On the robustness of the Hβ Lick index as a cosmic clock in passive early-type galaxies
aa r X i v : . [ a s t r o - ph . GA ] F e b MNRAS , 1–20 (2016) Preprint 13 September 2018 Compiled using MNRAS L A TEX style file v3.0
On the robustness of the H β Lick index as a cosmic clockin passive early-type galaxies
Alice Concas, , , ⋆ L. Pozzetti, M. Moresco , and A. Cimatti Excellence Cluster Universe, Boltzmannstr. 2 D-85748 Garching, Germany Dipartimento di Fisica e Astronomia, Universit´a degli Studi di Bologna, V.le Berti Pichat, 6/2 - 40127, Bologna, Italy INAF - Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We examine the H β Lick index in a sample of ∼ massive ( log ( M / M ⊙ ) > . ) and passive early-type galaxies extracted from SDSS at z < β strength increases with redshift as expected in passive evolutionmodels, and shows at each redshift weaker values in more massive galaxies. However,a detailed comparison of the observed index with the predictions of stellar popula-tion synthesis models highlights a significant tension, with the observed index beingsystematically lower than expected. By analyzing the stacked spectra, we find a weak[NII] λ emission line (not detectable in the single spectra) which anti-correlateswith the mass, that can be interpreted as a hint of the presence of ionized gas. We es-timated the correction of the H β index by the residual emission component exploitingdifferent approaches, but find it very uncertain and model-dependent. We concludethat, while the qualitative trends of the observed H β -z relations are consistent withthe expected passive and downsizing scenario, the possible presence of ionized gas evenin the most massive and passive galaxies prevents to use this index for a quantitativeestimate of the age evolution and for cosmological applications. Key words: galaxies: general – galaxies: evolution – galaxies: formation – galaxies:stellar content – galaxies: fundamental parameters – cosmology: cosmological param-eters – ⋆ E-mail: [email protected] (KTS)c (cid:13)
A. Concas et al.
Early-type galaxies (ETGs) are perfect candidates to inves-tigate both galaxy formation and evolution theories and,at the same time, to put constraints on the expansion his-tory of the Universe. Many recent observations show thatmost massive galaxies contain the oldest stellar populationsup to z ∼ − (e.g. Spinrad et al. 1997; Cowie et al. 1999;Heavens et al. 2004; Thomas et al. 2005; Cimatti et al.2008; Thomas et al. 2010; Moresco et al. 2011) and thatonly few percent of their current stellar mass was formedafter z ∼ . Moreover, studies on the stellar mass function atdifferent redshifts (e.g. Bundy et al. 2005; Borch et al. 2006;Bundy et al. 2006; Ilbert et al. 2010; Pozzetti et al. 2010;Maraston et al. 2013) showed that most massive galaxies ( M ∼ M ⊙ ) are characterized by an increase of their stel-lar mass density at z ∼ field) and a subsequent negligible evolutionin number density from z ∼ to the present (Cimatti et al.2006; Pozzetti et al. 2010; Moresco et al. 2013). All theseobservational evidences suggest that these massive, red andpassively evolving galaxies represent the oldest objects in theUniverse below z ∼ . For this reason, a study based on thevariation of ETGs properties, such as age, chemical compo-sition, dynamic, at different redshifts, could rightly help toexpand our current knowledge of the physical process thatdrive the formation and evolution of galaxies. Moreover, asfirstly pointed out by Jimenez & Loeb (2002), the differen-tial age evolution of ETGs can be also used to put severalcosmological constrains. In particular, by estimating the rel-ative differential age ( ∆ t age ) between ETGs, formed at thesame cosmic time, but observed at different redshifts ( ∆ z ),it is possible to determine the derivative of redshift withrespect to cosmic time dz / dt .This quantity is directly related to the cosmologi-cal expansion history described by the Hubble parameter: H ( z ) = − + z dzdt , which can be used to estimate many cos-mological parameters such as H , Ω , M , Ω , Λ and w Λ . Thistechnique, known as “cosmic chronometers” method, hasbeen used recently in several works and obtained promis-ing results in the estimate of the Hubble parameter andof the dark energy equation of state (Simon et al. 2005; Stern et al. 2010; Moresco et al. 2012a,b; Zhang et al. 2012;Moresco et al. 2016b). The basic problem of this method isthe fact that it relies on the measure of stellar populationage, which presents, when estimated from a fit of the spec-trum and/or spectral energy distribution (SED), significantdegenerations with other parameters, such as metallicity,star formation history (SFH) and dust content. An alter-native method to mitigate these degeneracies is to identifya particular spectral feature that is sensitive to the agingof the stellar population. An example of this approach isprovided by Moresco et al. (2011, 2012a), Moresco (2015)and Moresco et al. (2016a), in which the expansion historyof the Universe is determined by studying the redshift de-pendence of the ˚A break. Despite the high potential ofthe method, the break at ˚A is particularly sensitive notonly to the age, but also to the variation of the metallicity ofthe stellar population, which has to be taken into account asa systematic error in the estimate of cosmological parame-ters. It is evident the need to find a new spectral feature thatminimize the dependence systematic and able to translatethe amount dz / dt in the observable dz / d (feature) and thenable to determine the cosmological parameter with higheraccuracy.In the effort of exploiting reliable age indicators, wepresent a new study of ETGs relative age evolution basedon the variation of the H β Lick index with redshift. Thisindex, firstly introduced by Burstein et al. (1984) and rede-fined by Worthey et al. (1994), has been identified as theone with the maximum dependence on the variation of theage of the stellar population, and the minimal dependenceon metallicity and chemical composition (Trager et al. 1998;Lee & Worthey 2005; Thomas et al. 2011). In detail, wemeasure the H β Lick index in a sample of passive galax-ies selected from the Sloan Digital Sky Survey (SDSS), tocheck if this particular spectral feature is actually able toprovide a reliable differential dating of galaxy stellar ages,in order to derive constraints both on galaxy evolution andformation and on the expansion history of the Universe.This paper is organized as follows. In Section 2 we intro-duce the data sample. We describe the physical parametersof the passive galaxies sample, and our method for the H β MNRAS000
Early-type galaxies (ETGs) are perfect candidates to inves-tigate both galaxy formation and evolution theories and,at the same time, to put constraints on the expansion his-tory of the Universe. Many recent observations show thatmost massive galaxies contain the oldest stellar populationsup to z ∼ − (e.g. Spinrad et al. 1997; Cowie et al. 1999;Heavens et al. 2004; Thomas et al. 2005; Cimatti et al.2008; Thomas et al. 2010; Moresco et al. 2011) and thatonly few percent of their current stellar mass was formedafter z ∼ . Moreover, studies on the stellar mass function atdifferent redshifts (e.g. Bundy et al. 2005; Borch et al. 2006;Bundy et al. 2006; Ilbert et al. 2010; Pozzetti et al. 2010;Maraston et al. 2013) showed that most massive galaxies ( M ∼ M ⊙ ) are characterized by an increase of their stel-lar mass density at z ∼ field) and a subsequent negligible evolutionin number density from z ∼ to the present (Cimatti et al.2006; Pozzetti et al. 2010; Moresco et al. 2013). All theseobservational evidences suggest that these massive, red andpassively evolving galaxies represent the oldest objects in theUniverse below z ∼ . For this reason, a study based on thevariation of ETGs properties, such as age, chemical compo-sition, dynamic, at different redshifts, could rightly help toexpand our current knowledge of the physical process thatdrive the formation and evolution of galaxies. Moreover, asfirstly pointed out by Jimenez & Loeb (2002), the differen-tial age evolution of ETGs can be also used to put severalcosmological constrains. In particular, by estimating the rel-ative differential age ( ∆ t age ) between ETGs, formed at thesame cosmic time, but observed at different redshifts ( ∆ z ),it is possible to determine the derivative of redshift withrespect to cosmic time dz / dt .This quantity is directly related to the cosmologi-cal expansion history described by the Hubble parameter: H ( z ) = − + z dzdt , which can be used to estimate many cos-mological parameters such as H , Ω , M , Ω , Λ and w Λ . Thistechnique, known as “cosmic chronometers” method, hasbeen used recently in several works and obtained promis-ing results in the estimate of the Hubble parameter andof the dark energy equation of state (Simon et al. 2005; Stern et al. 2010; Moresco et al. 2012a,b; Zhang et al. 2012;Moresco et al. 2016b). The basic problem of this method isthe fact that it relies on the measure of stellar populationage, which presents, when estimated from a fit of the spec-trum and/or spectral energy distribution (SED), significantdegenerations with other parameters, such as metallicity,star formation history (SFH) and dust content. An alter-native method to mitigate these degeneracies is to identifya particular spectral feature that is sensitive to the agingof the stellar population. An example of this approach isprovided by Moresco et al. (2011, 2012a), Moresco (2015)and Moresco et al. (2016a), in which the expansion historyof the Universe is determined by studying the redshift de-pendence of the ˚A break. Despite the high potential ofthe method, the break at ˚A is particularly sensitive notonly to the age, but also to the variation of the metallicity ofthe stellar population, which has to be taken into account asa systematic error in the estimate of cosmological parame-ters. It is evident the need to find a new spectral feature thatminimize the dependence systematic and able to translatethe amount dz / dt in the observable dz / d (feature) and thenable to determine the cosmological parameter with higheraccuracy.In the effort of exploiting reliable age indicators, wepresent a new study of ETGs relative age evolution basedon the variation of the H β Lick index with redshift. Thisindex, firstly introduced by Burstein et al. (1984) and rede-fined by Worthey et al. (1994), has been identified as theone with the maximum dependence on the variation of theage of the stellar population, and the minimal dependenceon metallicity and chemical composition (Trager et al. 1998;Lee & Worthey 2005; Thomas et al. 2011). In detail, wemeasure the H β Lick index in a sample of passive galax-ies selected from the Sloan Digital Sky Survey (SDSS), tocheck if this particular spectral feature is actually able toprovide a reliable differential dating of galaxy stellar ages,in order to derive constraints both on galaxy evolution andformation and on the expansion history of the Universe.This paper is organized as follows. In Section 2 we intro-duce the data sample. We describe the physical parametersof the passive galaxies sample, and our method for the H β MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies Lick measurement. In Section 3 we present the results aboutthe H β − z and H β − mass relations and compare them withthe theoretical predictions of the stellar population synthesismodels. We discuss the effect of possible contamination bythe emission lines in the observed H β absorption line in theSection 4, and finally in Section 5 we list our conclusions.Throughout the paper we assume a H = kms − M pc − , Ω , M = . and Ω Λ = . cosmology. The galaxies analyzed in this work are selected from thespectroscopic catalogue of the Sixth Data Release of SloanDigital Sky Survey (SDSS-DR6). The SDSS-DR6 providesphotometry in the u, g, r, i, z bands and the spectrum ofabout galaxies, extracted with Petrosian magnitude r < . . Each spectrum is measured from to ˚Awith a resolution λ / ∆λ ≈ − . The SDSS data areprovided in vacuum wavelengths. To be meaningfully com-pared with atomic transitions, we converted them in the airsystem . To have a wider photometric coverage, we decidedto analyze the sample provided by Moresco et al. (2011),where SDSS galaxies are matched with the Two Micron AllSky Survey (2MASS), with photometry in the J, H and Kbands. This wider coverage allows a better accuracy in thestellar mass estimates from the SED-fitting, and a more pre-cise selection based on photometric data (see Sec. 2.1). This study strongly relies on the selection of a sample ofpassively evolving galaxies which, having assembled most oftheir mass at high redshifts, are able to trace homogeneouslythe age-evolution of the Universe. To select the purest pos-sible sample of passive galaxies, with no evidence of recent The conversion relation from vacuum wavelengths to air wave-lengths, proposed in Morton et al. (1991), is the following: λ AIR = λ VAC (cid:18) . + . E − + . λ VAC + . E λ VAC (cid:19) (1)with λ AIR and λ VAC expressed in ˚A. episodes of star formation, we followed the approach de-scribed in Moresco et al. (2011), and selected galaxies with: • no strong emission lines. Starting from the equiv-alent width measurements provided by the analysis of theMPA-JHU DR7 , we select only the objects with a restframeequivalent width EW(H α ) > -5 ˚A and EW([OII] λ > -5 ˚A, where, by convention, the measures are given in nega-tive values when in emission. • spectral energy distribution matching the red-dest passive ETG templates. Following the approachof Zucca et al. (2006), the SED of each galaxy has beencompared with a library of 62 empiric SEDs described inIlbert et al. (2006), comprising galaxies with both old stellarpopulations and intense star formation activity. The galax-ies are divided according to their SED, and we select thosegalaxies matching an early-type template, corresponding tothe four reddest templates.With this selection, we obtain a sample of ∼ galaxies.For more details, we refer to Moresco et al. (2011).In order to investigate the evolution of our sample, westudy their physical properties, focusing in particular on thestellar mass, stellar metallicity and velocity dispersion. Weuse the stellar mass estimates from Moresco et al. (2011),obtained by a multi-colour SED-fitting procedure ( pho-tometric bands from u to K). We apply a further masscut, selecting only the most massive galaxies with a stel-lar mass log ( M / M ⊙ ) ≥ . . This choice is made to se-lect only the most massive objects that, according to thedownsizing scenario, should correspond to the oldest objects(Thomas et al. 2010). In the mass-downsizing scenario, themost massive galaxies were formed earlier and over a shorterperiod than those in less massive galaxies. For this rea-son, we decide to split our sample in four narrow mass bins( ∆ log ( M / M ⊙ ) = . ), to have a more homogeneous samplingof the redshift of formation: . < log ( M / M ⊙ ) < (BinI), < log ( M / M ⊙ ) < . (BinII), . < log ( M / M ⊙ ) < . (BinIII) and log ( M / M ⊙ ) > . (BinIV) (see Fig. 1). Further-more, for this sample we have a measure of the Star Forma-tion History (SFH) estimated by Moresco et al. (2011) with , 1–20 (2016) A. Concas et al. l og ( M / M O • ) Figure 1.
Stellar mass − redshift distributions of the four masssubsamples (red, green, blue and black curves respectively for theBinIV, BinIII, BinII and BinI, from top to bottom). The blackdotted vertical lines indicate the redshift division of the sample(see Tab. 1 for the stellar mass median values). (A color versionof this figure is available in the online journal.) an exponential delayed SFH: SFR ( t , τ ) ∝ (cid:0) t / τ (cid:1) exp ( − t / τ ) (with τ in the range of values . ≤ τ ≤ Gyrs). The medianvalue of the our total sample is τ = . Gyrs.In Fig. 1 we present the mass-redshift distribution. Itis evident that the median mass increases with the redshiftdue to magnitude limit effect of the survey. Therefore, toavoid possible biases, we select the galaxies having z ≤ . , z ≤ . , z ≤ . and z ≤ . , respectively for the BinI, BinII,BinIII and BinIV. In this way, we limit the difference in themedian mass along the redshift range to . dex on average(see Fig. 1).As mentioned in the previous section, the H β Lick in-dex is the less sensitive to metallicity variations compared toall other indices of the Lick system. However, in the wave-length range where the index is defined, there may be weakmetal absorption lines and, for this reason, the metallicitydependence of the H β index is not totally negligible. Thesample has been therefore cross-matched with the SDSS-DR4 subsample obtained by Gallazzi et al. (2005), for whichthe stellar metallicities of the galaxies are estimated fromthe simultaneous fit of several spectral features (D4000, H β ,H δ a + H γ a , [Mg Fe] and [MgFe]’). We study the metallicity-redshift relation. In order to minimize the possible metallic-ity effect, we made a further cut in redshift, selecting onlygalaxies with redshift z ≥ . for BinI and BinII, z ≥ . for BinIII, and z ≥ . for BinIV. The median metallicity of σ [ k m / s ] Figure 2.
Velocity dispersion-redshift relations, averaged in binof redshift, for the different mass subsamples, BinIV, BinIII, BinIIand BinI from top to bottom (see Tab. 1 for the median values).(A color version of this figure is available in the online journal.) the final sample is Z / Z ⊙ ∼ . (with a total spread of about . within the total redshift range analyzed and of ∼ ∆ z ∼ . − . ), showing only a slightvariation with redshift, in agreement with the recent metal-licity measurements obtained by total spectral fitting of ourstacked spectra (Citro et al. 2015). We note, further, thatthere is no significant difference in the median metallicity ofthe different mass subsamples.In this paper, we adopt the velocity dispersion derivedby the Princeton group . Figure 2 shows the velocity dis-persion relations for all mass subsamples. We find that thevelocity dispersion is constant in each subsample (see Tab 1for the median values).Finally, the observed optical spectrum can be contam-inated by the presence of night sky emission lines (seeHanuschik 2003). Particularly the night sky emission linesat ˚A ([OI]) and at . , . (NaI) ˚A are verystrong, and leave significant contamination in H β measure-ment.In order to avoid this source of contamination, we decideto excluded the galaxies having a redshift between . < z < . and . < z < . , which are the redshifts for whichthose lines fall into the H β definition range.After all the cuts adopted, the final sample consists of ∼ galaxies. The median values and the respective er- The data are available on the websitehttp://spectro.princeton.edu/ MNRAS000
Velocity dispersion-redshift relations, averaged in binof redshift, for the different mass subsamples, BinIV, BinIII, BinIIand BinI from top to bottom (see Tab. 1 for the median values).(A color version of this figure is available in the online journal.) the final sample is Z / Z ⊙ ∼ . (with a total spread of about . within the total redshift range analyzed and of ∼ ∆ z ∼ . − . ), showing only a slightvariation with redshift, in agreement with the recent metal-licity measurements obtained by total spectral fitting of ourstacked spectra (Citro et al. 2015). We note, further, thatthere is no significant difference in the median metallicity ofthe different mass subsamples.In this paper, we adopt the velocity dispersion derivedby the Princeton group . Figure 2 shows the velocity dis-persion relations for all mass subsamples. We find that thevelocity dispersion is constant in each subsample (see Tab 1for the median values).Finally, the observed optical spectrum can be contam-inated by the presence of night sky emission lines (seeHanuschik 2003). Particularly the night sky emission linesat ˚A ([OI]) and at . , . (NaI) ˚A are verystrong, and leave significant contamination in H β measure-ment.In order to avoid this source of contamination, we decideto excluded the galaxies having a redshift between . < z < . and . < z < . , which are the redshifts for whichthose lines fall into the H β definition range.After all the cuts adopted, the final sample consists of ∼ galaxies. The median values and the respective er- The data are available on the websitehttp://spectro.princeton.edu/ MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies redshift mass median median galaxiesz range mass velocity dispersion log ( M / M ⊙ ) log ( M / M ⊙ ) σ [km s − ] BinI . − .
18 10 . − . . ± .
001 207 . ± . BinII . − .
22 11 . − .
25 11 . ± .
001 234 . ± . BinIII . − .
25 11 . − . . ± .
001 259 . ± . BinIV . − . > . . ± .
002 286 . ± . Tot . − . > .
75 11 . ± .
001 226 . ± . Table 1.
Redshift range, mass range, median mass and median velocity dispersion of the passive galaxies in different mass subsamples. F λ (r e l a t i v e e r g c m − s − Å − ) [MgI] Ca,Fe NaD[OII] H K G band H β [OIII] H α [NII] BinIBinIIBinIIIBinIV
Figure 3.
Median stacked spectra of the four passive galaxies mass subsamples. (from top to bottom respectively for the BinI, BinII,BinIII and BinIV, left panel). In the range between − ˚A there are not significant emission lines ([OII], [OIII], H α and [NII] λ β line show a typical absorption feature (right panel) in all the mass bins (from black to light gray for BinI, BinII, BinIII andBinIV respectively). The spectra are normalized between and ˚A restframe. (A color version of this figure is available in theonline journal.) rors ; of mass and velocity dispersion for the different masssubsamples are reported in Table 1. In the same table, wealso report the number of galaxies in each bin.Fig. 3 shows the median stacked spectra for the fourmass subsamples. From the left panel, it is evident that allspectra show typical features of a passive population, with(i) absence of emission lines ( [OII], H β , [OIII], and H α ),(ii) strong absorption features (H β , H α , G band, Ca H andK), and (iii) strong D4000 break. We notice that there isstill present a weak emission at ˚A [NII], and that theamplitude of this feature is mass-dependent, being most ev-ident in the less massive subsample (BinI). For more details, The error on the median are evaluated as the medianabsolute deviation / √ N , MAD = , ∗ median ( | x − median ( x ) | ) (seeHoaglin et al. 1983). see Section 4. We highlight the region near H β line (rightpanel); all the four spectra show a typical and unperturbedabsorption profile. β index We measure the H β Lick absorption line index for all galaxies. We implement an IDL (Interactive Data Lan-guage ) code in order to perform measures coherently on ob-servational data and models. We use the Lick H β index def-inition by Worthey et al. (1994); the bandpasses are shownin Fig. 3. In the standard Lick system, the indices are de-fined on low resolution spectra ( ∼ ˚A FWHM in H β region).However, the modern spectroscopic surveys, and in particu- , 1–20 (2016) A. Concas et al. lar the SDSS, provide spectra with a much higher resolution( ∼ . − . ˚A FWHM), comparable with the new stellar pop-ulations synthesis models (for example Bruzual & Charlot2003 and Maraston & Str¨omb¨ack 2011 ). In order to mea-sure coherently this feature in the models and observations,we decide to perform the analysis directly on the observedspectra, without altering the resolution.Before applying our code to real data, we test its re-liability to reproduce the H β Lick values tabulated in theBC03 templates. We find a very good agreement betweenthe two measurements with a negligible median offset of − . ˚A and a standard deviation of . ˚A , whichis comparable with the average measured error. Therefore,we find that the two independent methods are consistent,and without any significant biases. β We derive the median H β -redshift relations in each masssubsample; we use narrow redshift bins ( ∆ z ∼ . − . )for the three most populated mass subsamples, while in themore massive subsample we use ∆ z ∼ . because of thelower statistic with respect to the other samples.The results are shown in Fig. 4. From this figure, wenote two main trends: • a clear H β − redshift relation for each subsample, withan increase in the index strength of ∼
10% along the redshiftrange. • a clear trend with mass; i.e., at each redshift more mas-sive galaxies present a lower H β index with respect to lessmassive ones ( ∼ ).It is interesting to note that both effects can easily beseen even by direct inspection of the median spectra. Asan example, we show the stacked spectra at different red-shifts for the sample with < log ( M / M ⊙ ) < . (BinII,see Fig. 5, left panel), from which it is evident a deeper ab-sorption line with redshift. The trend with the mass is also H β [ Å ] O • )<11.0011.00
Median H β -redshift relation for passive galaxies in dif-ferent mass subsamples (circles, squares, triangles and diamondsfor BinI, BinII, BinIII and BinIV respectively). (A color versionof this figure is available in the online journal.) visible in the stacked spectra of galaxies at fixed redshift,with most massive galaxies showing a smaller absorptionline than lower-mass ones (see Fig. 5, right panel).Both these trends are qualitatively consistent with ageneral aging of the stellar population and a mass-agerelation (“mass-downsizing”), also found by Thomas et al.(2010). Our results also concur with a recent work ofChoi et al. (2014). By modeling the full optical spectrum ofa quiescent galaxy sample at low and intermediate redshift( . < z < . from the SDSS and . < z < . from AGNand Galaxy Evolution Survey, AGES), Choi et al. (2014)found that the best-fit SSP-equivalent age is higher for themost massive galaxies and it increases with decreasing red-shift at fixed stellar mass. This correspondence between twodifferent methods highlights the potential of our H β line asa tracer of aging in the stellar population. We test this in-terpretation in Sec. 3.1. The H β index is not totally immune to metallicity ( Z / Z ⊙ )effects for the integrated stellar population (Worthey et al.1994). Furthermore, this index is sensitive to the galaxy ve-locity dispersion ( σ ). To exclude the possibility that thetrends found are due to a σ or Z / Z ⊙ variation, we studythe impact of these parameters using stellar population syn-thesis (SPS) models. We consider Bruzual & Charlot (2003)and Maraston & Str¨omb¨ack (2011) models (hereafter BC03 MNRAS000
Median H β -redshift relation for passive galaxies in dif-ferent mass subsamples (circles, squares, triangles and diamondsfor BinI, BinII, BinIII and BinIV respectively). (A color versionof this figure is available in the online journal.) visible in the stacked spectra of galaxies at fixed redshift,with most massive galaxies showing a smaller absorptionline than lower-mass ones (see Fig. 5, right panel).Both these trends are qualitatively consistent with ageneral aging of the stellar population and a mass-agerelation (“mass-downsizing”), also found by Thomas et al.(2010). Our results also concur with a recent work ofChoi et al. (2014). By modeling the full optical spectrum ofa quiescent galaxy sample at low and intermediate redshift( . < z < . from the SDSS and . < z < . from AGNand Galaxy Evolution Survey, AGES), Choi et al. (2014)found that the best-fit SSP-equivalent age is higher for themost massive galaxies and it increases with decreasing red-shift at fixed stellar mass. This correspondence between twodifferent methods highlights the potential of our H β line asa tracer of aging in the stellar population. We test this in-terpretation in Sec. 3.1. The H β index is not totally immune to metallicity ( Z / Z ⊙ )effects for the integrated stellar population (Worthey et al.1994). Furthermore, this index is sensitive to the galaxy ve-locity dispersion ( σ ). To exclude the possibility that thetrends found are due to a σ or Z / Z ⊙ variation, we studythe impact of these parameters using stellar population syn-thesis (SPS) models. We consider Bruzual & Charlot (2003)and Maraston & Str¨omb¨ack (2011) models (hereafter BC03 MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies F λ (r e l a t i v e e r g c m − s − Å − ) fixed mass 4820 4840 4860 4880 49000.880.900.920.940.960.981.001.02 F λ (r e l a t i v e e r g c m − s − Å − ) fixed z Figure 5.
Median stacked spectra in the H β line region. Left panel: stacked spectra with the same mass ( < log ( M / M ⊙ ) < . , BinII)and different mean redshift z = . , . and . (from light gray to black, respectively). Right panel: stacked spectra with the sameredshift, z = . , for different mass subsamples (black, gray and light gray for BinI, BinII, and BinIV respectively). For illustrativepurposes the BinI and BinII spectra are smoothed to the common velocity dispersion of BinIV. and MaStro, respectively). BC03 models are available at aresolution of ˚A FWHM in the wavelength range between − ˚A; MaStro models are available with a resolutionof ∼ . ˚A FWHM between − ˚A . Both modelsshare a resolution very similar to the one of SDSS spectra( ≈ − between to ˚A). This is particularlyuseful since it allows a direct comparison between the ob-served spectra with the theoretical SED without having tomodify the spectral resolution.These models are used to create libraries of syntheticspectra with different velocity dispersions ( σ = , , and km s − ) and different metallicity ( Z / Z ⊙ = , . , . obtained by interpolating quadratically between Z / Z ⊙ = . , , . available in BC03 and Z / Z ⊙ = . , , in MaStro).The grid has been created with age . ≤ t ≤ Gyr, with de- More precisely, in Beifiori et al. (2011) it is shown that the spec-tral resolution of the MaStro models, based on the library stellarMILES is about . ˚A FWHM, instead of the nominal . ˚A layed exponential SFH, SFR ( t , τ ) ∝ ( t / τ ) exp ( − t / τ ) , where τ is chosen in the range . ≤ τ ≤ Gyr.
To check the effect of the velocity dispersion in our H β Lickmeasures, we perform several tests. By using the theoreticalspectra described in the previous section, we verify that anincrease of velocity dispersion causes an apparent decreaseof the observed H β index strength only due to a broadeningeffect. We further estimate the maximum percentage differ-ence in H β between our mass bins which can be attributedto σ from the analysis of SPS models; we find that the per-centage difference in H β between a single stellar population(SSP) with σ = km s − and σ = km s − is < . ,and is < between σ = km s − and σ = km s − , forboth models. We underline that given the range of σ of ourdata, these two estimates represent the maximum differencein H β which can be attributed to a σ effect between our MNRAS , 1–20 (2016)
A. Concas et al. mass subsamples, and they are always lower than the meanpercentage difference in our subsamples with similar σ differ-ences. Indeed, the mean percentage difference in H β medianvalues between BinI and BinIII is ∼ ∼
9% betweenBinI and BinIV (similarly, we get a difference of ∼
4% be-tween BinII and BinIII, and ∼
6% between BinII and BinIV).Moreover, we note that all SPS models analyzed show thatSEDs with different velocity dispersions have a difference influx in the red pseudo-continuum region ( . − . ), but the stacked spectra of the same mass subsample donot show this trend (see Fig. 5).For this reason, we exclude that the velocity dispersionby itself can cause the observed mass segregation betweenthe H β -z relation in different mass subsamples.Finally, we verified that in our data the median velocitydispersion (see Table 1 for median values of BinI, BinII,BinIII and BinIV) shows almost no redshift evolution in eachmass bin (see Fig. 2). For this reason, we exclude that theobserved H β index increase with redshift can be due to avelocity dispersion effect. The models are also used to establish the effect in the H β index due to the stellar metallicity. While there is no sig-nificant difference in the median metallicity of the differentmass subsamples, each mass bin instead shows a slight de-crease of the median metallicity with redshift.We create a library of H β indices as a function of ageusing stellar population models with different metallicity: , . and . Z / Z ⊙ . The study of this H β synthetic indicesshows that even an extreme variation of metallicity, between Z / Z ⊙ = to Z / Z ⊙ = . , . , implies a H β variation of only ∼ − on average, always lower than H β trend observed.Moreover, to further check the metallicity effect, not only inthe models but also on our data, we create a control sampleof galaxies with a narrow metallicity range (e.g., ∆ ( Z / Z ⊙ ) = . for the BinI). Even in this subsample we find a steadytrend of growth in the H β − z relations.From these analyses, we find that the increase of the H β equivalent width with redshift (at fixed mass) and decreasewith mass (at fixed redshift) of passive galaxies cannot be only due to σ or Z / Z ⊙ variation, and hence can be mostlyexplained by an age-evolution effect, in particular with theage of the stellar population decreasing with increasing red-shift, and increasing with increasing mass. β -age: Comparison with SPS models To interpret the evolution of H β with redshift and its de-pendence on mass in the context of passive galaxies evo-lution, we proceed with a direct comparison between theobserved data and the index values calculated on the SEDprovided by SPS models, hereafter theoretical H β . Both theobserved and theoretical measurements are obtained by thesame method, described in Section 2.2. The theoretical H β curves as a function of age are transformed into H β -z rela-tions assuming a Λ CDM cosmology (see Section 1 for theparameters used), and a formation redshift. For our studies,we chose to probe different redshifts of formation for ourgalaxies, namely z F = , , , and ∞ . For this comparisonwe use two different stellar populations synthesis models,BC03 and MaStro and the theoretical models of H β Lickindexes of Thomas et al. (2011) (hereafter TMJ), calculatedby theoretically manipulating the index response functions.For BC03 and MaStro models, we adopt a Chabrier IMFinstead the TMJ models have a Salpeter IMF. However, us-ing BC03 models, we verify that a IMF variation does notaffect significantly the H β value. In particular, in the caseof solar metallicity, the choice of a Salpeter IMF instead ofa Chabrier causes an index decrease of < %. Furthermore,in the BC03 and MaStro models we use a delayed exponen-tially SFH, in particular we use models with τ = . Gyrswhich correspond a the τ median value estimate for the oursample (see Section 2.1 ). We investigate also the possiblevariation of H β value with different τ values. We compareSPS models with τ = . and τ = . Gyrs, and we find thatfor SPS older than Gyr the H β Lick index decreases of ≤ % in the SPS with τ = . Gyrs to respect at SPS with τ = . Gyrs. Since the median metallicity of the sample is Z / Z ⊙ ∼ . , for the comparison with the data we interpolatedquadratically the H β values of all models in the three metal-licities provided, in order to have an estimate of the indexat Z / Z ⊙ = . . The BC03 and MaStro models are convolved MNRAS000
6% between BinII and BinIV).Moreover, we note that all SPS models analyzed show thatSEDs with different velocity dispersions have a difference influx in the red pseudo-continuum region ( . − . ), but the stacked spectra of the same mass subsample donot show this trend (see Fig. 5).For this reason, we exclude that the velocity dispersionby itself can cause the observed mass segregation betweenthe H β -z relation in different mass subsamples.Finally, we verified that in our data the median velocitydispersion (see Table 1 for median values of BinI, BinII,BinIII and BinIV) shows almost no redshift evolution in eachmass bin (see Fig. 2). For this reason, we exclude that theobserved H β index increase with redshift can be due to avelocity dispersion effect. The models are also used to establish the effect in the H β index due to the stellar metallicity. While there is no sig-nificant difference in the median metallicity of the differentmass subsamples, each mass bin instead shows a slight de-crease of the median metallicity with redshift.We create a library of H β indices as a function of ageusing stellar population models with different metallicity: , . and . Z / Z ⊙ . The study of this H β synthetic indicesshows that even an extreme variation of metallicity, between Z / Z ⊙ = to Z / Z ⊙ = . , . , implies a H β variation of only ∼ − on average, always lower than H β trend observed.Moreover, to further check the metallicity effect, not only inthe models but also on our data, we create a control sampleof galaxies with a narrow metallicity range (e.g., ∆ ( Z / Z ⊙ ) = . for the BinI). Even in this subsample we find a steadytrend of growth in the H β − z relations.From these analyses, we find that the increase of the H β equivalent width with redshift (at fixed mass) and decreasewith mass (at fixed redshift) of passive galaxies cannot be only due to σ or Z / Z ⊙ variation, and hence can be mostlyexplained by an age-evolution effect, in particular with theage of the stellar population decreasing with increasing red-shift, and increasing with increasing mass. β -age: Comparison with SPS models To interpret the evolution of H β with redshift and its de-pendence on mass in the context of passive galaxies evo-lution, we proceed with a direct comparison between theobserved data and the index values calculated on the SEDprovided by SPS models, hereafter theoretical H β . Both theobserved and theoretical measurements are obtained by thesame method, described in Section 2.2. The theoretical H β curves as a function of age are transformed into H β -z rela-tions assuming a Λ CDM cosmology (see Section 1 for theparameters used), and a formation redshift. For our studies,we chose to probe different redshifts of formation for ourgalaxies, namely z F = , , , and ∞ . For this comparisonwe use two different stellar populations synthesis models,BC03 and MaStro and the theoretical models of H β Lickindexes of Thomas et al. (2011) (hereafter TMJ), calculatedby theoretically manipulating the index response functions.For BC03 and MaStro models, we adopt a Chabrier IMFinstead the TMJ models have a Salpeter IMF. However, us-ing BC03 models, we verify that a IMF variation does notaffect significantly the H β value. In particular, in the caseof solar metallicity, the choice of a Salpeter IMF instead ofa Chabrier causes an index decrease of < %. Furthermore,in the BC03 and MaStro models we use a delayed exponen-tially SFH, in particular we use models with τ = . Gyrswhich correspond a the τ median value estimate for the oursample (see Section 2.1 ). We investigate also the possiblevariation of H β value with different τ values. We compareSPS models with τ = . and τ = . Gyrs, and we find thatfor SPS older than Gyr the H β Lick index decreases of ≤ % in the SPS with τ = . Gyrs to respect at SPS with τ = . Gyrs. Since the median metallicity of the sample is Z / Z ⊙ ∼ . , for the comparison with the data we interpolatedquadratically the H β values of all models in the three metal-licities provided, in order to have an estimate of the indexat Z / Z ⊙ = . . The BC03 and MaStro models are convolved MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies H β [ Å ] MaStroTMJ HR Miles σ =0 km/s z F =1z F =2z F =3z F =4z F = ∞ BC03 σ = 200−300 km/s Figure 6.
Comparison between the observed H β -z relations (circles, squares, triangles and diamonds for BinI, BinII, BinIII and BinIVrespectively) and different models. The black solid lines are the BC03 models with σ = km s − Z / Z ⊙ = . and different formationredshifts ( z F = , , , and ∞ ). For z F = ∞ we show also the models with σ = and km s − , open triangles and open squaresrespectively. The MaStro and TMJ models are shown for z F = (dashed and dash and dot lines, respectively). (A color version of thisfigure is available in the online journal.) with a velocity dispersion σ = km s − , comparable tothe median value of our sample. In Fig. 6, we show as anexample the observed H β − z relations and the theoreticalcurves (BC03 models) for different formation redshifts. ForMaStro and TMJ models we find similar results, as shownin the case of formation redshift z F = .From the comparison with theoretical models, as canbe clearly seen from Fig. 6, we find that they do not repro-duce the observed H β median relations, since, the modelspredict higher H β values than the median H β measured onour samples, so that in most cases the observed values wouldrequire an age greater than the age of the Universe. For themost massive sample the minimum shift between data andmodels is of the order of ∆ H β = . .Since the models are built with the same metallicity andvelocity dispersion found in the data, we exclude that this in-consistency is due to one of these two parameters. We verifythat also by imposing an extreme velocity dispersion for our sample ( σ = km s − ) the models do not reproduce theobservations. Regarding the metallicity, we instead find thatthe H β − z relations can be reproduced only by consideringmodels with metallicity approximately Z / Z ⊙ = , that areinconsistent with the metallicity estimated for this sample.Furthermore, comparing the metallicity estimated byThomas et al. (2010) for a morphological selected sampleof ETGs at . ≤ z ≤ . , we notice that for a subsamplewith velocity dispersion similar to our values they estimate aslightly higher metallicity than those considered in this work(Gallazzi et al. 2005). In particular, for σ = km s − (me-dian value of the less massive sample, BinI) Thomas et al.(2010) find a metallicity Z / Z ⊙ ∼ . , and for the medianvalue of the total sample, σ = km s − , they estimate ametallicity of the order of Z / Z ⊙ ∼ . (for more details, referto Thomas et al. 2010). These higher metallicity values arealso confirmed in a more recent work by Citro et al. (2015).In this study the authors find a median Z / Z ⊙ ∼ . ± . . MNRAS , 1–20 (2016) A. Concas et al.
Even these higher values are not enough to completely rec-oncile models with data.
In this section, we further investigate possible causes of theoffset between the model predictions and the measures ofthe H β Lick index showed in Section 3.2. In particular,we explore the possibility that our sample, despite the se-lection criteria (see Section 2.1), is still contaminated byan emission-line component. This potential emission com-ponent would contaminate the measurement of the H β in-dex by filling the line and producing a less intense absorp-tion feature, consistent with the recent results showed byServen & Worthey (2010) for a SDSS low redshift ( . < z < . ) galaxy sample. As discussed in Section 2, we select only the galaxies that notshowing significant emission lines in H α and [OII] (EW < -5 ˚A). We check that also cutting the sample by adoptinga more stringent H α limit (S/N < ), the offset betweenthe H β lick index in our data and models is not removed.However, a more detailed analysis of the stacked spectrashows the presence of a weak [NII] emission at ˚A(see Fig. 3). Since the first ionization potential of the ni-trogen is very similar to that of hydrogen, the presenceof an emission line in [NII] λ λ of the to-tal sample have an equivalent width EW([NII] λ >
3, consistent with the clearly visible [NII] λ equivalent width of the total sample The dispersion is evaluated whit the median absolute deviation , MAD . are EW([NII] λ ± λ λ λ λ λ λ β emission line, we analyzethe galaxies most affected by this contamination. We se-lect the galaxies with a [NII] λ λ >
10; in this way, we select galax-ies (5% of the total sample). Figure 7 shows the medianspectrum relative to this subsample. It can be seen that,differently from the stacked spectrum of the global sam-ple (see Fig. 3), in this spectrum, together with a strong[NII] λ λ λ α , [SII] λ λ β region, there is not a clear emission component (Fig. 7bottom left panel). The H β absorption line only shows aparticular shape, different from that expected for a simpleabsorption, probably caused by an overlapping with a weakemission line contamination.Following this result, we decide to apply a furthercut to our sample, by selecting only the galaxies with a[NII] λ λ <
3; this sam-ple is composed by galaxies ( ∼
57% of the total sam-ple). We find that, even for this sample there is a resid-ual [NII] λ λ ∼ − . ± . ˚A. The residual emission can In this work, we decide to cut the sample above this limit (S/N([NII] λ >
10 ) because enabled us to select only thoseobjects in which the [NII] line is detected effectively while main-taining a good statistic (1145 galaxies).MNRAS000
10 ) because enabled us to select only thoseobjects in which the [NII] line is detected effectively while main-taining a good statistic (1145 galaxies).MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies restframe wavelength [Å]0.00.20.40.60.81.01.21.4 F λ (r e l a t i v e e r g c m − s − Å − ) [OII] H K G band H β [OIII] H α [NII][MgI] Ca,Fe NaD F λ (r e l a t i v e e r g c m − s − Å − ) O • )<11.0011.00
Top panel: stacked spectrum of the sample with [NII] λ >
10 ( galaxies), it shows some evident emission lines:[OII], [OIII], H α and [NII] λ λ >
10 stacked spectrum (red dash dot lines),[NII] λ < β region (left panel) are not evident emission lines, instead,in the H α region there are evident emissions ([NII] λ α , [NII] λ λ λ = Gyrs, σ = km s − calculated by BC03 model. (A color version of this figure is available in the online journal.) E W ( [ N II] ) O • )<11.0011.00
3, we calculate also the median H β -z relations at different mass,the results are shown in Fig. 9. We note that the cut in[NII] λ β index (on average to ∼ . ˚A for the BinIand BinII, ∼ . for the BinIII and ∼ . for the BinIV). The offset found between data and observations of thetotal sample is reduced. However, there is still a significantdisagreement between data and theoretical H β -z curves, es-pecially for the more massive sample (Bin IV). However,despite this discrepancy, we find similar H β -z and H β -Massrelationships as seen in the total sample, but with slightlydifferent slopes and normalizations. These variations makeimpossible to use the median H β values for an accurate es-timate of the absolute and differential age evolution of thestellar populations with the redshift. Consequently, it is notpossible to place constraints on the redshift of formation of MNRAS , 1–20 (2016) A. Concas et al. H β [ Å ] z F =2z F =3z F =4z F = ∞ O • )<11.0011.00
Comparison between H β -z relations (circles, squares, triangles and diamonds for BinI, BinII, BinIII and BinIV respectively)of the total sample (dotted curves) and the sample with EW([NII] λ < the galaxies and even the use of the H β -z relation in themethod of the cosmic chronometers appears inadequate. The SDSS galaxies spectra are extensively used for manypurposes, such as stellar mass and star formation historyestimates (Kauffmann et al. 2003), age and metallicity esti-mates in the local universe (Gallazzi et al. 2005), environ-ment effects in the galaxy formation (Thomas et al. 2010),and many other. In these previous works, before interpretingthe observed spectra, and therefore before using the stellarabsorption-line indices, standard procedures are followed toremove the contamination by nebular emission lines. In thissection we try to apply these cleaning methods both in theindividual and in the stacked galaxies spectra.The method proposed by Tremonti et al. (2004), for ex-ample, makes a non-negative least-squares fit of the emis-sion line free-observed regions of the spectrum, using a spec-tral library built using BC03 models. Then, the fitted spec- trum is subtracted from the observed spectrum, and theresiduals can be fitted to Gaussian broadened emission linestemplates. Finally, the fitted emission lines are subtractedfrom the original observed spectrum to produce a “pure”absorption line spectrum (for further details, we refer toTremonti et al. 2004). To verify if this method of decontam-ination is actually able to producing a clean sample in theH β region, we use H β values measured by the MPA-JHUDR7 group, which are available both for the original ob-served spectra that for the ”pure” absorption line spectra.We select a sample consisting on galaxies without emissionlines, i.e. with no correction for emission lines based on themethod of Tremonti et al. (2004), which contains 19904 ob-jects. We measure the median H β -z relations also for thissubsample, with the same procedure described in Section 3.The H β -z relations obtained are consistent with those foundfor the subsample with S/N([NII] λ <
3. This suggeststhat, using objects with no emission lines detected by stan-dard correction method, the offset between the observed H β MNRAS000
3. This suggeststhat, using objects with no emission lines detected by stan-dard correction method, the offset between the observed H β MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies values and the predicted ones is not totally removed.In addition, we test the presence of weak H β emission linedirectly in the stacked spectra. We split our sample interms of stellar mass and redshift as we done in Section3 for the H β values, and then we built the median spec-tra for each mass and redshift bin. In order to separatethe stellar continuum from the nebular emission compo-nent, we decide to using a combination of the publicly avail-able IDL codes: penalized pixel-fitting (pPXF), devolopedby (Cappellari & Emsellem 2004) and gas and absorptionline fitting (GANDALF) write by (Sarzi et al. 2006). Wemeasure the line-of-sight velocity distribution (LOSVD) byusing pPXF code. Then, we perform the GANDALF analy-sis to convolve a set of input synthetic spectra with the pre-viously kinematic and to fit the observed stacked spectrumsimultaneously with the models and a Gaussian emissionlines template. The result is a superposition of an optimalcombination of the SSP templates with a set of Gaussiansthat represent the emission lines. Through the subtractionof the emission line spectrum from the observed one, we getthe clean absorption line spectrum free from emission linecontamination. First, we analyze the obtained H β emissionlines and then we explore the impact of this cleaning methodin the observed spectra. In order to test the robustness ofthe emission lines extraction, we repeat the methodologyby using three different spectral library: two based on theBC03 SSP with different age . ≤ t ≤ Gyr (here-after BC03 Gyr) and a more extended age . ≤ t ≤ Gyr (hereafter BC03 Gyr); and the third library builtwith MaStro models with and age . ≤ t ≤ Gyr. Wefind that, the recovered H β emission lines are model depen-dent: the equivalent width is systematically higher for theBC03 Gyr library than the BC03 Gyr ( ∆ EW ∼ . ˚A)and the differences increase if we compare BC03 with MaS-tro models, ∆ EW ∼ . ˚A . The median equivalent widthare : EW ∼ − . ± . , ∼ − . ± . and ∼ − . ± . ˚A for BC03 Gyr, BC03 Gyr and MaStro library, re-spectively. This result is consistent with the study showed The BC03 and MaStro stellar population templates have aChabrier IMF and metallicity Z / Z ⊙ = . , . , , . and Z / Z ⊙ = . , , , respectively. in Singh et al. (2013); their figure shows that at low H β fluxes there are differences in the flux extraction by usingGANDALF code with SSP instead of the stellar templates.Therefore, the correction for very low emission in the ab-sorption H β line depends on the templates library used inthe continuum fit. Furthermore, we find that, in all the threelibraries, the H β emission lines are detected with a very lowconfidence level, the amplitude over noise is always A/N ≤ (the noise is defined as the dispersion of fluctuations in thefit residuals).Finally, we test the more recent emission correctionfor the hydrogen features proposed by Serven & Worthey(2010). Serven & Worthey (2010) derived emission correc-tions of the Balmer series Lick indices for a SDSS quies-cent galaxy spectral sample (Graves et al. 2007) by compar-ing the H α -Mg b diagram from the SDSS stacked spectrawith the measurements obtained for 13 Virgo galaxies. Byusing the same prescriptions showed in Serven & Worthey(2010), we re-calibrate the H α -Mg b diagram and then theH β emission correction in our stacked spectra. We find thatfor the more massive sample (BinIV), the mean Mg b valueis . ± . ˚A and the mean H β emission correction factoris on the order of − . ± . ˚A , that it is in good agree-ment with the emission values obtained with the GANDALFmethod mentioned before. However, we stress that, also inthis case, the method is model-dependent, since the contin-uum correction was determined by using the Worthey et al.(1994) and Trager et al. (1998) models (see Section 2 ofServen & Worthey 2010). Moreover, rescaling the H α -Mg brelation from the SDSS values to the Virgo data could beage-dependent if the two samples have different mean ages.We conclude that for our sample, also in the stacked spec-tra, is very difficult measure a well detected and model-age-indipendent H β emission line and than correct our observedspectra in order to obtain a ”pure” absorption H β line. β self-diluted emission line In order to have a qualitative estimate of the hiddenEW(H β ) emission related to the observed [NII] λ MNRAS , 1–20 (2016) A. Concas et al. (Baldwin et al. 1981) diagram, hereafter BPT diagram.The equivalent width measurements for [OIII], H β , H α and [NII] λ >
3, the subsam-ple with EW([NII] λ >
10, and the sub-sample with EW([NII] λ <
3. In the firsttwo cases, we find that the majority of the objectsare located in the LINERs region (Low Ionization Nu-clear Emission line Regions, Heckman 1980). For the firstand the second sample, the median and dispersion for log ( EW ([ NII ]) / EW ( H α )) are − . ± . and . ± . , and for log ( EW ([ OIII ]) / EW ( H β )) are . ± . and . ± . , respectively. In the last subsample, thedispersion in the data is larger because of the lower sig-nal to noise ratio (see Fig. 10). In this last case, themedian value of the sample is located in the compos-ite region ( log ( EW ([ NII ]) / EW ( H α )) ∼ − . ± . and log ( EW ([ OIII ]) / EW ( H β )) ∼ . ± . ).By using the median EW([NII] λ α ) valuesand the median EW([NII] λ α ) contribution. Then, we estimate the EW(H β )by assuming no absorption by dust, and hence an emis-sion line ratio, H α / H β ∼ . (Osterbrock et al. 1989), forelectron density of n = cm − and electron temperature T e = K ).In the sample with EW([NII] λ < λ ≃ -0.26 ± β ) emission in the range − . to − . ˚A(by considering the EW([NII] λ α ) dispersion),or weaker in case of dust extinction.The same conclusions can be drawn for the sample withthe larger [NII] λ λ > λ ± log ( EW ([ NII ]) / EW ( H α ) issmaller, ∼ . ± . . Then, we expect an H β emissionline equivalent width between − . and − . ˚A in case of noabsorption by dust, or weaker otherwise.In order to verify whether the H β emission line values,expected in the two different samples, S/N([NII] λ < >
10, can be effectively detected in the observed spec- tra, we perform some simulations, described in the followingsection. β emission line simulations Starting from the theoretical SED (in which only the ab-sorption component is taken into account) of SPS models(BC03), we simulate the presence of an emission line byadding a Gaussian component with variable amplitude andFWHM.Since different physical processes can give rise to emis-sion lines with different FWHM, we perform two differentsimulations: • SIMUL A , lines with FWHM=5 ˚A, mainly due tostar formation. The analysis of a spectrum of a typical star-forming galaxy from SDSS has shown a typical FWHM ofthe emission lines of ∼ ˚A. • SIMUL B , lines with FWHM=9 ˚A. Since, in the caseof emission lines due to different processes than star forma-tion, such as AGN activity, the lines are broader than theones found for star-forming galaxies.By changing the FWHM and the EW line in theoreticalemission lines, we study the variation of the absorption lineprofile with the contamination of this different emissions.The results of the simulations (for the case of a SSP SEDwith age=10 Gyr) are shown in Fig 11. In both simulations(A and B) it is possible to identify a threshold of emissionbelow which it is not possible to detect the H β emissioncomponent on the absorption line. We can appreciate thedistortion of the H β line due to the introduction of an emis-sion line, with increasing EW, only after EW ≤ − . ˚A orEW ≤ − . ˚A for SIMUL A or B, respectively. Emissionssmaller than these values are not able to change the shapeof the line, but however, they cause a intensity decrease inthe absorption line, producing a drastic variation in the H β lick index measure, with ∆ ( H β ) max ∼ . ˚A or ∆ ( H β ) max ∼ . ˚A in SIMUL A and B, respectively. From this analysis, wecan see that, for galaxies spectra with a resolution of the or-der of ˚A FWHM, there is a threshold detection limit of theH β emission line. As seen in previous section, the presenceof [NII] λ MNRAS000
10, can be effectively detected in the observed spec- tra, we perform some simulations, described in the followingsection. β emission line simulations Starting from the theoretical SED (in which only the ab-sorption component is taken into account) of SPS models(BC03), we simulate the presence of an emission line byadding a Gaussian component with variable amplitude andFWHM.Since different physical processes can give rise to emis-sion lines with different FWHM, we perform two differentsimulations: • SIMUL A , lines with FWHM=5 ˚A, mainly due tostar formation. The analysis of a spectrum of a typical star-forming galaxy from SDSS has shown a typical FWHM ofthe emission lines of ∼ ˚A. • SIMUL B , lines with FWHM=9 ˚A. Since, in the caseof emission lines due to different processes than star forma-tion, such as AGN activity, the lines are broader than theones found for star-forming galaxies.By changing the FWHM and the EW line in theoreticalemission lines, we study the variation of the absorption lineprofile with the contamination of this different emissions.The results of the simulations (for the case of a SSP SEDwith age=10 Gyr) are shown in Fig 11. In both simulations(A and B) it is possible to identify a threshold of emissionbelow which it is not possible to detect the H β emissioncomponent on the absorption line. We can appreciate thedistortion of the H β line due to the introduction of an emis-sion line, with increasing EW, only after EW ≤ − . ˚A orEW ≤ − . ˚A for SIMUL A or B, respectively. Emissionssmaller than these values are not able to change the shapeof the line, but however, they cause a intensity decrease inthe absorption line, producing a drastic variation in the H β lick index measure, with ∆ ( H β ) max ∼ . ˚A or ∆ ( H β ) max ∼ . ˚A in SIMUL A and B, respectively. From this analysis, wecan see that, for galaxies spectra with a resolution of the or-der of ˚A FWHM, there is a threshold detection limit of theH β emission line. As seen in previous section, the presenceof [NII] λ MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies −2−1012 l og ( [ O III] / H β ) All S/N>3 −2−1012 l og ( [ O III] / H β ) [NII] S/N>10 −1.5 −1.0 −0.5 0.0 0.5log([NII] /H α )−2−1012 l og ( [ O III] / H β ) [NII] S/N<3 Figure 10.
Distribution of the galaxies in the BPT diagram for the sample with all EW S/N >
3, EW([NII] λ >
10 andEW([NII] λ <
3, respectively from the top downwards. The gray cloud is the total sample. The dashed curve is the theo-retical demarcation of Kewley et al. (2001) , that separates star-forming galaxies and composites from AGN. The solid curve indicatethe empirical division between pure star-forming galaxies from composite and AGN of Kauffmann et al. (2003). The median value anddispersion of the distribution are shown with the black symbols, in each subsample. (A color version of this figure is available in theonline journal.) ence of a weak H β emission line with EW ≥ − . ˚A for thesample whit S/N([NII] λ < ≥ − . ˚A for thesample whit S/N([NII] λ >
10. These values are near tothe threshold limit identified by simulations, therefore con-sistent with not being detectable in emission in our spectra.However, this potential hidden emission line can explain thedetected offset between observational data and theoreticalmodels discussed in the Section 3.2.Performing the same simulations for SSP models withdifferent ages (5 and 13 Gyr), we find that the detectionlimit for the H β emission line does not change significantly. We find that even the less contaminated passive galax-ies (sample with EW([NII] λ <
3) may present anemission line contamination in the H β absorption line. As discussed in Section 4.3 using the BPT diagrams, wefound that by selecting samples with higher S/N (sam-ple with all lines S/N > λ > T ∼ K) in ETGs, with line ratios typically classified asLINERs. Despite the number of studies, two fundamentalquestions remain open: what is the origin of this ISM in theETGs and what is the physical mechanism that determinesits ionization?Studies carried out on the kinematics of the gas, in mostcases, show a misalignment between gas and stellar compo-
MNRAS , 1–20 (2016) A. Concas et al.
FWHM=9Å
EQW= −2.01 H β = −0.305 Å EQW= −1.82 H β = −0.105 Å EQW= −1.62 H β = 0.0941 Å EQW= −1.43 H β = 0.293 Å EQW= −1.24 H β = 0.493 Å EQW= −1.05 H β = 0.693 Å EQW= −0.862 H β = 0.893 Å EQW= −0.670 H β = 1.09 Å EQW= −0.479 H β = 1.29 Å EQW= −0.383 H β = 1.39 Å EQW= −0.287 H β = 1.49 Å EQW= −0.191 H β = 1.59 Å EQW=−0.0958 H β = 1.69 Å BC03 model H β =1.79 Å F λ (r e l a t i v e e r g c m − s − Å − ) FWHM=5Å
EQW= −1.11 H β = 0.626 Å EQW= −1.01 H β = 0.737 Å EQW= −0.904 H β = 0.848 Å EQW= −0.798 H β = 0.959 Å EQW= −0.691 H β = 1.07 Å EQW= −0.585 H β = 1.18 Å EQW= −0.479 H β = 1.29 Å EQW= −0.372 H β = 1.40 Å EQW= −0.266 H β = 1.51 Å EQW= −0.212 H β = 1.57 Å EQW= −0.159 H β = 1.62 Å EQW= −0.106 H β = 1.68 Å EQW=−0.0532 H β = 1.73 Å BC03 model H β =1.79 Å Figure 11. H β emission line simulations. We show the emission line effect within the H β absorption line (Simul A in the lower paneland Simul B in the upper panel). The different EW contaminations are plotted according with the labels (with different colors in theonline journal). In both figures we can identify a threshold limit above which it is possible to detect an emission contamination (thickcurves). The absorption model is a SSP with Z / Z ⊙ = , age = Gyrs and σ = km s − . nent, suggesting an external origin of the gas (Caon et al.2000). This observational evidence is in agreement with re-cent estimates of the gas emission metallicity, which seemsto indicate an external source (Annibali et al. 2010).However, as reported in Sarzi et al. (2006), the angu-lar momenta measured do not seem to be consistent with apurely external origin.The nature of the mechanism of ionization in LIN-ERs is still not clear, but currently, the most accreditedare photo-ionization by AGN activity (e.g. Ho 1999, 2000;Kewley et al. 2006), photo-ionization by post-asymptotic gi-ant branch (post-AGB) stars (Binette et al. 1994) and fastshocks (e.g. Dopita & Sutherland 1995). The AGN activ-ity, in fact, produces a source of energetic photons (X-rays and UV) able to ionize the interstellar medium; thisis confirmed by some observed bubbles in LINERs galax-ies (Baldi et al. 2009). For some objects, the presence of AGN activity was also confirmed by observations of the ra-dio core and X-rays point sources in their centers and UVvariability (e.g. Ho 2008). Nevertheless, recent works haveshown that in many cases the gas emissions are not onlyneighboring to the center, but an extended emission com-ponent also exists (Sarzi et al. 2006; Annibali et al. 2010;Yan & Blanton 2012; Singh et al. 2013). For this reason,the AGNs are not considered as the main cause of theLINERs-like emission lines in ETGs in favor of spatially ex-tended ionizing sources, that in some cases follow the profileof stellar density (Yan & Blanton 2012). These propertiesare found in another source proposed for the first time byBinette et al. (1994): the post-AGB stars in the old stellarpopulations. These stars, after the AGB phase, are oftensurrounded by material ejected during their thermal pulses.After that, this material is dispersed in the ISM, and theAGB stars, having very high temperatures ( ∼ K ), are ca- MNRAS , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies pable of producing a diffuse radiation field. Recent spatiallyresolved spectroscopy observations obtained with a proto-type of MANGA instrument, confirm the presence of an ex-tended LINERs-like emission associated with spectral fea-tures of old and metal rich stars, see Belfiore et al. (2015).This scenario is also supported by the fact that post-AGBsare able to reproduce the variation of the parameter of ion-ization (defined as the ratio of the ionizing photon flux den-sity to the electron density) with the radius of the galaxy(Yan & Blanton 2012). As expected in Binette et al. (1994)and Cid Fernandes et al. (2009), the post-AGBs are able toproduce weak emission lines: H α ∼ − . , − . ˚A for a stel-lar population of and Gyrs respectively. This is veryinteresting because if this emission is expressed in terms ofH β emissions, similar to what was seen in the Section 4.3,we find a measure of EW(H β ) ∼ − . , − . ˚A emission lineperfectly consistent with what is expected for our sample, es-pecially with regard to the subsample with EW([NII] λ < In this paper, we explore the properties of the H β Lick indexof massive and passive ETGs, to estimate its robustness asan age indicator, being the Lick index more sensitive to thestellar population age and less affected by stellar metallic-ity, as suggested since the pioneering work of Worthey et al.(1994). The aim of this work is to establish its reliability as“cosmic chronometer” to trace the age evolution of the Uni-verse as a function of redshift and to provide new constraintson the age of formation and evolution of galaxies stellar pop-ulations, eventually allowing measurement of the Hubble pa-rameter H ( z ) through the “cosmic chronometers” approach(Jimenez & Loeb 2002; Moresco et al. 2012a; Moresco 2015;Moresco et al. 2016a).Using photometric and spectroscopic information, weselect the most massive, passive and red ETGs in the SDSS-DR6 survey. The final sample consists of about galax-ies with stellar mass log ( M / M ⊙ > . ) in the redshift range . ≤ z ≤ . . We divide the sample into four mass subsam-ples ( ∆ log ( M / M ⊙ ) = . ) in order to avoid possible biasesdue to mass downsizing effect, and obtained four homoge-neous subsamples in redshift of formation. All the samplesare further divided into redshift bins and the spectra an-alyzed to measure the H β Lick index, obtaining a median H β − z relation in each mass subsample.The main results of this analysis may be summarised asfollows. • Despite the rather strict selection criteria, all the spec-tra present characteristic features of a passive population, wefind in the median stacked spectra of each mass bin clear ev-
MNRAS , 1–20 (2016) A. Concas et al. idence of a weak [NII] emission line, with equivalent width ofthe order of − . ˚A, which can be interpreted as a hint of thepresence of ionized gas. This residual emission line contam-ination may have a significant impact on the H β Lick indexmeasures. To address this issue, we split our samples on thebase of the [NII] line, having a purer sample of 13626 galaxiesselected with SN([NII]) <
3, and a more contaminated sam-ple with SN([NII]) >
10. The analysis of these two subsamplesconfirmed the first hypothesis of a possible hidden contami-nation, with the sample with SN([NII]) >
10 presenting clearemission lines also in H α ,[OIII] and H β . We also find thatthe amplitude of the [NII] emission line anti-correlates withstellar mass. • The analysis of all mass subsamples reveals a clear evo-lution of the H β Lick index as a function of redshift, with theindex decreasing with cosmic time. These trends are qualita-tively consistent with a passive evolution, and are proven tobe independent on many effects that can affect the analysis.These trends are also confirmed on both the original sam-ples, and on the “purest” one obtained after selecting onlygalaxies with SN([NII]) < • At each redshift more massive galaxies present a me-dian H β index lower than less massive ones, confirming amass-downsizing scenario for which more massive systemshave assembled their stars earlier and faster. This result hasbeen demonstrated not to depend on a selection effect dueto the different velocity dispersions and metallicities of thesamples; also in this case, this trend is found in both theoriginal and the “purest” samples. • The comparison with SPS models highlights an incon-sistency with observable data, for which observed galaxiesappear, in most cases, to be older than the age of the Uni-verse at the given redshifts. These differences are greaterthan ∆ H β ∼ . ˚A and seems not reconcilable with any pos-sible further re-selection of the samples. Only a stellar metal-licity systematically higher than the one found in these sam-ples ( Z / Z ⊙ ∼ ) may alleviate the tension between the dataand models. • We tested the presence of a weak H β emission linein our stacked spectra by using GANDALF code and theemission corrections for the hydrogen features proposed by Serven & Worthey (2010). We find that the recovered emis-sion lines are very uncertain, detected with a very low confi-dence level and are model dependent. The median emissionequivalent width ranges from ∼ − . to ∼ − . ˚A. • We also find that in the stacked spectrum obtained fromthe “purest” sample with SN([NII]) <
3, there is a residual[NII] emission line contamination, even if very weak (EW ∼− . ). • Throughout simulations, we demonstrate that it existsa threshold limit below which an emission line componentwithin the H β absorption features would not be detectable;this threshold depends on the FWHM of the line, beingEW(H β ) ≤ -0.9 ˚A or ≤ -0.2 ˚A respectively for a broaderand narrower FWHM (characteristic of star formation orAGN activity). We note that this EW is compatible withthe observed offset between models and data.In order to obtain a quantitative estimate of the age offormation of the galaxies and to test the feasibility of usingthis index as a “cosmic chronometers”indicator, the observedH β -z relations should be calibrated on SPS models. How-ever, the dependence of the normalization and of the slopeof these relations on the different possible selections, and theapparent inconsistency with theoretical models, makes H β an index that is difficult to rely on to estimate both absoluteand relative ages, and this, as discussed, is due to a possi-ble contamination of the line by an undetectable emissioncomponent. We discuss the possible candidates of ioniza-tion sources, finding a better agreement with post-AGB andslightly higher tension with AGN.Despite this index has been historically identified as thebest suited to constrain the age of a galaxy population, allthe highlighted issues do not allow to use it for an accu-rate estimate of the absolute and differential age evolutionof the stellar populations with redshift. Therefore, it is notpossible to place constraints on the galaxies redshift of for-mation, and even the use of the H β -z relation in the “cosmicchronometers” approach appears inadequate.Finally, higher SN and resolution spectra may help inmitigating these problems during the selection phase, and tobetter disentangle a narrow emission line component for a MNRAS000
3, there is a residual[NII] emission line contamination, even if very weak (EW ∼− . ). • Throughout simulations, we demonstrate that it existsa threshold limit below which an emission line componentwithin the H β absorption features would not be detectable;this threshold depends on the FWHM of the line, beingEW(H β ) ≤ -0.9 ˚A or ≤ -0.2 ˚A respectively for a broaderand narrower FWHM (characteristic of star formation orAGN activity). We note that this EW is compatible withthe observed offset between models and data.In order to obtain a quantitative estimate of the age offormation of the galaxies and to test the feasibility of usingthis index as a “cosmic chronometers”indicator, the observedH β -z relations should be calibrated on SPS models. How-ever, the dependence of the normalization and of the slopeof these relations on the different possible selections, and theapparent inconsistency with theoretical models, makes H β an index that is difficult to rely on to estimate both absoluteand relative ages, and this, as discussed, is due to a possi-ble contamination of the line by an undetectable emissioncomponent. We discuss the possible candidates of ioniza-tion sources, finding a better agreement with post-AGB andslightly higher tension with AGN.Despite this index has been historically identified as thebest suited to constrain the age of a galaxy population, allthe highlighted issues do not allow to use it for an accu-rate estimate of the absolute and differential age evolutionof the stellar populations with redshift. Therefore, it is notpossible to place constraints on the galaxies redshift of for-mation, and even the use of the H β -z relation in the “cosmicchronometers” approach appears inadequate.Finally, higher SN and resolution spectra may help inmitigating these problems during the selection phase, and tobetter disentangle a narrow emission line component for a MNRAS000 , 1–20 (2016) n the robustness of the H β Lick index as a cosmic clock in passive early-type galaxies less biased measurement. Another possible option is to studyhigher order Balmer lines (H γ , H δ ), as e.g. suggested by thework of Vazdekis & Arimoto (1999), since those lines shouldbe less affected by an underlying emission component. Thisanalysis will be further exploited in a following paper. ACKNOWLEDGEMENTS
The authors would like to thank the referee, Guy Worthey,for useful suggestions. We also thank Marco Mignoli, Clau-dia Maraston, Daniel Thomas, Jonas Johansson, MarcellaBrusa and Gianni Zamorani for the stimulating discussions.We acknowledge Anna Gallazzi and Jarle Brinchmann forthe SDSS data availability and their clarifications. AC is alsograteful to Annalisa Citro and Salvatore Quai for sharing apreview of their results on SDSS stacked spectra analysis.Part of this work was supported by the INAF, OsservatorioAstronomico di Bologna and by the Dipartimento di Fisica eAstronomia, Universit`a degli Studi di Bologna. We acknowl-edge the grants ASI n. I/023/12/0 ”Attivit`a relative alla faseB2/C per la missione Euclid” and PRIN MIUR 2010-2011”The dark Universe and the cosmic evolution of baryons:from current surveys to Euclid”. ACi, LP and MM acknowl-edge the PRIN MIUR 2015 ”Cosmology and FundamentalPhysics: illuminating the Dark Universe with Euclid”.
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