SHARDS: stellar populations and star formation histories of a mass-selected sample of 0.65<z<1.1 galaxies
Antonio Hernán-Caballero, Almudena Alonso-Herrero, Pablo G. Pérez-González, Nicolás Cardiel, Antonio Cava, Ignacio Ferreras, Guillermo Barro, Laurence Tresse, Emanuele Daddi, Javier Cenarro, Christopher J. Conselice, Rafael Guzmán, Jesús Gallego
aa r X i v : . [ a s t r o - ph . C O ] J un Mon. Not. R. Astron. Soc. , 1– ?? (2013) Printed 9 November 2018 (MN L A TEX style file v2.2)
SHARDS: stellar populations and star formation histories of amass-selected sample of 0.65 < z < Antonio Hern´an-Caballero, Almudena Alonso-Herrero, , Pablo G. P´erez-Gonz´alez, , Nicol´as Cardiel, Antonio Cava, Ignacio Ferreras, Guillermo Barro, , Laurence Tresse, Emanuele Daddi, Javier Cenarro, Christopher J. Conselice, Rafael Guzm´an, and Jes ´us Gallego Instituto de F´ısica de Cantabria, CSIC-UC, Avenida de los Castros s / n, 39005, Santander, Spain. E-mail: [email protected] Augusto G. Linares Senior Research Fellow Departamento de Astrof´ısica y Ciencias de la Atm´osfera, Facultad de CC. F´ısicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain Associate Astronomer at Steward Observatory, The University of Arizona, Tucson, USA Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK UCO / Lick Observatory, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA Aix Marseille Universit´e, CNRS, LAM (Laboratoire dAstrophysique de Marseille), UMR 7326, F-13388 Marseille, France CEA, Laboratoire AIM, Irfu / SAp, F-91191 Gif-sur-Yvette, France Centro de Estudios de F´ısica del Cosmos de Arag´on, Plaza San Juan 1, Planta 2, E-44001 Teruel, Spain School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, UK Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611, USA
Accepted ........ Received ........;
ABSTRACT
We report on results from the analysis of a stellar mass-selected (log(M ∗ / M ⊙ ) > < z < AB < ∼ n (4000), an excellent age indicator for the stellar populations of quiescentgalaxies] for all galaxies at z ∼ ∗ / M ⊙ ) ∼
9. The D n (4000) index cannot beresolved from broad-band photometry, and measurements from optical spectroscopic surveysare typically limited to galaxies at least ×
10 more massive. When combined with the rest-frame U-V colour, (U-V) r , D n (4000) provides a powerful diagnostic of the extinction a ff ectingthe stellar population that is relatively insensitive to degeneracies with age, metallicity or starformation history. We use this novel approach to estimate de-reddened colours and light-weighted stellar ages for individual sources. We explore the relationships linking stellar mass,(U-V) r , and D n (4000) for the sources in the sample, and compare them to those found in localgalaxies. The main results are: a) both D n (4000) and (U-V) r correlate with M ∗ . The dispersionin D n (4000) values at a given M ∗ increases with M ∗ , while the dispersion for (U-V) r decreasesdue to the higher average extinction prevalent in massive star-forming galaxies. b) for massivegalaxies, we find a smooth transition between the blue cloud and red sequence in the intrinsicU-V colour, in contrast with other recent results. c) at a fixed stellar age, we find a positivecorrelation between extinction and stellar mass. d) the fraction of sources with declining orhalted star formation increases steeply with the stellar mass, from ∼
5% at log(M ∗ / M ⊙ ) = ∼
80% at log(M ∗ / M ⊙ ) >
11, in agreement with downsizing scenarios.
Key words: galaxies: evolution – galaxies: high-redshift – galaxies: fundamental parameters– galaxies: stellar content – galaxies: statistics – infrared: galaxies
In the last decade it has been established that the colours andmorphologies of galaxies show bimodal distributions at leastup to z ∼ © A. Hern´an-Caballero et al.
Figure 1.
Dependency of the rest-frame U-V colour, (U-V) r , and the 4000 Å index (D n (4000); Balogh et al. 1999) with stellar age, extinction and metallicity.The tracks represent the evolution with time of the (U-V) r and logD n (4000) colours of an instantaneous burst for A V = / Z ⊙ = / Z ⊙ = V for both (U-V) r and logD n (4000) . The segmented arrows represent the e ff ect of A V =
1, 2,and 3 magnitudes assuming a Draine (2003) extinction law with Milky Way grain size distribution (Weingartner & Draine 2001) and R V = In the local Universe, massive galaxies (M ∗ > M ⊙ ) are typ-ically spheroids with old stellar populations, which define the so-called red sequence in a color-magnitude diagram (CMD), whilethe less massive ones (mostly discs) have young stellar popula-tions and reside in a more spread blue cloud (Strateva et al. 2001;Kau ff mann et al. 2003b; Baldry et al. 2004). Galaxies with inter-mediate colours (located in the so-called green valley) are less nu-merous and are considered to be either dusty star-forming systems,or galaxies transitioning from the blue cloud to the red sequenceafter switching o ff their star formation.At higher redshift, only increasingly massive galaxies be-long to the red sequence, and the total mass contained in it at z ∼ n (4000), is an excellent age indicator forthe stellar populations of quiescent galaxies (Balogh et al. 1999;Kau ff mann et al. 2003a,b; Kriek et al. 2006; Moresco et al. 2010).Since D n (4000) is much less a ff ected by extinction compared to theU-V colour (see Figure 1), it has also been used to separate star-forming and passively evolving galaxies (e.g. Vergani et al. 2008).Large spectroscopic surveys, in particular the Sloan Digi-tal Sky Survey, have provided a clear picture of the interdepen-dency of stellar mass, surface density, and star formation history(Kau ff mann et al. 2003b; Heavens et al. 2004; Panter et al. 2007;Cid Fernandes et al. 2007). Nevertheless, the spectra of stellar pop-ulations forming all their mass at z ∼ ∗ = M ⊙ galaxy at z = ∼
24 (AB) in the I band,which matches the current faint limit for the deepest spectroscopicsurveys, such as VVDS-deep (Le F`evre et al. 2004, 2005). Conse-quently, spectroscopic surveys favour the most massive galaxies,while the analysis of the stellar populations in lower-mass systemshas remained constrained by the limitations of broadband SEDs.Recently, Kriek et al. (2011) demonstrated that the 4000 Åbreak can be successfully measured in average SEDs frommedium-band photometry. In this work we use the ultra-deep(m AB < σ ) optical medium-band spectro-photometry pro-vided by the Survey for High-z Absorption Red and Dead Sources(SHARDS; P´erez-Gonz´alez et al. 2013) in combination with ac-curate photometric and spectroscopic redshifts and stellar massesfrom the Rainbow database (P´erez-Gonz´alez et al. 2008; hereafterPG08) to analyse the stellar populations and star formation histo-ries of a mass-selected sample of galaxies at 0.65 < z < in the GOODS-North field with GTC / OSIRIS in 24 contiguous medium-band(R ∼
50) filters covering the spectral range 500–950 nm. At the time https: // rainbowx.fis.ucm.es © , 1– ?? tellar populations of z ∼ of this writing, the entire survey area has been observed in the 15filters covering the spectral range 636–883 nm, and one half of thearea has also been observed in the F619W17 filter (central wave-length: 619 nm, FWHM: 17 nm).We measure the 4000 Å index in the SHARDS SED of in-dividual galaxies, and demonstrate that SHARDS photometry of-fers accurate estimates (when compared to higher resolution spec-troscopy) if corrected for the limited spectral resolution. We alsoexplore the relationships linking stellar mass, rest-frame (U-V)colour, and D n (4000) index for the sources in the sample, andcompare them to those found in local galaxies. Using a novel ap-proach, we combine information from the restframe (U-V) colourand D n (4000) to obtain an estimate of the extinction a ff ecting thestellar population that is relatively insensitive to degeneracies withage, metallicity, and SFH.The paper is structured as follows: §2 describes the sampleselection and basic sample properties. §3 describes the methodused to measure the strength of the 4000 Å break in the SHARDSphotometry, its uncertainties, and the calibration performed usinghigher resolution spectra. §4 presents the main results and §5 dis-cusses the implications for the downsizing scenario. Throughoutthis paper, we use a cosmology with H =
70 km s − Mpc − , Ω M = Ω Λ = In this paper we analyse a stellar mass selected sample. Our parentsample is the GOODS-North catalog from Rainbow (PG08), withIRAC 3.6 µ m as the selection band. The IRAC catalog is estimatedto be 75% (90%) complete at S . = µ Jy.We restrict the sample to galaxies within the 141 arcmin areasurveyed by SHARDS, and also apply stellar mass and redshiftconstraints to ensure a highly complete sample with reliable mea-surements of the 4000 Å break in the SHARDS SED (see §2.4 forthe details on the sample selection).The SHARDS filterset consists of 24 contiguous medium-band optical filters. All of them have FWHM =
170 Å except thetwo reddest ones, which have FWHM =
350 Å. As of May 2013SHARDS observations are still ongoing, and the current spectralcoverage is limited to 16 filters spanning the 619–883 nm range.The reduction and calibration procedures applied to SHARDSdata are described in great detail in P´erez-Gonz´alez et al. (2013).We produced source catalogs by merging the lists of sources de-tected in individual filters, and then forcing measurements at allbands. The FWHM of the point spread function (PSF) of the im-ages varies between 0.78” and 1.05”, depending on the observingconditions.Photometry was extracted using apertures of radii r = ff erence between photometry in apertures with radii0.88” and 1” is < ff ected.The median SNR increase going from 0.88” to 1” is 4% for brightsources (m < < m <
26 sources.We found the closest SHARDS counterpart to each Rainbowsource using a 1” search radius. However, the typical distance ismuch lower (median: 0.27”, 95th percentile: 0.6”). Some Rainbowsources do not have a SHARDS counterpart within 1”. These turnout to be mostly faint sources in the vicinity of a bright star. Since they represent a small fraction ( < ff ected. The GOOODS-N field has been thoroughly explored by redshiftsurveys, resulting in a large fraction of sources having spectro-scopic redshifts down to very faint magnitudes. We use the spectro-scopic redshift catalog from the Rainbow database, which containsreliable spectroscopic redshifts for 80% of the sources brighter than R =
24. However, since we aim at a mass-complete sample, pho-tometric redshifts are required to avoid underepresentation of thefaintest sources within our mass and redshift limits.The photometric redshifts of Rainbow sources are describedin PG08. They use standard template-fitting through χ minimi-sation with a large set of SPS models covering a range of starformation histories and extinction. A preliminary catalog of pho-tometric redshifts using both broadband and SHARDS photome-try is also available for sources brighter than K =
24 (Ferreras etal., in preparation). It uses a template-matching technique, compar-ing both broadband photometry (from U to Spitzer / IRAC 3.6 µ m)and the medium band SHARDS data with a grid of 2000 synthetictemplates built from the models of Bruzual & Charlot (2003). Themodels explore a wide range of star formation histories, includingdust and emission lines. A comparison with the available spectro-scopic redshifts in GOODS-N gives an accuracy ∆ ( z ) / (1 + z ) = K <
24 in the red-shift interval of our working sample (with a 1- σ scatter about themedian of just 0 . ∼ The procedure used to estimate stellar masses is described ingreat detail by PG08. Very briefly, they used a maximum likeli-hood estimator to find the SPS model that best fits all the avail-able photometric data points for wavelengths < µ m (rest-frame).The stellar emission in the models was taken from the PEGASEcode (Fioc& Rocca-Volmerange 1997) assuming a Salpeter (1955)IMF with 0.1 < M ∗ / M ⊙ < τ and age t [i.e, SFR( t ) ∝ e − t /τ ]. Stellar masses calculated in this way are con-sidered to be accurate to within a factor of 2–3. The 75% com-pleteness limit of Rainbow for a passively evolving population is atlog(M ∗ / M ⊙ ) = z = ∗ / M ⊙ ) = z = ∗ ∼ . M ⊙ galaxies at theseredshifts are actively forming stars and are therefore significantlybrighter than this limit. Since only 7% of galaxies in the 9.0–9.5mass interval are red [(U-V) r > ∗ ∼ . M ⊙ . Rest-frame optical colours are frequently used to distinguish youngfrom old galaxies in photometric surveys (e.g. Strateva et al. 2001;Blanton et al. 2003; Baldry et al. 2004). This is because older stel-lar populations usually have redder optical SEDs compared toyounger ones (albeit extinction by dust can also redden the opti-cal SED of a young galaxy, see Figure 1).We compute rest-frame magnitudes in several UV and opti-cal broadband filters by convolving the SPS model that best fits the © , 1– ?? A. Hern´an-Caballero et al. broadband SED of each source with the filter transmission curve, asdescribed in PG08. The broad spectral coverage of Rainbow pho-tometry implies that rest-frame photometry is interpolated betweenobserved bands. Owing to the accurate photometric redshifts, theuncertainty in rest-frame colours is comparable to the uncertaintyin observed colours, ∼ r , which is particularly sensitive to theage and metallicity of the stellar population because it straddlesthe 4000 Å break, and has been widely used in the literature (e.g.Sandage & Visvanathan 1978; Bower et al. 1992; Bell et al. 2004;Silverman et al. 2009; Cardamone et al. 2010). The current wavelength coverage of the SHARDS photometry al-lows for measurement of the 4000 Å break in sources at red-shift 0.65 z z ∼ ∗ > . M ⊙ sources. In summary, the selection criteriaare as follows:i) Rainbow source in the GOODS-North field with a 3.6 µ mdetectionii) within the area covered by the SHARDS surveyiii) 0.65 z ∗ / M ⊙ ) > / SHARDS sources meeting these cri-teria. Table 1 summarises the overall properties of the sample. 837[51%] of the sources in the sample have reliable spectroscopic red-shifts (hereafter, the z spec subsample) and the remaining 807 [49%]depend on a photometric redshift estimate (hereafter, the z phot sub-sample). 562 of the z phot sources have redshift estimates from thecombined SHARDS and broadband SEDs, while the remaining 245have redshifts from broadband alone.The redshift distribution (Figure 3) is rather inhomogeneousdue to the small size of the survey area, which makes it sensitive tolarge scale structure. However, we consider the impact of environ-ment on the results of this work to be negligible (see §4.3).Stellar masses could be overestimated in sources where emis-sion from an AGN increases the observed flux in the near- and mid-infrared bands. A cross-correlation with the Chandra 2 Ms catalogfrom Alexander et al. (2003) finds 56 X-ray sources in the mass-selected sample, but 54 out of the 56 show a clear 1.6 µ m bump,suggesting the stellar population dominates the rest-frame near-infrared emission (Hern´an-Caballero et al., in preparation; see alsoAlonso-Herrero et al. 2008).Figure 4 shows the distribution of the optical magnitudes,measured in apertures of radius 0.88 arcseconds, for two SHARDSbands close to the blue and red ends of the SHARDS spectral range,namely F636W17 and F857W17. The magnitude distribution peaksat m =
25 (24) in the F636W17 (F857W17) bands. Note that thereduction in the number counts for fainter magnitudes is due tothe redshift and mass constraints of the sample selection and notthe depth of the SHARDS data, which reaches m = σ ) in allbands (P´erez-Gonz´alez et al. 2013).The typical F636W17-F857W17 color index is ∼ > Figure 2.
Stellar masses versus redshift for sources with spectroscopic(blue) and photometric (grey) redshifts studied in this work. The solid greenline represents the 75% completeness limit of Rainbow for a passivelyevolving stellar population (PG08).
Figure 3.
Redshift distribution for the sources in the sample. The blacksolid line represents the total density of sources per unit of redshift, whilegrey bars and blue spikes represent the populations with photometric andspectroscopic redshift, respectively.
The break in the stellar continuum at 4000 Å is the strongest discon-tinuity in the optical spectrum of galaxies older than ∼ ff ectively decreasing the opacity, and therefore O and B type starshave much weaker breaks compared to later spectral types (Bruzual1983). Since hot (massive) stars have short lives, the strength of the4000 Å break for a single stellar population (SSP) increases withits age. There is also a dependency with the metallicity, but it onlybecomes significant for old stellar populations (see Figure 1). Inthe integrated spectrum of a galaxy, emission from hot young starscan easily outshine the old population and produce a weak 4000 Å © , 1– ?? tellar populations of z ∼ Figure 4.
Distribution of optical magnitudes in the SHARDS bandsF636W17 (blue) and F857W15 (red) for sources in the mass-selected sam-ple. break even if they only represent a small fraction of the total stellarmass in the galaxy. Therefore, the 4000 Å break provides a light-weighted characteristic age for the galaxy, which is close to themass-weighted age only for passively evolving galaxies.The strength of the 4000 Å break is commonly measured us-ing one of two definitions: the “regular” one, D(4000), measures theratio between average spectral flux densities (f ν ) in the rest-framebands [4050,4250] and [3750,3950] Å (Bruzual 1983; Hamilton1985), while the “narrow” index, D n (4000), uses the ratio betweenthe bands at [4000,4100] and [3850,3950] Å (Balogh et al. 1999).The narrow index has the advantage of being less sensitive to ex-tinction and is the preferred choice in most recent studies (e.g.Kau ff mann et al. 2003b; Martin et al. 2007; Silverman et al. 2009;Gobat et al. 2012).To calculate the average f ν in each of these bands, we shift theSHARDS SED to the rest-frame of the source, and perform a linearinterpolation of the spectrum between adjacent photometric points.Visual inspection of all the individual SHARDS SEDs reveals66 sources with features close to 4000 Å rest-frame that do notcorrespond with a 4000 Å break. Only 8 out of these 66 sourceshave spectroscopic redshifts. This suggests many of them couldhave larger than usual redshift errors. We cautiously put aside thesesources in the analysis of the 4000 Å break strengths. Since theyrepresent just 4% of the sample, our results will not be significantlya ff ected.There are three main sources of uncertainty a ff ecting the4000 Å break measurements: photometric errors, interpolation er-rors, and redshift uncertainty. We discuss them in the following.Photometric errors are lower than 0.1 magnitudes for 83% ofsources in the F636W17 band, and 93% in the F857W17 band.Nevertheless, the correlation between stellar mass and optical mag-nitude implies that the photometric errors increase with decreasingstellar masses. For galaxies in the lowest bin of mass consideredhere (9.0 log(M ∗ / M ⊙ ) < Figure 5.
Rest-frame 300–450 nm SHARDS SED of four representativesources from the sample. Error bars represent the 1- σ uncertainty due tonoise variance in the flux; the uncertainty in the photometric zero-point(0.05–0.07 magnitudes) is not included. The grey and red bars representthe bands that define the D(4000) and D n (4000) indices, respectively. Thelarge spike at ∼
375 nm is due to the [O ii ] 3727 Å emission line enteringone of the SHARDS filters. ing the D n (4000) index, and 2 or 3 in the case of the D(4000) index.Figure 5 shows the SHARDS SED and integration bands for a fewtypical sources.Compared to a high resolution spectrum, the degradation inthe spectral resolution introduced by the convolution with the trans-mission profiles of the SHARDS filterset reduces the contrast of the4000 Å break, and thus it tends to decrease the measurement of theindex. This decrement is larger for D n (4000) compared to D(4000).For sources with intense emission in the [O ii ] 3727 Å line, theblue band defining the D(4000) index can be contaminated (seetop left panel in Figure 5), reducing the apparent strength of thebreak. To mitigate this issue, in sources with clear [O ii ] emissionwe substitute the observed flux in the a ff ected band by a log-linearinterpolation of the adjacent ones.To quantify the influence of the photometric and interpolationerrors in the 4000 Å break measurement, we obtained syntheticSHARDS photometry on a large sample of optical spectra drawnfrom the zCOSMOS (Lilly et al. 2007) Data Release 2. We com-pared D(4000) and D n (4000) values measured in the synthetic pho-tometry with those from the full-resolution spectrum, and obtaineda calibration that converts raw D(4000) values into interpolationcorrected D n (4000) values. Our procedure for obtaining the syn-thetic photometry and the calibration is similar to that described byKriek et al. (2011), but it uses real spectra as reference instead ofSPS models, and is applied to individual galaxies instead of aver-age SEDs. Further details on the calibration method are providedin the appendix at the end of this paper.The systematic error in D n (4000) introduced by the calibrationmodel is at most ∼ σ dispersion of D n (4000) valuesobtained from the synthetic photometry for a given D n (4000) is ∼
5% and ∼
8% for photometric uncertainties of ∆ m = n (4000) measurements of SHARDSsources due to the combination of photometric, interpolation, andcalibration errors is estimated to be ∼
6% and ∼ = © , 1– ?? A. Hern´an-Caballero et al.
Figure 6.
Distribution of the relative di ff erence between D n (4000)values obtained using the photometric and spectroscopic redshift, ∆ D n (4000) / D n (4000), for the sources where both redshifts are within the0.65 z | ∆ D n (4000) | / D n (4000) < | ∆ D n (4000) | / D n (4000) < on a photometric redshift estimate, that is, about half of the sample(see §2). Comparison of photometric and spectroscopic redshiftsfor the other half indicates that the distribution of relative errors ∆ ( z ) / (1 + z ) in the photometric redshifts has median 0.02 and stan-dard deviation 0.03.Redshift uncertainties of this order are still su ffi ciently large tomove in a few cases both bands defining the index to the same sideof the 4000 Å break, potentially compromising the measurement.Nevertheless, comparison of D n (4000) values obtained using boththe photometric and spectroscopic redshifts for the z spec subsampleindicates that they are within 5% (10%) of each other in 80% (93%)of cases (Figure 6). Since the z spec subsample is biased in favourof sources with emission lines, the impact of photometric redshifterrors in D n (4000) values for the z phot subsample should be evenlower.In summary, the accuracy of D n (4000) measurements for themass-selected sample of SHARDS galaxies is expected to rangefrom ∼
5% in massive galaxies with spectroscopic redshifts to ∼ / ACS spectrafrom the PEARS project which have no signs of contaminationfrom other PEARS sources in their slitless grism spectra. Compar-ison of D(4000) from the PEARS spectrum and the SHARDS SEDshows that both estimates are compatible within their uncertainties(the 1- σ dispersion in ∆ D(4000) / D(4000) is 0.081).
It is well known that the colour distribution of galaxies depends onboth luminosity and redshift (e.g. Bell et al. 2004). For a fixed ab- Downloaded from the database at http: // archive.stsci.edu / prepds / pears / .See also Ferreras et al. (2009). Figure 7.
Rest-frame (U-V) colour versus absolute V-band magnitude forthe sources with spectroscopic (blue) and photometric (grey) redshifts. Theupper and lower dashed lines represent the limit of the red sequence asdefined by Bell et al. (2004) for redshifts z = solute magnitude, (U-V) r decreases with increasing redshift, whileat a given redshift (U-V) r increases with the luminosity.Using a large sample of ∼ < z r for red sequence galaxies withabsolute V-band magnitude M V = -20 is: h ( U − V ) i M V = − = . − . z (1)where we have included the 0.77 magnitudes di ff erence between U-V colours in the AB and Vega systems. Given the limited redshiftrange covered by our sample, the evolution of the red sequenceis expected to be small ( ∼ z = z = r colour of indi-vidual galaxies).The slope of the red sequence, d h ( U − V ) i dM V , is between -0.05 and0.1 both in local cluster and field galaxies (Schweizer & Seitzer1992; Bower et al. 1992; Terlevich et al. 2001; Baldry et al. 2004).For consistency, we assume the value -0.08 used by Bell et al.(2004) in their analysis.Figure 7 shows the (U-V) r versus M V color-magnitude dia-gram (CMD) of our sample. The dashed lines represent the red se-quence cuts for redshifts 0.65 and 1.07, using the definition fromBell et al. (2004):( U − V ) r > . − . z − . M V +
20) (2)With this definition, the red sequence contains 350 of the 1669sources in the sample.The bimodality in the distribution of the (U-V) colour is moreclearly observed if we correct for the dispersion introduced by thedependency with z and M V . We define the equivalent (U-V) colourat redshift z = V = -20 as:( U − V ) = ( U − V ) r + . z − . + . M V + . (3)Figure 8 shows the distribution of (U-V) for the sample. Thedistribution has a main peak at (U-V) = ∼ ∼ = © , 1– ?? tellar populations of z ∼ Figure 9.
The mass dependency of the medium band (left) and broadband (right) SEDs of SHARDS galaxies. Each SED is the average of all the sources inthe sample within a given stellar mass interval, normalised at λ = µ m for the SHARDS SED and 1.6 µ m for the Rainbow SED. The two parallel stripes inthe left plot represent the bands defining the D n (4000) index, while the dashed line marks the position of the [O ii ] 3727 Å emission line. Figure 8.
Distribution of rest-frame (U-V) colour corrected for the depen-dency with absolute magnitude and redshift as defined by Bell et al. (2004).The correction is 0.0 for a M V = -20 galaxy at z = ± Figure 9 compares the stacked SED for the sources contained in5 intervals of log(M ∗ / M ⊙ ), from 9.0–9.5 to 11.0–12.0. SEDs fromthe broadband photometry are normalised at the 1.6 µ m peak of thestellar emission. The NIR SED ( λ = µ m) of these sources showslittle dependency with the stellar mass, unlike the rest-frame opti-cal range, where there is a clear trend of increasingly red SEDs athigher stellar masses. This is the expected result if the more mas-sive galaxies contain on average older stellar populations, but itcould also be produced by increased obscuration or higher metal- licity in more massive galaxies. Further insight is provided by thestacked SHARDS SEDs (left panel in Figure 9). The SEDs for thethree lower mass intervals show strong emission in the [O ii ] 3727Å line and a weak 4000 Å break, both features indicative of a youngstellar population. On the other hand, the SEDs of the two highermass intervals shown no significant [O ii ] emission and a stronger4000 Å break, hinting at older average stellar ages. This suggeststhat stellar age and not obscuration is the main driver of the corre-lation between optical colours and stellar mass (see also §4.4).When considering individual sources, both the D n (4000) indexand the (U-V) r colour correlate with the stellar mass, albeit with ahigh dispersion (see Figure 10). In the (U-V) r vs M ∗ diagram thereseems to be a smooth transition between the blue cloud and thered sequence, with galaxies in the 10.0 < log(M ∗ / M ⊙ ) < r and log(M ∗ ) issomewhat stronger if considering only the z spec subsample. ( r = r = r colours at low masses are found almost exclusively in z phot sources.This does not necessarily imply poor accuracy in the (U-V) r mea-surements of z phot sources, since redshift uncertainties are too lowcompared to the width of the U and V filters to a ff ect significantlythe (U-V) r color. Rather, it illustrates the bias of spectroscopic sam-ples (which usually only detect low mass galaxies if they showprominent emission lines) relatively to a mass-limited sample. Inparticular, the z phot subsample shows what looks like a continuationof the red sequence (i.e., redder (U-V) r colours) down to the masslimit of the sample. As Figure 11 demonstrates, many of the sourcesin the extended red sequence have low D n (4000) values consistentwith a young but obscured stellar population. However, some ofthem show larger D n (4000) values, consistent with a transitioningor quiescent galaxy.The distribution of D n (4000) versus M ∗ shows the same gen-eral trend of increasing D n (4000) values at higher masses. AverageD n (4000) values remain nearly constant at D n (4000) = © , 1– ?? A. Hern´an-Caballero et al. M ∗ ∼ . M ⊙ , but they increase steadily for more massive galaxies(see also Table 1).While the dispersion in (U-V) r for a given mass is roughlyconstant in the entire mass range, maybe even decreasing at thevery high end, for D n (4000) the dispersion increases significantlywith M ∗ . This di ff erent behaviour is probably due to the higher in-fluence of extinction on the (U-V) r colour (see §4.4).An old massive galaxy with M ∗ = M ⊙ and D n (4000) = ∗ = . M ⊙ at z ∼
1. Given that, it is noteworthy the rarity of old(D n (4000) > ∗ < . M ⊙ .The region defined by M ∗ < M ⊙ and D n (4000) > z spec sources. Sources with photometric red-shift in this region are mainly the galaxies with red (U-V) r in theextended red sequence, but there are also a few young starburstswhere D n (4000) is grossly overestimated due to the [O ii ] 3727 Åemission line entering the red band defining the D n (4000) indexbecause of an overestimated photometric redshift. The latter canbe identified because of their inconsistently low (U-V) r values (see§4.4).Although the correlation of (U-V) r and D n (4000) with the stel-lar mass is mainly driven by an increase in the average stellar agein more massive galaxies, the e ff ects of metallicity and extinctioncannot be dismissed. In fact, it is well known that metallicity istightly correlated with the stellar mass at least up to z ∼ n (4000) is much less sensitive to extinction comparedto (U-V) r and nearly independent of metallicity for stellar popula-tions younger than ∼ r colour and thestellar mass by selecting subsamples of sources within narrow in-tervals of D n (4000).Figure 11 shows that there is a general trend of increasing (U-V) r with M ∗ at a fixed D n (4000), albeit with high dispersion. Thissuggests that for a given stellar age, extinction tends to be higher inthe more massive galaxies. Higher extinction in massive but younggalaxies would explain our finding of a lower dispersion in the (U-V) r values of massive galaxies compared to their D n (4000) values.For galaxies in the two higher D n (4000) bins (bottom row in Figure11) the correlation seems to flatten or even reverse, at least for the z spec subsample. However, the uncertainty in the slope is higher thanin younger subsamples because there are very few low mass galax-ies with high D n (4000) values, and nearly all of them have pho-tometric redshifts. In addition, we caution that in the older galax-ies (those with D n (4000) > ff ect of metallicity in D n (4000)and (U-V) r is no longer negligible. In §5.2 we revisit the mass-extinction relationship with quantitative estimates of A V . The redshift range covered by the sample equals 2 Gyr of cosmicevolution. If the so called downsizing in hierarchical galaxy forma-tion is significant from z = = Figure 10.
Rest-frame observed U-V colour (not corrected for extinction;top panel) and D n (4000) index (bottom panel) as a function of the stellarmass. Blue dots and grey squares represent sources with spectroscopic andphotometric redshifts, respectively. Typical uncertainties are shown in thelower right corner. The open diamonds connected by a solid line representmedian values in bins of mass 0.5 dex wide, while dashed lines indicatethe 16 th and 84 th percentiles. The shaded area in the top panel representthe location of the red sequence above the cut defined by Cardamone et al.(2010) for the redshift range 0.8 < z < shows the median values of D n (4000) and (U-V) r for the three sub-samples, separated into 5 mass bins.The U-V colour shows a small but significant evolution withredshift, being ∼ z ∼ z ∼
1. The redshift evolution seems to increase with the stellar mass,except maybe in the highest mass interval (M ∗ / M ⊙ > ) where thelarger error bars obfuscate the trend. In the diagram for D n (4000)the evolution is much less pronounced, with values being compati-ble within their uncertainties with a flat slope.For comparison, tracks corresponding to passive evolution areshown as grey lines in Figure 12. The slope of these tracks is muchsteeper compared to the redshift evolution observed in the sample,even in the 10.5–11.0 mass range, indicating that only a small frac-tion of the galaxies would be evolving passively. Observing signif-icant evolution in the (U-V) r colour but not in D n (4000) suggeststhat the redshift dependency of reddening in (U-V) r might in fact © , 1– ?? tellar populations of z ∼ Figure 11.
Rest-frame observed (U-V) colour (not corrected for extinction)versus stellar mass for several intervals of D n (4000). Blue dots and greysquares represent sources with spectroscopic and photometric redshifts, re-spectively. The dashed line represents the best fitting linear relation consid-ering both z spec and z phot sources, while the solid line represents the bestlinear fit when considering only sources with spectroscopic redshift. be related to increased obscuration or higher metallicity at lowerredshifts, instead of older average light-weighted stellar ages.In such a small field, clustering could contribute a fraction ofthe scatter observed. It is evident from Figure 3 that the volumesampled contains several overdensities and large voids. Neverthe-less, several works have demonstrated that the environment depen-dency of galaxy colours is weak, at least for early type galaxies(e.g. Balogh et al. 2004; Hogg et al. 2004; Bernardi et al. 2006). Inthe zCOSMOS survey, Cucciati et al. (2010) found that after ac-counting for the mass dependency in galaxy colours, the colour-density relation of M ∗ > . M ⊙ galaxies is flat up to z ∼
1, whileat lower masses the fraction of red galaxies at 0.1 < z < ff erence in the average (U-V) r of red galaxies between un-derdense and overdense regions of ∼ n (4000)this di ff erence is ∼ r and D n (4000) with z should besignificantly lower (unless blue galaxies have a much stronger en-vironment dependency). This implies that the trends with redshiftof (U-V) r shown in Figure 12 are real. n (4000) diagram The correlation between values of (U-V) r and D n (4000) for in-dividual galaxies is most evident when representing the formeragainst the latter (Figure 13). The top panel represents (U-V) r ver-sus D n (4000) for individual SHARDS galaxies, with color coding Figure 12.
Dependency with redshift of the median values of the rest-frame(U-V) colour (top) and the 4000 Å index (bottom) for several mass ranges.Solid symbols represent the median values in three redshift intervals foreach mass range, with error bars indicating the 67% confidence intervalcalculated with bootstrap resampling. The redshift scale is shown at thetop of the plot. The grey solid lines represent tracks for passive evolutionof a SSP with moderate extinction (A V = n (4000) index ofa SSP with di ff erent formation redshifts. for the stellar mass. In the bottom panel, contours represent thedensity distribution of z spec sources, while the black solid line repre-sents the median (U-V) r value for z spec sources in bins of D n (4000)of width ∆= r ∼ n (4000) ∼ ∗ < M ⊙ . On the other hand, the most massive galaxiescluster around a horizontal branch at (U-V) r ∼ r values as high as ∼ n (4000) . ff erentSFHs. The SED corresponding to each SFH was computed usingGALAXEV (Bruzual & Charlot 2003) with the STELIB stellar li-brary and Padova1994 isochrones (Bertelli et al. 1994), assumingsolar metallicity and a Salpeter (1955) initial mass function (IMF).Kau ff mann et al. (2003a) found that at fixed metallicity and age, thevariations in D n (4000) between STELIB and other stellar librariesare ∼ r and D n (4000) from eachSFH model vary as a function of the extinction A V . Dashed lines inFigure 13 represent tracks for SSP models, while dotted lines rep-resent SFHs for galaxies 6 Gyr old with an exponentially decliningSFR.The very steep slope of the tracks shows that, irrespectiveof the SFH of the galaxy, the U-V color index is much more af-fected by extinction than D n (4000). Nevertheless, the latter is alsoa ff ected, and ignoring extinction would lead to systematically over- © , 1– ?? A. Hern´an-Caballero et al.
Figure 13. (Top) rest-frame (U-V) color index versus D n (4000) for individ-ual SHARDS galaxies. Open (solid) symbols represent sources with photo-metric (spectroscopic) redshift. The color coding indicates the stellar massrange for each source. (Bottom) density countours for the distribution ofsources in the z spec subsample. The black solid line indicates their median(U-V) r in bins of D n (4000) of width 0.1. Dashed lines represent tracks asa function of extinction for SSP models with ages (left to right): 0.025,0.1, 0.2, 0.4, 0.6, 1.0, 1.5, 2.5, and 4 Gyr. Dotted lines represent a 6 Gyrold galaxy with an exponentially declining SFR and e-folding times τ = τ = ∞ representing a constant SFR. All templatesare computed with GALAXEV (Bruzual & Charlot 2003) and assume solarmetallicity and a Salpeter (1955) IMF. Each tick represents a 0.5 incre-ment in A V starting from A V = V = r and D n (4000) values that cannot be reproducedwith SSP models for any age, metallicity, or extinction. estimated stellar ages. In example, a 0.2 Gyr old SSP with A V = n (4000) index as a 0.4 Gyr old SSP with A V =
0. Fortunately, their (U-V) r colours are di ff erent, and therefore wecan combine the information provided by (U-V) r and D n (4000) toestimate A V and obtain de-reddened colours (see §4.5).The curve connecting the A V = r vsD n (4000) diagram whose values can be reproduced by the models.Outside of this region (dotted area in the bottom panel) there are nocombinations of SFH, metallicity, and extinction explaining theirD n (4000) and (U-V) r values.Interestingly, almost all of the sources found in this area ex-cluded by models have photometric redshifts. Since D n (4000) ismuch more sensitive to redshift uncertainty than (U-V) r , we as-sume that the deviations are mainly along the X axis. Given thetypical uncertainties expected for z phot sources from the simulationswith spectra ( ∆ D n (4000) / D n (4000) ∼ Figure 14.
Sketch illustrating how the extinction corrected (U-V) r andD n (4000) are estimated (see text). Solid symbols represent the observed (U-V) r and D n (4000) of a few representative sources from the sample. Opensymbols represent their maximum likelihood (ML) estimates after uncer-tainties have been considered, and red arrows indicate the de-reddening paththat takes them to the dust-free sequence containing all the extinction cor-rected estimates. The ellipses in the bottom right corner indicates the typical1- σ uncertainty in the observed values for a source in the z phot (blue) and z spec (black) subsamples. sion observed is consistent with these sources being scattered awayfrom the region covered by models due to random errors in theirmeasurement of D n (4000).There are a few outliers with very large or very smallD n (4000), all of them low mass z phot sources (open blue symbolsin Figure 13). One mechanism capable of producing large errorsin D n (4000) from a relatively small redshift error is an emissionline (in particular [O ii ] 3727 Å) entering one of the bands defin-ing the D n (4000) index. If the blue (red) band is contaminated thenthe strength of the break will be under- (over-)estimated. Visualinspection of these outliers reveals several cases of both kinds inthe sample. Since these sources are low-mass galaxies with blue(U-V) r colours, intense [O ii ] emission from a recent or ongoingstarburst is not surprising. Strong emission lines may also have anoticeable e ff ect on the broadband photometry. However, our rest-frame colour measurements are largely una ff ected because they areperformed on the SPS model that best fits the broadband SED ofeach galaxy. The (U-V) r colour and D n (4000) of A V = V = r vs D n (4000) diagram the dust-free se-quence (DFS). Variations in the age, SFH, and metallicity of themodels move galaxies along the DFS, but departures from it arevery small. As a consequence, extinction is the only model param-eter that can take galaxies away from the DFS. This provides uswith a new way of estimating A V that does not require SED fittingand –more importantly– is not a ff ected by the usual degeneracyamong age, extinction, and metallicity.The increment in (U-V) r due to extinction –that is, the colourexcess E(U-V)– is proportional to A V and independent of the spec- © , 1– ?? tellar populations of z ∼ trum of the galaxy. The increment in logD n (4000) due to extinction, ∆ logD n (4000), is also proportional to A V . While the proportional-ity constant for each of them is somewhat dependent on the specificextinction law assumed, the ratio E(U-V) /∆ logD n (4000) is largelyinsensitive to changes in the slope of the extinction curve becausethe bands defining the D n (4000) index are between the U and V bands. Therefore, E(U-V) and ∆ logD n (4000) are the components ofa vector in the (U-V) r vs logD n (4000) plane (the −→ A V vector) whosedirection depends only on the e ff ective wavelengths of the U and V bands and those defining the D n (4000) index, but is independent ofany physical property of the galaxy.Since extinction shifts the DFS in parallel to the −→ A V vector,we define the permitted zone (PZ) as the area of the (U-V) r vslogD n (4000) plane that is scanned by the DFS at increasing val-ues of A V . The PZ contains all the combinations of (U-V) r vslogD n (4000) that can be reproduced by models for any age, SFH,metallicity, or extinction.Due to the significant uncertainty in logD n (4000) ( ∼ z spec sources, ∼ z phot ones) and to a lesser extent also in(U-V) r ( ∼ n (4000) and (U-V) r are uncorrelatedand have a normal distribution, then the probability distribution forthe true values of logD n (4000) and (U-V) r is a bidimensional gaus-sian function g ( D n , UV ) centered on the observed values. If we alsoassume that the true values must be inside the PZ, then the max-imum likelihood (ML) estimates are no longer the observed ones,but the average –weighted by the probability distribution– of valuesinside the PZ. That is:log D n (4000) ML = " PZ g ( D n , UV ) D n dD n dUV (4)( U − V ) ML = " PZ g ( D n , UV ) UV dD n dUV (5)Figure 14 shows that this weighted average moves sources in theFZ to the PZ, and also shifts sources close to the borders of the PZto inner regions of it. To obtain de-reddened values for (U-V) r andlogD n (4000) we only need to move the position of the ML estimatealong a line parallel to −→ A V until it intersects the DFS. The length ofthe segment traveled is then proportional to the implied absorptionin the restframe V band, A V . Assuming a Draine (2003) extinctionlaw with Milky Way grain size distribution (Weingartner & Draine2001) and R V = V implies E(U-V) = ∆ logD n (4000) = , as a function of M ∗ for the sources in the sample. The less mas-sive galaxies (M ∗ . M ⊙ ) concentrate in a narrow blue cloudaround (U-V) ∼ , albeit with a high dispersion.The position of the blue cloud is consistent with that foundby Cardamone et al. (2010) for the extinction corrected U-V colourof the Extended Chandra Deep Field South galaxies at 0.8 < z < V estimates are sensitive to the selec-tion of SPS models, which determine the shape and location of theDFS. However, changes in the DFS are negligible when switching Figure 15.
Extinction corrected rest-frame U-V colour as a function of thestellar mass, with colour coding for A V . to the models from Maraston (2005), because di ff erences betweenthe two sets of models are important in the near-infrared, but not somuch between the U and V bands.The method used to estimate the amount of extinctionmay have a larger impact on the outcome. In the work ofCardamone et al. (2010), they use FAST (Kriek et al. 2009) to esti-mate the stellar mass, star-formation time scale, star-formation rate,and A V by fitting the observed SED with single-burst SPS mod-els. Although the near-infrared photometry helps to break the age-extinction degeneracy, their A V estimate is influenced by all thestars in the galaxy, and not just those that dominate the emission inthe U and V bands. If the extinction a ff ecting di ff erent stellar pop-ulations within the galaxy varies with their age or metallicity, it isconceivable that the de-reddened U-V colours could be biased.We also find that galaxies with M ∗ & M ⊙ show a correla-tion between (U-V) and A V : the more obscured sources also havebluer de-reddened U-V colours. This is consistent with the expec-tation of younger starforming galaxies being more dusty than qui-escent galaxies, but other mechanisms could be responsible for thistrend. For instance, if the amount of extinction is somehow over-estimated then we will over-correct the U-V colour, obtaining thesame correlation.An independent confirmation of the validity of A V estimateswith the method of projection into the DFS can be obtained usingthe rest-frame V-J colour. This colour has a smaller dependency onthe age of stellar populations compared to U-V, and a larger oneon extinction (since the V band is much more a ff ected by extinc-tion compared to the J band). Because of this, it has been widelyused in combination with another restframe colour, in particu-lar U-V, to break the age-extinction degeneracy (e.g. Wuyts et al.2007; Williams et al. 2009; Cardamone et al. 2010; Brammer et al.2011).In Figure 16 we show A V versus rest-frame V-J, with sepa-rate colours identifying sources in distinct intervals of D n (4000).The correlation between A V and V-J is evident only when consider-ing galaxies with comparable D n (4000) values, because the depen-dency of the V-J colour with age is small but not negligible, and thetypically lower extinction a ff ecting older stellar populations com-pensates to some extent their redder intrinsic V-J colour. Given thelarge dispersion, we take the bisector of the linear fits of A V vs V-J © , 1– ?? A. Hern´an-Caballero et al.
Figure 16.
Attenuation in the rest-frame V band as a function of therest-frame V-J colour. Colours identify subsamples according to theirD n (4000)values. The continuous lines represent the bisector of the best-fitting linear relations for A V vs V-J and V-J vs A V for each subsample. and V-J vs A V as the best linear model for the relationship betweenthe two variables (solid lines in Figure 16).Assuming a Draine (2003) extinction law with Milky Waygrain size distribution (Weingartner & Draine 2001) and R V = J ∼ V . Therefore,the theoretical expectation for the slope of the best fitting linearmodel is A V E ( V − J ) ∼ V estimates are broadly consistent with the observedrestframe V-J colour. Real galaxies have complicated SFHs, and finding a single valuerepresenting a characteristic stellar age for the entire stellar pop-ulation is not straightforward. Furthermore, the dependency ofD n (4000) and (U-V) r with metallicity for old ( > t ssp , as the age of a solar-metallicity SSP thathas a D n (4000) equal to the extinction corrected D n (4000) of thegalaxy. While the less massive galaxies in the sample are expectedto have sub-solar metallicity, this does not invalidate t ssp estimatessince (U-V) r and D n (4000) are nearly insensitive to metallicity forthe typical ages of low mass galaxies (see Figure 1). On the otherhand, for galaxies with old stellar populations and sub-(super-)solarmetallicity, t ssp will under-(over-)estimate the actual age of theirstellar populations.Values of t ssp may di ff er significantly from the mean or themedian age of individual stars in the galaxy. In particular, a recentburst of star formation can easily outshine the older stellar popu-lation in the UV-optical range and make the entire galaxy appearyoung, even if young stars only represent a small fraction of thestellar mass in the galaxy. Therefore, we interpret t ssp only as anindicator of the recent SFH of the galaxies. Figure 17.
Distribution of D n (4000) values for several stellar mass inter-vals. The black line represents the observed D n (4000) values, while thesolid histogram represents their maximum likelihood estimates based onthe method described in §4.5. For comparison, the distribution found byKau ff mann et al. (2003a) in SDSS galaxies is also shown (red histogram).Dotted lines indicate the median value of each distribution. In a large flux-limited sample of local galaxies from the SDSS,Kau ff mann et al. (2003b) found a sharp transition in the physicalproperties of galaxies at M ∗ = . M ⊙ , with galaxies below thatvalue having lower surface mass densities, lower concentration in-dices, and younger stellar populations compared to galaxies aboveit. Figure 17 shows the distribution of D n (4000) values in binsof mass 0.5 dex wide for both their local sample and our interme-diate redshift one. The D n (4000) distributions for the 0.65 < z < n (4000) values observed forlocal galaxies is not well developed in our intermediate redshiftsample, and we can only marginally resolve the two peaks in the10 . < M ∗ / M ⊙ < mass bin (see Figures 17 and 18). This is be-cause even the most massive galaxies in our sample have not hadenough time to evolve su ffi ciently their stellar populations. Further-more, while in the local sample there is a significant population ofquiescent galaxies for all mass bins except the lowest one, in the0.65 < z < n (4000) values only in galaxiesabove 10 . M ⊙ , and a significant population of relatively younggalaxies even in the highest mass ranges.In the local sample, the relative abundances of young and © , 1– ?? tellar populations of z ∼ Figure 18.
Distribution of light-weighted stellar ages for several stellarmass intervals. The histogram shows the number of sources in intervalsof log t ssp of width 0.25, while the continuous curve shows the cumulativefraction of sources younger than a given age. The dotted line marks themedian (50% cumulative fraction) of each distribution. old galaxies vary slowly with the stellar mass, while in the0.65 < z < ∗ ∼ . M ⊙ from a distribution dominated by young populationsto another where there are comparable numbers of galaxies withyoung and old stars. Studies with large spectroscopic samples from the SDSS haveshown that the fundamental property governing extinction of the H α emission in star-forming galaxies is the stellar mass (Garn & Best2010; Zahid et al. 2012, 2013). Here we discuss whether the stellarmass also influences the extinction a ff ecting the stellar population.Figure 19 shows A V as a function of M ∗ in four intervals of t ssp . Most galaxies concentrate in a relatively narrow band of A V values between 0.5 and 1.0, and there is not any significant trendwith mass for the sample as a whole other than an increase in dis-persion in the 10 –10 M ⊙ range. Nevertheless, when sources aregrouped by their light weighted stellar ages, and mean A V valuesare calculated in bins of stellar mass, a pattern emerges in whichthe mean A V for a given age interval increases with the stellar mass,reaching a maximum in the 10–10.5 or 10.5–11 mass bin, and sta-bilises or decreases at higher masses.The sources with A V > –10 M ⊙ , with moderate D n (4000) values indicating relativelyyoung stellar populations and red V-J confirming high extinction.These galaxies are among the most massive of the (intrinsic) bluegalaxies (see Figure 15), and their mass distribution is strongly Figure 19.
Apparent absorption in the rest-frame V band versus stellarmass, with colour coding for the light-weighted stellar age. Big squaresrepresent mean values of M ∗ and A V in bins of stellar mass 0.5 dex wide. biased against lower mass galaxies compared to less obscuredsources.For a given mass interval, the mean A V decreases with increas-ing stellar age. This trend is stronger among the massive galax-ies (M ∗ > . M ⊙ ), where the average A V is > t ssp < ∼ t ssp > t ssp is also the expected result if A V issomehow underestimated. The light-weighted average stellar age does not provide informa-tion about the entire SFH of the galaxies. In particular, for galax-ies experiencing a recent burst of star formation, the pre-burstSFH cannot be inferred from these data, since emission from hotyoung stars outshines the old population and produces (U-V) r andD n (4000) values very close to those of a SSP with the age of theburst. However, we can still set some interesting constraints on theSFH of most galaxies. The track for constant SFR in Figure 13overlaps with that of a SSP 0.3 Gyr old. This implies that galaxieswith log t ssp < <
300 Myr) increase intheir SFR, while those with larger values are experiencing a declinein their SFR at least in the last few hundred Myr.Figure 20 shows the fraction of galaxies with t ssp > ∗ for both our sam-ple and the local SDSS sample of Kau ff mann et al. (2003a). In thelatter we assumed solar metallicity and a typical extinction of A V = n (4000) values to t ssp ( t ssp = n (4000) = t ssp > ∼
5% in thelowest mass bin to ∼
80% in the highest. This indicates that at z ∼ . M ⊙ , inqualitative agreement with the downsizing paradigm. On the otherhand, in the local SDSS sample the SFR is predominantly in declineexcept perhaps in the lowest mass bin, and the fraction of t ssp > © , 1– ?? A. Hern´an-Caballero et al.
Figure 20.
Fraction of sources with declining SFR ( t ssp > t ssp > z ∼ ply that these galaxies will undergo passive evolution down to z ∼ < z < n (4000) distribution at z ∼ n (4000) ∼ n (4000) > t ssp > t ssp > t ssp > < M ∗ / M ⊙ < . since z ∼ t ssp > z galaxies might never reactivate their star for-mation but instead evolve passively until the present time.In the intermediate mass bins (10 < M ∗ / M ⊙ < ), about 50%is increasing its SFR and the other 50% decreasing in the SHARDSsample. Their distribution peaks close to log t ssp = n (4000) values observed in the sample, ∼ t ssp ∼ τ = z ∼ ∗ > M ⊙ , only 10% of them has t ssp > We have presented the analysis of the stellar populations of a mass-selected sample of galaxies at z ∼ AB < ∼
50) photometry from the Survey forHigh-z Absorption Red and Dead Sources (SHARDS). We demon-strate that the spectral resolution of SHARDS allows for a consis-tent measure of the D n (4000) index for all galaxies at 0.65 < z < ∗ = M ⊙ , roughly 1 / th the threshold of similar studiesbased on spectroscopy.The stacked SHARDS SEDs of sources grouped by their stel-lar mass show increasingly red continua, stronger 4000 Å breaks,and weaker [O ii ] emission with increasing stellar mass, suggest-ing that stellar age, and not extinction, is the dominant factor driv-ing the correlation between optical colours and stellar mass. Whenconsidering individual sources, both D n (4000) and (U-V) r correlatewith M ∗ . The dispersion in D n (4000) values at a given M ∗ increaseswith M ∗ , while for (U-V) r decreases due to the higher average ex-tinction prevalent in massive star-forming galaxies.We find a small but significant evolution with redshift of therestframe U-V colour within the sample. Galaxies at z ∼ z ∼ . –10 . M ⊙ ).We present a new method for obtaining A V estimates based onthe di ff erences in sensitivity of the (U-V) r and logD n (4000) coloursto extinction. This method allows us to break the degeneracy be-tween age and extinction, and to produce extinction-corrected ob-servables.The extinction corrected U-V colour of blue cloud galaxies inour sample is consistent with other studies at similar redshifts. Nev-ertheless, for massive galaxies we find a smooth transition towardsthe red sequence, with many sources at intermediate colours, incontrast to the strong bimodality found by Cardamone et al. (2010).We interpret the discrepancy as due to di ff erences in the methodsused to estimate the extinction a ff ecting the stellar population.Compared to local galaxies, the distributions of D n (4000) forour sample peak at lower values indicative of younger stellar popu-lations for all mass ranges. The bimodal distribution of D n (4000) israther absent at z ∼ ffi ciently their stellar popu-lations. We find a relatively sharp transition at M ∗ ∼ . M ⊙ froma distribution dominated by young stellar populations to anotherwhere there are comparable numbers of galaxies with young andold stars.When galaxies are grouped by their light weighted stellarages, we find a weak positive correlation between extinction andstellar mass, which probably arises from the well-known correla-tion between stellar mass and metallicity.The fraction of SHARDS sources where star formation isin decline increases steadily with the stellar mass, from ∼
5% atlog(M ∗ / M ⊙ ) = ∼
80% at log(M ∗ / M ⊙ ) >
11. This indicatesthat at z ∼ . , in qualitative agreement with the downsizing paradigm.For the more massive galaxies, the comoving density of z ∼ t ssp > n (4000) values observed in the SHARDS samplecorrespond to t ssp ∼ © , 1– ?? tellar populations of z ∼ lar mass in these galaxies was already in place at z ∼ < ∗ > M ⊙ galaxies. ACKNOWLEDGEMENTS
A.H.-C. and A.A.-H. acknowledge funding by the Universidad deCantabria Augusto Gonz´alez Linares program. We acknowledgesupport from the Spanish Programa Nacional de Astronom´ıa yAstrof´ısica under grants AYA2009-07723-E and AYA2009-10368.SHARDS has been funded by the Spanish MICINN / MINECO un-der the Consolider-Ingenio 2010 Program grant CSD2006-00070:First Science with the GTC. This work has made use of the Rain-bow Cosmological Surveys Database, which is operated by theUniversidad Complutense de Madrid (UCM). Based on observa-tions made with the Gran Telescopio Canarias (GTC), installed atthe Spanish Observatorio del Roque de los Muchachos of the In-stituto de Astrof´ısica de Canarias, in the island of La Palma. Wethank all the GTC Sta ff for their support and enthusiasm with theSHARDS project, and we would like to especially acknowledge thehelp from Antonio Cabrera and Ren´e Rutten. We thank the anony-mous referee for their useful comments that helped to improve thispaper. REFERENCES
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Mass range N total N z spec N D n (4000) h log(M ∗ / M ⊙ ) i h z i h (U-V) r i h D n (4000) i © , 1– ?? A. Hern´an-Caballero et al.
APPENDIX A: CALIBRATION OF D n (4000)MEASUREMENTS USING ZCOSMOS SPECTRAA1 Simulation of SHARDS photometry We simulated SHARDS photometry by convolving a library of op-tical spectra with the transmission profiles of the SHARDS filters.The library was selected from the zCOSMOS (Lilly et al. 2007)Data Release 2, and includes the 1377 sources in the 0.5 < z < i band. Thecut in optical magnitude ensures the spectrum has a well detectedcontinuum and the 4000 Å break can be properly measured in thefull resolution spectrum.Photometric errors are simulated by adding to each magnitudean error term m err = σ , where σ is a random variable with nor-mal distribution. This roughly corresponds to the 1- σ uncertaintyof the SHARDS photometry at AB magnitude ∼ ∼ n (4000) indices are measured in the sim-ulated photometry using the same procedure employed for theSHARDS data. Figure A1 compares values of the D(4000) andD n (4000) indices measured directly on the full resolution zCOS-MOS spectra (D4 C and Dn4 C ) with those recovered from the syn-thetic photometry (D4 P and Dn4 P ).The dispersion in D4 P is markedly uniform in the entire rangeof 4000 Å break strengths, at about 5% of its average value, whilefor Dn4 P the dispersion is significantly higher, and also has strongerbias towards lower values of the index in the simulated photometrycompared to the full resolution spectrum. A2 Corrected D n (4000) values Most recent studies prefer the narrow definition of the 4000 Å in-dex due to its lower dependency on extinction. This is thus the mostconvenient definition for comparison with results from other sam-ples. Nevertheless, we just showed that at the spectral resolution ofthe SHARDS SED (R ∼
50) the measurement of D n (4000) is signif-icantly more a ff ected by the interpolation error when compared toD(4000).To overcome this issue, we calculate D n (4000) values cor-rected for the interpolation bias from the D(4000) measurementson the SHARDS photometry. The correction terms are obtainedfrom polynomial fitting of Dn4 C values as a function of D4 P in thezCOSMOS sample. To this aim, the individual zCOSMOS sourcesare sorted by their D4 P values, and the mean and standard devia-tion of their D4 P and Dn4 C values and are calculated in bins of 30sources each.Figure A2 shows Dn4 C versus D4 P and the best fitting linearand parabolic models. In both cases, the expected values, Dn4 M , arecomfortably within one standard deviation from the observed ones,Dn4 C , with the only exception of the lowest and highest D4 P binsfor the linear and parabolic models, respectively. Nevertheless, thelinear model fails to predict the convergence of D4 P and Dn4 C val-ues at D4 P = Dn4 C =
1, which is caused by the index measurementbecoming insensitive to the spectral resolution in sources with aflat spectrum near 4000 Å. On the other hand, the parabolic modelreproduces this feature accurately.The residuals ( δ M = Dn4 C - Dn4 M ) show that the parabolicfit reproduces much better the observed values except in the1.8 < D4 P < Figure A1.
Comparison between 4000 Å indices for simulated SHARDSphotometry and those from full resolution zCOSMOS spectra. The bluedots represent measurements of the “regular” D(4000) index, while the redones represent the “narrow” version D n (4000). Figure A2.
Comparison between D n (4000) values measured in the full res-olution spectrum and D(4000) values measured in the synthetic SHARDSphotometry. Black dots represent individual zCOSMOS sources, while redasterisks mark the average values in bins of 30. Error bars indicate the 1- σ dispersion in each bin. The green and blue lines represent the best fittinglinear and parabolic models, respectively. ues than observed (Figure A3). Because of this issues, the parabolicmodel is preferred over the linear one.From the coe ffi cients of the parabolic model we obtain thecorrection term, ∆ , that needs to be subtracted from the D(4000)values measured in the SHARDS photometry to obtain correctedD n (4000) values: ∆ = . D P − − . D P − (A1)which implies corrections of 0.00, 0.17, and 0.22 at D4 P = M introduced by the parabolic © , 1– ?? tellar populations of z ∼ Figure A3.
Residuals in D n (4000) after subtraction of the best fitting linear(top) and parabolic (bottom) models. Symbols as in Figure A2. model is at most ∼ σ dispersion of Dn4 M values fora given Dn4 C is ∼ A3 Dependency with the photometric errors
The calibration used to obtain corrected D n (4000) values assumesphotometric uncertainties around 0.1 magnitudes, but in somesources (particularly the more massive galaxies) these can be anorder of magnitude lower. Repeating the above calibration steps onsimulated SHARDS data with 0.01 magnitudes uncertainties yieldsnearly identical calibration coe ffi cients. Furthermore, the disper-sion of residuals is only slightly lower (Figure A4), indicating thatit is the interpolation error, and not the photometric errors, the maincause of dispersion in the Dn4 M versus Dn4 C relationship. Figure A4.
Distribution of relative errors in the D n (4000) index measure-ment for simulated SHARDS data with photometric errors ∆ m = ∆ m = © , 1–, 1–