Dashed lines contain 68.2% of the distribution. Galaxies withlog M ∗ /M ⊙ ≤ . M ∗ /M ⊙ > . α flux (top left), H α /H β (top right), N2 (bottom left) and O3N2 (bottomright) contained in the SDSS aperture at different redshifts to the corresponding values within acircular aperture of 10 kpc diameter as a function of redshift for the (52) CALIFA spirals whose10 kpc diameter aperture is completely covered by PMAS/PPAK. Lower dashed, solid and upperdashed lines correspond to 15.86%, 50% and 84.14% of the distributions. 29 –Fig. 16.— Ratio of the H α flux (top left), H α /H β (top right), N2 (bottom left) and O3N2 (bottomright) contained in the SDSS aperture at different redshifts to the corresponding values within acircular aperture of 3.3 kpc diameter as a function of redshift for the (96) CALIFA spirals whose3.3 kpc diameter aperture is completely covered by PMAS/PPAK. Lower dashed, solid and upperdashed lines correspond to 15.86%, 50% and 84.14% of the distributions. 30 –Fig. 17.— Ratio of the H α flux (top left), H α /H β (top right), N2 (bottom left) and O3N2 (bottomright) contained in the SAMI aperture at different redshifts to the corresponding values within acircular aperture of 10 kpc diameter as a function of redshift for the (52) CALIFA spirals whose10 kpc diameter aperture is completely covered by PMAS/PPAK. Lower dashed, solid and upperdashed lines correspond to 15.86%, 50% and 84.14% of the distributions. 31 –Fig. 18.— Ratio of the H α flux (top left), H α /H β (top right), N2 (bottom left) and O3N2 (bottomright) contained in the SAMI aperture at different redshifts to the corresponding values within acircular aperture of 3.3 kpc diameter as a function of redshift for the (96) CALIFA spirals whose3.3 kpc diameter aperture is completely covered by PMAS/PPAK. Lower dashed, solid and upperdashed lines correspond to 15.86%, 50% and 84.14% of the distributions. 32 –Fig. 19.— Left: x (OH ) for two different morphological type bins, and the three empiricalcalibrations of N2: PP04, PMC09 and M13. Right: x (OH ) for two different morphological typebins, and the three empirical calibrations of O3N2: PP04, PMC09 and M13.Fig. 20.— Left: x (OH ) for two different morphological type bins, estimated with N2 (M13).Solid lines correspond to median values. Dashed lines contain 68.2% of the distribution. Sa-Sbcand Sc-Sm galaxies are represented in blue and red respectively. Right:
Same as left for x (OH eff ). 33 –Fig. 21.— Left: x (OH ) for two different stellar mass bins, estimated with N2 (M13). Solidlines correspond to median values. Dashed lines contain 68.2% of the distribution. Galaxies withlog M ∗ /M ⊙ ≤ . M ∗ /M ⊙ > . Right:
Same as left for x (OH eff ). 34 –Fig. 22.— Left: x (OH ) for two different morphological type bins, estimated with O3N2 (M13).Solid lines correspond to median values. Dashed lines contain 68.2% of the distribution. Sa-Sbcand Sc-Sm galaxies are represented in blue and red respectively. Right:
Same as left for x (OH eff ).Fig. 23.— Left: x (OH ) for two different stellar mass bins, estimated with O3N2 (M13). Solidlines correspond to median values. Dashed lines contain 68.2% of the distribution. Galaxies withlog M ∗ /M ⊙ ≤ . M ∗ /M ⊙ > . Right:
Same as left for x (OH eff ). 35 –Fig. 24.— BPT diagram corresponding to the SDSS sample. 36 –Fig. 25.— Left:
Cumulative Distribution Function (CDF) of x (OH ) estimated with N2, forgalaxies with log M ∗ /M ⊙ ≤ . Right:
Cumulative Distri-bution Function (CDF) of x (OH ) estimated with N2, for galaxies with log M ∗ /M ⊙ > . Left:
Cumulative Distribution Function (CDF) of x (OH ) estimated with O3N2,for galaxies with log M ∗ /M ⊙ ≤ . Right:
CumulativeDistribution Function (CDF) of x (OH ) estimated with O3N2, for galaxies with log M ∗ /M ⊙ > . α growth curve and average dispersion of IP13 with the ones obtainedin this work for all the spiral galaxies disregarding the stellar mass, morphological types andinclination. r / R x ( α ) σ ( x ( α )) x ( α ) σ ( x ( α ))(IP13) (This work)0.3 0.091 0.074 0.085 0.0600.5 0.194 0.119 0.182 0.1020.7 0.301 0.156 0.283 0.1260.9 0.419 0.158 0.397 0.1321.1 0.530 0.146 0.506 0.1341.3 0.629 0.130 0.620 0.1211.5 0.718 0.117 0.715 0.1211.7 0.798 0.101 0.801 0.1041.9 0.854 0.079 0.865 0.0782.1 0.917 0.070 0.920 0.0502.3 0.961 0.039 0.965 0.027 38 –Table 2: Description of the sizes of the two subsamples after each of the filters imposed. S S eff Initial sample 402 Initial sample 394 † Excluding Es and S0s 301 Excluding Es and S0s 296Excluding AGNs 212 Excluding AGNs 208 R ≤ .
4” 171 R eff ≤
24” 138 f (H α ) ≥ σ (H α )/ f (H α ) ≤ .
333 165 f (H α ) ≥ σ (H α )/ f (H α ) ≤ .
333 133 † The initial number of galaxies in S eff is different than that in S because R eff could not bedetermined for 8 galaxies, and thus they are excluded from the analysis. 39 –Table 3: Basic properties of the samples S and S eff : Median values of the stellar masses, R and R eff ; Number of galaxies split in two bins of morphological types. S S eff h log M ∗ /M ⊙ i h R i (”) 11.04 h R eff i (”) 20.31Sa+Sab+Sb+Sbc 107 85Sc+Scd+Sd+Sdm+Sm 85 48 40 –Table 4: x ( α ) for two bins of morphological types assuming the same weight for all the galaxies.(1) Aperture radius in units of R . (2)-(4) Values of x (H α ) corresponding to 15.86%, 50% and84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x (H α ) corresponding to 15.86%,50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x (H α ) correspondingto 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R Sa-Sbc Sc-Sdm All − σ x ( α ) + σ − σ x ( α ) + σ − σ x ( α ) + σ x ( α eff ) for two bins of morphological types assuming the same weight for all the galaxies.(1) Aperture radius in units of R eff . (2)-(4) Values of x (H α ) corresponding to 15.86%, 50% and84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x (H α ) corresponding to 15.86%,50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x (H α ) correspondingto 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R eff Sa-Sbc Sc-Sdm All − σ x ( α eff ) + σ − σ x ( α eff ) + σ − σ x ( α eff ) + σ x ( α ) for two bins of stellar masses assuming the same weight for all the galaxies. (1)Aperture radius in units of R . (2)-(4) Values of x (H α ) corresponding to 15.86%, 50% and 84.14%of the distribution for log M ∗ ≤ . x (H α ) corresponding to 15.86%,50% and 84.14% of the distribution for log M ∗ > . r / R log M ∗ ≤ . M ∗ > . − σ x ( α ) + σ − σ x ( α ) + σ x ( α eff ) for two bins of stellar masses assuming the same weight for all the galaxies. (1)Aperture radius in units of R eff . (2)-(4) Values of x (H α ) corresponding to 15.86%, 50% and 84.14%of the distribution for log M ∗ ≤ . x (H α ) corresponding to 15.86%,50% and 84.14% of the distribution for log M ∗ > . r / R eff log M ∗ ≤ . M ∗ > . − σ x ( α eff ) + σ − σ x ( α eff ) + σ x ( αβ ) for two bins of morphological types assuming the same weight for all the galaxies.(1) Aperture radius in units of R . (2)-(4) Values of x ( αβ ) corresponding to 15.86%, 50% and84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x ( αβ ) corresponding to 15.86%,50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x ( αβ ) correspondingto 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R Sa-Sbc Sc-Sdm All − σ x ( αβ ) + σ − σ x ( αβ ) + σ − σ x ( αβ ) + σ x ( αβ eff ) for two bins of morphological types assuming the same weight for all the galaxies.(1) Aperture radius in units of R eff . (2)-(4) Values of x ( αβ eff ) corresponding to 15.86%, 50% and84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x ( αβ eff ) corresponding to 15.86%,50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x ( αβ eff ) correspondingto 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R eff Sa-Sbc Sc-Sdm All − σ x ( αβ eff ) + σ − σ x ( αβ eff ) + σ − σ x ( αβ eff ) + σ x ( αβ ) for two bins of stellar masses assuming the same weight for all the galaxies.(1) Aperture radius in units of R . (2)-(4) Values of x ( αβ ) corresponding to 15.86%, 50% and84.14% of the distribution for log M ∗ ≤ . x ( αβ ) corresponding to15.86%, 50% and 84.14% of the distribution for log M ∗ > . r / R log M ∗ ≤ . M ∗ > . − σ x ( αβ ) + σ − σ x ( αβ ) + σ x ( αβ eff ) for two bins of stellar masses assuming the same weight for all the galaxies.(1) Aperture radius in units of R eff . (2)-(4) Values of x ( αβ eff ) corresponding to 15.86%, 50% and84.14% of the distribution for log M ∗ ≤ . x ( αβ eff ) corresponding to15.86%, 50% and 84.14% of the distribution for log M ∗ > . r / R eff log M ∗ ≤ . M ∗ > . − σ x ( αβ eff ) + σ − σ x ( αβ eff ) + σ x (N2 ) for two bins of morphological types assuming the same weight for all the galaxies.(1) Aperture radius in units of R . (2)-(4) Values of x (N2 ) corresponding to 15.86%, 50% and84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x (N2 ) corresponding to 15.86%,50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x (N2 ) correspondingto 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R Sa-Sbc Sc-Sdm All − σ x (N2 ) + σ − σ x (N2 ) + σ − σ x (N2 ) + σ x (N2 eff ) for two bins of morphological types assuming the same weight for all the galaxies.(1) Aperture radius in units of R eff . (2)-(4) Values of x (N2 eff ) corresponding to 15.86%, 50% and84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x (N2 eff ) corresponding to 15.86%,50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x (N2 eff ) correspondingto 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R eff Sa-Sbc Sc-Sdm All − σ x (N2 eff ) + σ − σ x (N2 eff ) + σ − σ x (N2 eff ) + σ x (N2 ) for two bins of stellar masses assuming the same weight for all the galaxies.(1) Aperture radius in units of R . (2)-(4) Values of x (N2 ) corresponding to 15.86%, 50% and84.14% of the distribution for log M ∗ ≤ . x (N2 ) corresponding to15.86%, 50% and 84.14% of the distribution for log M ∗ > . r / R log M ∗ ≤ . M ∗ > . − σ x (N2 ) + σ − σ x (N2 ) + σ x (N2 eff ) for two bins of stellar masses assuming the same weight for all the galaxies.(1) Aperture radius in units of R eff . (2)-(4) Values of x (N2 eff ) corresponding to 15.86%, 50% and84.14% of the distribution for edge-on log M ∗ ≤ . x (N2 eff ) corre-sponding to 15.86%, 50% and 84.14% of the distribution for face-on log M ∗ > . r / R eff log M ∗ ≤ . M ∗ > . − σ x (N2 eff ) + σ − σ x (N2 eff ) + σ x (O3N2 ) for two bins of morphological types assuming the same weight for all thegalaxies. (1) Aperture radius in units of R . (2)-(4) Values of x (O3N2 ) corresponding to15.86%, 50% and 84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x (O3N2 ) cor-responding to 15.86%, 50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x (O3N2 ) corresponding to 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R Sa-Sbc Sc-Sdm All − σ x (O3N2 ) + σ − σ x (O3N2 ) + σ − σ x (O3N2 ) + σ x (O3N2 eff ) for two bins of morphological types assuming the same weight for all thegalaxies. (1) Aperture radius in units of R eff . (2)-(4) Values of x (O3N2 eff ) corresponding to15.86%, 50% and 84.14% of the distribution for Sa-Sbc galaxies. (5)-(7) Values of x (O3N2 eff ) cor-responding to 15.86%, 50% and 84.14% of the distribution for Sc-Sdm galaxies. (8)-(10) Values of x (O3N2 eff ) corresponding to 15.86%, 50% and 84.14% of the distribution for all galaxies. r / R eff Sa-Sbc Sc-Sdm All − σ x (O3N2 eff ) + σ − σ x (O3N2 eff ) + σ − σ x (O3N2 eff ) + σ x (O3N2 ) for two bins of stellar masses assuming the same weight for all the galaxies.(1) Aperture radius in units of R . (2)-(4) Values of x (O3N2 ) corresponding to 15.86%, 50% and84.14% of the distribution for log M ∗ ≤ . x (O3N2 ) correspondingto 15.86%, 50% and 84.14% of the distribution for log M ∗ > . r / R log M ∗ ≤ . M ∗ > . − σ x (O3N2 ) + σ − σ x (O3N2 ) + σ x (O3N2 eff ) for two bins of stellar masses assuming the same weight for all the galaxies.(1) Aperture radius in units of R eff . (2)-(4) Values of x (O3N2 eff ) corresponding to 15.86%, 50% and84.14% of the distribution for log M ∗ ≤ . x (O3N2 eff ) correspondingto 15.86%, 50% and 84.14% of the distribution for log M ∗ > . r / R eff log M ∗ ≤ . M ∗ > . − σ x (O3N2 eff ) + σ − σ x (O3N2 eff ) + σ a + a x + a x + a x + a x + a x .Aperture Selection a a a a a a correction criterion x ( α ) All 0.0000 0.1599 0.5027 − − − − − M ∗ /M ⊙ ≤ . − . ≤ log M ∗ /M ⊙ − x ( αβ ) All 1.1253 0.0274 − − − − − − M ∗ /M ⊙ ≤ . − − − . ≤ log M ∗ /M ⊙ − − x (N2 ) All 0.0812 0.0477 − − − − − − − M ∗ /M ⊙ ≤ . − − . ≤ log M ∗ /M ⊙ − − x (O3N2 ) All − − − − − − − − − − − M ∗ /M ⊙ ≤ . − − − − . ≤ log M ∗ /M ⊙ − − − − x ( α eff ) All 0.0000 0.2469 1.8195 − − − − − − M ∗ /M ⊙ ≤ . − − . ≤ log M ∗ /M ⊙ − − x ( αβ eff ) All 1.1100 0.0648 − − − − − − M ∗ /M ⊙ ≤ . − − − . ≤ log M ∗ /M ⊙ − − − x (N2 eff ) All 0.0729 0.0320 − − − − − − M ∗ /M ⊙ ≤ . − − − . ≤ log M ∗ /M ⊙ − − x (O3N2 eff ) All − − − − − − − − − − − − M ∗ /M ⊙ ≤ . − − − − . ≤ log M ∗ /M ⊙ − − − α flux contained in the SDSS or SAMI apertures at different redshifts tothe H α flux within a circular aperture of 10 or 3.3 kpc diameter for the CALIFA spirals whose10 or 3.3 kpc diameter aperture is completely covered by PMAS/PPAK. (1) Angular diameterof SDSS/SAMI aperture † . (2) Linear diameter of fixed reference aperture. (3) Redshift. (4)-(6)Values corresponding to 15.86%, 50% and 84.14% of the distribution. Only the first values arelisted. A complete version of the table, including SAMI apertures and fixed circular apertures of3.3 kpc diameter, are be available in the electronic edition.Ang. Diam. Lin. Diam. z − σ ( α Ang / α Lin ) + σ (“) (kpc)3.0 10. 0.010 0.030 0.061 0.2073.0 10. 0.011 0.030 0.060 0.2063.0 10. 0.012 0.030 0.059 0.2053.0 10. 0.013 0.029 0.058 0.2043.0 10. 0.014 0.029 0.057 0.2043.0 10. 0.015 0.029 0.056 0.203 † Where the 3” aperture is for SDSS and the 15” aperture is for SAMI.Table 22: Ratio of the H α /H β contained in the SDSS or SAMI apertures at different redshifts tothe H α /H β within a circular aperture of 10 or 3.3 kpc diameter for the CALIFA spirals whose10 or 3.3 kpc diameter aperture is completely covered by PMAS/PPAK. (1) Angular diameterof SDSS/SAMI aperture † . (2) Linear diameter of fixed reference aperture. (3) Redshift. (4)-(6)Values corresponding to 15.86%, 50% and 84.14% of the distribution. Only the first values arelisted. A complete version of the table, including SAMI apertures and fixed circular apertures of3.3 kpc diameter, are be available in the electronic edition.Ang. Diam. Lin. Diam. z − σ ( αβ Ang / αβ Lin ) + σ (“) (kpc)3.0 10. 0.010 0.985 1.120 1.2873.0 10. 0.011 0.985 1.120 1.2883.0 10. 0.012 0.985 1.120 1.2883.0 10. 0.013 0.984 1.120 1.2893.0 10. 0.014 0.984 1.120 1.2893.0 10. 0.015 0.984 1.120 1.290 † Where the 3” aperture is for SDSS and the 15” aperture is for SAMI. 58 –Table 23: Difference of the N2 contained in the SDSS or SAMI apertures at different redshiftsto the N2 within a circular aperture of 10 or 3.3 kpc diameter for the CALIFA spirals whose10 or 3.3 kpc diameter aperture is completely covered by PMAS/PPAK. (1) Angular diameterof SDSS/SAMI aperture † . (2) Linear diameter of fixed reference aperture. (3) Redshift. (4)-(6)Values corresponding to 15.86%, 50% and 84.14% of the distribution. Only the first values arelisted. A complete version of the table, including SAMI apertures and fixed circular apertures of3.3 kpc diameter, are be available in the electronic edition.Ang. Diam. Lin. Diam. z − σ (N2 Ang − N2 Lin ) + σ (“) (kpc)3.0 10. 0.010 0.012 0.079 0.2343.0 10. 0.011 0.011 0.079 0.2343.0 10. 0.012 0.011 0.079 0.2343.0 10. 0.013 0.011 0.079 0.2343.0 10. 0.014 0.011 0.079 0.2343.0 10. 0.015 0.011 0.080 0.233 † Where the 3” aperture is for SDSS and the 15” aperture is for SAMI.Table 24: Difference of the O3N2 contained in the SDSS or SAMI apertures at different redshiftsto the O3N2 within a circular aperture of 10 or 3.3 kpc diameter for the CALIFA spirals whose10 or 3.3 kpc diameter aperture is completely covered by PMAS/PPAK. (1) Angular diameterof SDSS/SAMI aperture † . (2) Linear diameter of fixed reference aperture. (3) Redshift. (4)-(6)Values corresponding to 15.86%, 50% and 84.14% of the distribution. Only the first values arelisted. A complete version of the table, including SAMI apertures and fixed circular apertures of3.3 kpc diameter, are be available in the electronic edition.Ang. Diam. Lin. Diam. z − σ (O3N2 Ang − O3N2
Lin ) + σ (“) (kpc)3.0 10. 0.010 -0.402 -0.180 0.0603.0 10. 0.011 -0.402 -0.180 0.0603.0 10. 0.012 -0.402 -0.181 0.0603.0 10. 0.013 -0.403 -0.181 0.0603.0 10. 0.014 -0.403 -0.181 0.0603.0 10. 0.015 -0.403 -0.181 0.060 † Where the 3” aperture is for SDSS and the 15” aperture is for SAMI. 59 –Table 25: Differential (fiber-based vs. integrated) oxygen abundance of the SDSS galaxies estimatedwith the N2 and O3N2 indicators at three redshift bins. (1) Stellar mass bin; (2) Number of galaxies;(3) Average over 25 random draws of the median values of logO/H
SDSS − logO/H int estimated usingN2; (4) Average over 25 random draws of the median values of logO/H SDSS − logO/H int estimatedusing O3N2. N gal h Median(∆ logO/H N2 ) i h Median(∆ logO/H
O3N2 ) i (dex) (dex)0 . < z < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . < z < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . < z < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . < z < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . < z < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . < z < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < . . ≤ log M ∗ /M ⊙ < ..