Spectroscopic versus Photometric Metallicities: Milky Way Dwarf Spheroidal Companions as a Test Case
aa r X i v : . [ a s t r o - ph . C O ] M a y Astronomy&Astrophysicsmanuscript no. lgklg c (cid:13)
ESO 2018October 2, 2018
Spectroscopic versus Photometric Metallicities : Milky Way DwarfSpheroidal Companions as a Test Case
S. Lianou ,⋆ , E. K. Grebel , and A. Koch , Astronomisches Rechen-Institut, Zentrum f¨ur Astronomie der Universit¨at Heidelberg, M¨onchhofstrasse 12-14, D-69120Heidelberg, Germanye-mail: [email protected]; [email protected] University of Leicester, Department of Physics and Astronomy, University Road, LE1 7RH Leicester, UKe-mail: [email protected] Landessternwarte, Zentrum f¨ur Astronomie der Universit¨at Heidelberg, Koenigstuhl, D-69117 Heidelberg, GermanyReceived March 31, 2011; accepted May 21, 2011
ABSTRACT
Aims.
The method of deriving photometric metallicities using red giant branch stars is applied to resolved stellar populations under thecommon assumption that they mainly consist of single–age old stellar populations. We explore the e ff ect of the presence of mixed–agestellar populations on deriving photometric metallicities. Methods.
We use photometric data sets for the five Galactic dwarf spheroidals Sculptor, Sextans, Carina, Fornax, and Leo II in orderto derive their photometric metallicity distribution functions from their resolved red giant branches using isochrones of the DartmouthStellar Evolutionary Database. We compare the photometric metallicities with published spectroscopic metallicities based on theanalysis of the near–infrared Ca triplet (Ca T), both on the metallicity scale of Carretta & Gratton and on the scale defined by theDartmouth isochrones. In addition, we compare the photometric metallicities with published spectroscopic metallicities based onspectral synthesis and medium–resolution spectroscopy, and on high resolution spectra where available.
Results.
The mean properties of the spectroscopic and photometric metallicity samples are comparable within the intrinsic scatter ofeach method although the mean metallicities of dSphs with pronounced intermediate–age population fractions may be underestimatedby the photometric method by up to a few tenths of dex in [Fe / H]. The star-by-star di ff erences of the spectroscopic minus thephotometric metallicities show a wide range of values along the fiducial spectroscopic metallicity range, with the tendency to havesystematically lower photometric metallicities for those dwarf spheroidals with a higher fraction of intermediate–age populations.Such discrepancies persist even in the case of the purely old Sculptor dSph, where one would na¨ıvely expect a very good matchwhen comparing with medium or low resolution metallicity measurements. Overall, the agreement between Ca T metallicities andphotometric metallicities is very good in the metallicity range from ∼ − ∼ − ff ect on determiningmetallicities from photometry alone. Finally, we note that the comparison of spectroscopic metallicities of the same stars obtainedwith di ff erent methods reveals similarly large discrepancies as the comparison with photometric metallicities. Key words.
Galaxies: dwarf – Galaxies: stellar content – (Galaxies:) Local Group – Galaxies: abundances
1. Introduction
There are several techniques one can use to derive the photo-metric metallicities of a stellar system using its resolved oldred giant branches (RGBs). These include the use of the ( V − I ) o color of the RGB stars at the luminosity corresponding to M I = − . M I = − . ff (1990;DA90), in Armandro ff et al. (1993), and in Lee, Freedman &Madore (1993); the use of the fiducial ridge lines or analyticfunctions (Saviane et al. 2000a) describing the mean locus incolor–magnitude space of red giants in Galactic globular clus-ters (GCs) with known metal abundances; as well as the use oftheoretical stellar tracks or isochrones. The latter two techniquesserve to either bracket the range of the metal abundances or tointerpolate between them in order to derive the metallicity dis- ⋆ Fellow of the Heidelberg Graduate School of Fundamental Physics(HGSFP) and member of the International Max Planck ResearchSchool (IMPRS) for Astronomy & Cosmic Physics at the Universityof Heidelberg tribution function. Examples using the mean color of the RGBcan be found in Mould, Kristian & Da Costa 1983, Caldwellet al. 1998, Grebel & Guhathakurta 1999, Caldwell 2006; us-ing GC fiducials or analytic fits of GC fiducial loci in Harris,Harris & Poole 1999, Sarajedini et al. 2002; using interpolationbetween theoretical tracks or isochrones in Harris & Harris 2000,Mouhcine et al. 2005, Crnojevic, Grebel & Koch 2010, Bird etal. 2010, Lianou, Grebel & Koch 2010. In the case of GCs, dwarfspheroidals (dSphs), and the stellar haloes of galaxies, the as-sumption under which these techniques are used is that the redgiants represent populations of an old age ( ≥
10 Gyr). For suchold populations, a star’s locus in color–magnitude space is pri-marily sensitive to metallicity, while age spreads only produce asmall color spread (Grebel 1997; Frayn & Gilmore 2002).The case of the Local Group (LG) dwarf galaxies has shownthat all dwarfs studied in detail so far contain a population ofold stars (e.g., Grebel 2001; Grebel & Gallagher 2004). Someof these systems contain intermediate–age populations as well(from 1 Gyr up to less than 10 Gyr) in addition to early star for-
1. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case mation, thus presenting rather complex star formation histories(SFH; Grebel 1997; Mateo 1998; Tolstoy, Hill & Tosi 2009). Inparticular, this is the case for dwarf irregulars (dIrrs), transition–type dwarfs (dIrr / dSphs), dwarf ellipticals (dEs) and the many ofthe more luminous dSphs. Although spectroscopic observationsof individual stars provide the best means to reveal and break anage–metallicity degeneracy along the RGB in systems with com-plex SFHs, as for instance in the case of Carina (Smecker–Haneet al. 1994; Koch et al. 2006), such studies are limited to nearbyobjects within the LG due to the faintness of the stars to be tar-geted and due to crowding. Based on the fact that many of theLG dSphs show complex SFHs, the assumption of a single oldage for their stellar populations does not hold. In dwarf galaxiesin more distant systems there are clear indications of complexSFHs as well (as traced by, e.g., broad RGBs or the presenceof luminous asymptotic giant branch stars, red clump stars andoccasionally even luminous blue main sequences) but more de-tailed information about their SFHs is not available. Moreover,in these more distant systems spectroscopy of individual starsalong the RGB is not feasible with present–day instruments.Thus it is worth exploring how the assumption of a single oldage a ff ects the photometrically derived metallicities of compos-ite populations with a range of ages.In the present work we perform a comparison of the mean metallicity properties as well as a direct star–by–star compari-son between the spectroscopically and the photometrically de-rived metallicities. For individual star comparisons, we use thestars in common to both photometric and spectroscopic sam-ples of Galactic dSph companions that have been studied in theliterature. In order to perform such a star–by–star comparison,we use results for five Galactic dSphs, namely Carina, Leo II,Fornax, Sextans, and Sculptor. The three dSphs Carina, Leo II,and Fornax have complex star formation and chemical enrich-ment histories with di ff erent fractions of intermediate–age stel-lar populations, while Sextans and Sculptor are dominated byold populations.This paper is structured as follows. In § § mean metallicity properties aswell as on the star–by–star comparison. In § §
2. Data
The dSph sample was selected such that there are both spectro-scopic metallicities and photometric results available in the liter-ature. The adopted galaxies are the five Galactic dSphs Sculptor,Sextans, Carina, Fornax, and Leo II, which show a diversity intheir SFHs.More specifically, in the case of Sculptor and Sextans thedominant population is of an old age (e.g., Hurley–Keller, Mateo& Grebel 1999, Monkiewicz, Mould, Gallagher et al. 1999 forSculptor; Lee et al. 2003, 2009 for Sextans). Sculptor shows twodistinct old stellar components in terms of metallicity and kine-matics (e.g., Tolstoy et al. 2004), as well as a metallicity gradient(Harbeck et al. 2001). De Boer et al. (2011) suggest that Sculptorstopped forming stars 7 Gyr ago. Sextans shows a populationgradient based on its horizontal branch morphology (Harbeck etal. 2001), as well as a metallicity gradient, where the metal–richstars are more centrally concentrated and have colder kinematicsthan the metal–poor ones (Battaglia et al. 2011).
Table 1.
Global properties.
Galaxy A V A I ( m − M ) O TRGB(mag) (mag) (mag) (mag)(1) (2) (3) (4) (5)Sculptor 0 .
245 0 .
117 19 . ± .
14 15 . ± . .
03 0 .
02 19 . ± .
06 15 . ± . .
109 0 .
065 20 . ± .
10 16 . ± . .
186 0 .
116 20 . ± .
04 16 . ± . .
066 0 .
041 21 . ± .
13 17 . ± . I –band TRGB is adopted from:Rizzi et al. (2007) for Fornax; Lee et al. (2003) for Sextans; Bellazzini,Gennari & Ferraro (2005) for Leo II; own value for Carina and Sculptor. Carina experienced episodic star formation with at least threedistinct populations separated by quiescent phases lasting about4 Gyr (Smecker–Hane et al. 1994; Smecker–Hane et al. 1996;Mighell 1997; Hurley–Keller, Mateo & Nemec 1998; Monelliet al. 2003). The majority of the stars of Carina formed around7 Gyr ago (Hurley–Keller et al. 1998; Rizzi et al. 2003). Carinashows a mild radial metallicity gradient in the sense that themetal-rich population is more centrally concentrated (Koch etal. 2006). A similar trend is observed with respect to age suchthat the intermediate–age populations are more centrally con-centrated (Harbeck et al. 2001; Monelli et al. 2003). Leo II hasboth old and intermediate–age populations (Aaronson & Mould1985; Lee 1995; Mighell & Rich 1996; Gullieuszik et al. 2008).It appears that there is no significant metallicity gradient presentin Leo II (Koch et al. 2007). In the case of Fornax, the domi-nant population is of an intermediate–age (ca. 3–4 Gyr; Coleman& de Jong 2008) and it also contains old and a young popula-tions (Stetson, Hesser & Smecker–Hane 1998; Saviane, Held &Bertelli 2000b), while showing a strong radial metallicity gradi-ent (Battaglia et al. 2006).The global properties of the five dSphs, sorted by increasingdistance modulus, are listed in Table 1. We show in column (1)the galaxy name; in column (2) and (3) the V – and I –band ex-tinctions, respectively; in column (4) the distance modulus; incolumn (5) the I –band magnitude of the tip of the RGB (TRGB). The spectroscopic metallicities of individual stars in dSphs canbe inferred either directly by high–resolution measurements ofiron abundances, [Fe / H], from individual Fe lines, or throughlow / medium resolution spectroscopic measurements based ondi ff erent spectral indicators. The latter method is the one widelyused since it has the potential of providing spectra for a largenumber of stars within a reasonable integration time. One way to infer the overall spectroscopic metallicities (strictlyspeaking [M / H], however usually also denoted as [Fe / H]) is fromthe strength of the Ca II triplet (Ca T) lines at 8498 Å, 8542 Åand 8662 Å. The measured property is the sum of the equivalentwidths, Σ W , either of two or of a combination of all three Ca T
2. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case lines (e.g., Starkenburg et al. 2010). This is then used to derivethe reduced equivalent width, W ′ , using empirical calibrationsbetween the Σ W and ( V − V HB ), defined, e.g., in Armandro ff &Da Costa (1991; hereafter AD91). V HB is the V –band magnitudeof the horizontal branch. The calibration of Σ W as a function of( V − V HB ) is chosen because it removes, to first order, any depen-dencies on stellar gravity, reddening, and distance uncertainties(e.g., AD91). The width W ′ is then used to derive a metallicity,commonly based on a calibration of Galactic GCs with knownspectroscopic iron abundances.The Galactic GC metallicities are derived in various di ff er-ent ways. Thus, several metallicity scales have been defined sofar, which include the Zinn & West (1984; hereafter ZW84), theCarretta & Gratton (1997; hereafter CG97), the Kraft & Ivans2003; hereafter KI03) and the Carretta et al. (2009; hereafterCBG09) metallicity scales. The first one uses metallicity sensi-tive spectrophotometric indices of the integrated light of GalacticGCs, while the latter three use high resolution spectroscopicmeasurements of Galactic GC red giants to infer their iron abun-dance from individual Fe I and Fe II lines.Commonly used sets of such calibrations are given in AD91and Da Costa & Armandro ff (1995) for the ZW84 metallicityscale, and by Rutledge, Hesser & Stetson (1997; hereafter R97)for both the ZW84 and CG97 metallicity scales. Among thesecalibrations, the definition of the Ca T sum of the equivalentwidths, Σ W , is di ff erent, depending on how many lines wereused and with what weight. KI03 provide a similar calibrationbetween their scale of Fe II–based abundances and the reducedwidths W ′ of GCs, and so do CBG09.The Ca T method was initially calibrated via Galactic GCs,which are old populations and to first order simple stellar popu-lations of a single metallicity. They have a di ff erent chemical en-richment history than the dSphs (AD91; Venn et al. 2004; Kochet al. 2008a, 2008b). Subsequently, Cole et al. (2004) extendedthis method to much younger ages down to 2.5 Gyr by includ-ing younger open and populous clusters in the Milky Way andin the Large Magellanic Cloud, while Carrera et al. (2007) usedGalactic open and globular clusters to further extend the methodto ages as young as 0.25 Gyr. The Ca T method is widely usedto derive the metallicities of galaxies that have more complexstar formation and chemical enrichment histories than those ofthe calibrating Galactic GCs and populous clusters. The implica-tions of the di ff erent chemical enrichment and star formation his-tory in the dSphs and the Galactic GCs for the Ca T method havebeen discussed in Da Costa & Hatzidimitriou (1998), Cole etal. (2000, 2004), Pont et al. (2004), Bosler et al. (2007), Carreraet al. (2007), Battaglia et al. (2008b) and Koch et al. (2008a).Cole et al. (2004) have shown that the e ff ect of age on the metal-licity calibration is negligible as compared to the intrinsic scatterof the Ca T method for the metallicity ranges on the CG97 metal-licity scale between − − / H], while Carreraet al. (2007) extended this metallicity range for three metallic-ity scales between − + ff orts focused on extending the scale to even lower metallici-ties. Starkenburg et al. (2010) recalibrated the empirical relationbetween Ca T equivalent width and metallicity, extending the va-lidity range of the Ca T method to − − ≤ [Fe / H] ≤ + ≤ age ≤
13 Gyr ( Cole et al. 2004; Carrera etal. 2007; Starkenburg et al. 2010).
An alternative method to infer the metallicity of individual starsrelies on medium–resolution stellar spectra ( R ∼ e ff , log g ,and composition. The adopted metallicity for each individualstar is the metallicity of the best–fit template spectrum to theobserved one. This technique is di ff erent from the Ca T method,in the sense that the entire available spectroscopic features inthe observed spectrum are used, not only to derive the metal-licity, but also to simultaneously pinpoint all stellar parameters(e ff ective temperature, surface gravity, and an empirical micro-turbulence). We note that the spectral resolution of this methodis equivalent to the one of the Ca T method. A complete de-scription of the medium–resolution method is given in Kirbyet al. (2010; and references therein), while possible systemat-ics a ff ecting the derived metallicities as well as a comparisonwith high–resolution spectroscopic metallicities are discussed inKirby et al. (2009, 2010). We use two sources for the spectroscopic metallicities, bothadopted from available literature data.The first spectroscopic sample consists of Ca T–based spec-troscopic metallicities for all five dSphs. For Carina, the Ca Tdata are adopted from Koch et al. (2006), for Leo II from Kochet al. (2007), for Fornax from Battaglia et al. (2006), for Sextansfrom Battaglia et al. (2011; and private communication), and forSculptor from Battaglia et al. (2008b). We refer to these publi-cations for the description of the spectroscopic observations andanalysis. In all cases, the strength of the Ca T lines is used as ametallicity indicator for the individual red giant stars from ei-ther low or medium resolution spectroscopy. The spectroscopicmetallicities for Carina, Leo II, Fornax and Sculptor are inferredthrough the calibration in the sense of R97, while for Sextans thecalibration defined in Starkenburg et al. (2010) is used. The maindi ff erence between the calibration in Starkenburg et al. (2010)and in the earlier calibrations is that in the new calibrations therelation between metallicity and line strength is not linear, whileit is in the earlier calibrations. In addition, the Starkenburg etal. (2010) calibration is valid for metallicities from − − − − The photometry of Carina, Fornax and Sculptor is adopted fromWalker et al. (2009a; and private communication), of Leo II from
3. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case
Bellazzini et al. (2005), and of Sextans from Lee et al. (2003).We refer to these works for further details on the photometricobservations and analysis. In all the studied dSphs the final pho-tometric datasets are placed on a common
V, I photometry scalein the Johnsons–Cousins photometric system (Carina: Walkeret al. 2007; Fornax: Walker et al. 2006; Leo II: Bellazzini etal. 2005; Sextans: Lee et al. 2003; Sculptor: Walker et al. 2006,Coleman, Da Costa, & Bland-Hawthorn 2005). We note that forCarina, Fornax, and Sculptor, there is WFI (Wide Field Imagercamera at MPG / ESO 2.2 m telescope) photometry available forthe spectroscopic targets (Carina: Koch et al. 2006; Fornax andSculptor: Battaglia et al. 2006, 2008b, and private communi-cation), but we choose not to use these datasets since they arepoorly calibrated.
3. Results
We show the color–magnitude diagrams (CMDs; small greydots) of the five Galactic dSphs Sculptor, Sextans, Carina,Fornax, and Leo II in Fig. 1, along with Dartmouth isochrones(Dotter et al. 2007, 2008) overplotted with a fixed age of12.5 Gyr and metallicities ranging from − − For the five studied Galactic dSphs, we derive their photomet-ric metallicities using linear interpolation between Dartmouthisochrones with a fixed age of 12.5 Gyr, with a range in metallic-ities from − − V –band and I –band and for the distance moduli,listed in columns (2), (3) and (4) of Table 1, respectively. Weanalyse all bona–fide RGB stars that lie within 3 mag below the I –band magnitude of the TRGB, listed in Table 1, regardless ofwhether they were observed spectroscopically, in order to derivethe mean photometric metallicity properties and compare themwith the mean spectroscopic properties. We impose a metallic-ity cut on the derived photometric metallicities so as to only in-clude stars that fall within the theoretical isochrones’ metallicityrange of − − σ scatter Table 2.
Galactic GC metallicities in di ff erent metallicity scales. [Fe / H] 47 Tuc NGC 3201 NGC 6397(1) (2) (3) (4)ZW84 − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± .
01 . . . − . ± . − . − . − . ff erential metallicityscale; Dartmouth stands for the metallicities derived using isochronefitting (Dotter et al. 2010). of the output random realisations is then adopted as the metal-licity error for each star.We show the derived photometric metallicity distributionfunctions (MDFs) with the white histograms in Fig. 2 forSculptor, Sextans, Carina, Fornax, and Leo II. In order to perform a direct comparison between the photomet-ric and the spectroscopic metallicities, it is important to clarifyto which metallicity scale the photometric metallicities conform.The photometric metallicities are tied to the isochrone mod-els that are used in the interpolation method. The Dartmouthisochrones used here are not explicitly tied to any of the spec-troscopic, standard abundance scales (i.e., ZW84; CG97; KI03;CBG09). Their metallicities are rather based on the mass frac-tions of the heavy elements and hydrogen in the models alongwith the adopted solar abundances. In that sense, the photo-metric metallicities based on the Dartmouth isochrones form ametallicity scale on their own. However, the Dartmouth modelstend to lie close to the ZW84 and to the KI03 metallicity scales(A. Dotter, private communication; see also Dotter et al. 2010).In Table 2 we show as an example the mean metallicitiesof three Galactic GCs with metallicities on the ZW84 (adoptedfrom R97; their Table 2, column 5), CG97 (adopted from R97;their Table 2, column 6), KI03, CBG09, and Koch & McWilliam(2008c; 2011, in prep.; hereafter KM08, 11) metallicity scales,as well as the metallicity derived through isochrone fitting usingDartmouth isochrones (Dotter et al. 2010). Indeed, the metallic-ities derived using isochrone fitting agree better with the metal-licities on the ZW84, KI03 and CBG09 scales and the di ff er-ential reference scale based on high–resolution spectroscopy ofKM08, 11 than with the CG97 metallicty scale. Furthermore, inFig. 3, upper panel, we plot the Galactic GC fiducials of M 15,NGC 6397, M 2, and Tuc 47, adopted from DA90, along withDartmouth isochrones for a fixed age of 12.5 Gyr. The metal-licities of the Galactic GC fiducials are − − − −
4. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case
V − I I Sculptor0.5 1 1.5 21515.51616.51717.51818.51919.520
V − I I Sextans0.5 1 1.5 215.51616.51717.51818.51919.52020.5
V − I I Carina0.5 1 1.5 215.51616.51717.51818.51919.520
V − I I Fornax0.5 1 1.5 215.51616.51717.51818.51919.52020.5
V − I I Leo II0.5 1 1.5 217.51818.51919.52020.52121.5
Fig. 1.
Color–magnitude diagrams of the five Galactic dSphs, shown as small grey dots. Dartmouth isochrones are overplotted assolid lines, for a fixed age of 12.5 Gyr, a range in metallicities from − − − − − − − − ff sets compared to the Dartmouth isochrones (Fig. 3,middle panel). When comparing the Dartmouth isochrones toSaviane’s et al. analytic fits on the CG97 scale, the slopes arequite similar, but the fiducials of Saviane et al. are systemati-cally too metal–poor. At the metal–rich end ( ∼ − / H] isoscale = . ( ± . [Fe / H] CG97 + . ( ± . , (1) and holds within the metallicity range of − . ≤ [Fe / H] CG ≤− . / H] onthe CG97 metallicity scale that also have [Fe / H] based on theDartmouth isochrone fitting. The transformation is plotted inFig. 4. The reversed metallicity transformation from the isoscaleto the CG97 metallicity scale reads as follows:[Fe / H] CG97 = . ( ± . [Fe / H] isoscale − . ( ± . , (2)and holds within the metallicity range of − . ≤ [Fe / H] isoscale ≤− . The white histograms in the middle and right panels ofFig. 2 show the Ca T–based spectroscopic MDFs on the CG97metallicity scale and on the isoscale, for Sculptor, Sextans,
5. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case [Fe/H] phot N Sculptor12.5Gyr−3 −2 −1 0020406080 [Fe/H]
CG97 N Sculptor−3 −2 −1 0010203040 [Fe/H] isoscale N Sculptor−3 −2 −1 00102030 [Fe/H] phot N Sextans12.5Gyr−3 −2 −1 001020304050 [Fe/H]
CG97 N Sextans−4 −2 001020304050 [Fe/H] isoscale N Sextans−3 −2 −1 002468 [Fe/H] phot N Carina12.5Gyr−3 −2 −1 00100200300 [Fe/H]
CG97 N Carina−3 −2 −1 0050100 [Fe/H] isoscale N Carina−3 −2 −1 0020406080100 [Fe/H] phot N Fornax12.5Gyr−3 −2 −1 002004006008001000 [Fe/H]
CG97 N Fornax−3 −2 −1 0050100150200 [Fe/H] isoscale N Fornax−3 −2 −1 0050100150200 [Fe/H] phot N Leo II12.5Gyr−3 −2 −1 0050100150200 [Fe/H]
CG97 N Leo II−3 −2 −1 00510152025 [Fe/H] isoscale N Leo II−3 −2 −1 00510152025
Fig. 2.
Left panels: The white histograms show the photometric MDFs of all the stars within 3 mag below the TRGB, for Sculptor,Sextans, Carina, Fornax, and Leo II, while the shaded histograms show the same but only for the common stars. Middle panels: Thewhite histograms show the Ca T–based MDFs on the CG97 metallicity scale for the full available spectroscopic sample, as describedon the text, while the shaded histograms show the same but only for the stars in common. Right panels: The open histograms showthe Ca T–based MDFs on the isoscale (discussed in Section 3.3), while the shaded histograms show the same but only for thecommon stars. In all panels, the vertical black dashed line corresponds to the median metallicity of the full sample, while the greydashed line corresponds to the one of the common stars. The vertical dotted–dashed line in all panels corresponds to the isoschrone’smetal–poor limit of roughly −
6. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case (V − I) M I Solid: Dartmouth isochrones −2.17, −1.91, −1.58, −0.71
Dashed: DA90 GCs fiducials −2.17, −1.91, −1.58, −0.71 (V − I) M I Solid: Dartmouth isochrones −1.99, −1.37, −1.23, −1.15 −0.7
Dashed: GCs analytic fits ZW84 −1.99, −1.37, −1.23, −1.15 −0.7 (V − I) M I Solid: Dartmouth isochrones −2.11, −1.67, −1.53, −1.33 −0.71
Dashed: GCs analytic fits CG97 −2.11, −1.67, −1.53, −1.33 −0.71
Fig. 3.
Upper panel: Galactic GC fiducials from DA90 shownas black dashed lines, along with Dartmouth isochrones shownas red solid lines. From left to right, the Galactic GC fidu-cials correspond to M 15, NGC 6397, M 2 and 47 Tuc, wherethe GCs have a metallicity of − − − − − − − − − − − − − − − ≤ [Fe / H] CG ≤− . − . ≤ [Fe / H] isoscale ≤ − . [ F e / H ] D a r t m ou t h [Fe/H] CG97
Galactic GCs−2 −1 0−2.5−2−1.5−1−0.50
Fig. 4.
Transformation from the CG97 metallicity scale to theDartmouth isochrone metallicity scale, simply called “isoscale”.The red thick dashed line corresponds to the error–weighted lin-ear least squares fit to the data. The black thin dashed line corre-sponds to unity. [Fe/H]
MRS N Sculptor−4 −2 0020406080100120 [Fe/H]
MRS N Sextans−4 −2 0010203040 [Fe/H]
MRS N Fornax−3 −2 −1 00100200300 [Fe/H]
MRS N Leo II−4 −2 0020406080100
Fig. 5.
The white histograms show the MRS MDFs for the fullavailable MRS sample for Sculptor, Sextans, Fornax, and Carina.The shaded histograms show the MRS MDFs for the stars incommon to both the MRS and photometric samples. In all pan-els, the vertical black dashed line corresponds to the medianmetallicity value of the full sample, while the grey dashed linecorresponds to the median metallicity value of the common stars.The vertical dotted–dashed line corresponds to the lower limit ofthe most metal–poor isochrone used of roughly − / H] and W ′ (or Σ W) is valid (Cole et al. 2004).For Sextans on the CG97 metallicity scale, we adopt themetallicity range of − ≤ [Fe / H] CG ≤ − . / H] basedon the sum of the Ca T lines, Σ W, on the CG97 metallicity scale.In Fig. 5 we show the MRS–based MDFs of the wholeavailable spectroscopic sample (white histograms) for Sculptor,Sextans, Fornax, and Leo II.
7. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case V [ m ag ] ∆ [Fe/H] SculptorIsoscale−1 0 117.51818.5 V [ m ag ] ∆ [Fe/H] CarinaIsoscale−1 0 117.51818.51919.5 V [ m ag ] ∆ [Fe/H] FornaxIsoscale−1 0 1 21818.51919.5 V [ m ag ] ∆ [Fe/H] Leo IIIsoscale−1 0 11919.52020.521
Fig. 6. V –band magnitude versus the di ff erence in spectroscopicminus the photometric metallicities on the isoscale for Sculptor,Carina and Fornax, and Leo II. The photometric and spectroscopic MDFs for those stars withboth photometric and Ca T–based spectroscopic measurementsare shown as the shaded histograms in Fig. 2 for Sculptor,Sextans, Carina, Fornax, and Leo II. In order to constructthe photometric MDFs of the common stars, only those starswithin the photometric metallicity range of − . < [Fe / H] phot ≤− . r c , 1.5 r c ,2 r c , 5 r c , 1.5 r c for Sculptor, Sextans, Carina, Fornax, and Leo II,respectively, where r c denotes the core radius of each dSphadopted from Irwin & Hatzidimitriou (1995). For the spectro-scopic MDFs of the common stars in addition to the photomet-ric metallicity cuts we impose the Ca T spectroscopic metallic-ity cuts as described in Section 3.4. The number of the commonstars that have metallicities both on the CG97 metallicity scaleand on the isoscale are listed in Table 5, except for Sextans. Asshown in Fig. 2, Sextans only has three stars for which we haveboth reliable photometry and Ca T spectroscopy. Thus we ex-clude Sextans from any further analysis regarding common stars.The di ff erences of the Ca T spectroscopic (on the isoscale)minus the photometric metallicities versus the V –band magni-tudes are shown in Fig. 6 for Sculptor, Carina, Fornax, andLeo II. There is a slight trend of the metallicity di ff erences tobecome negative as the V –band magnitude becomes fainter, andto become positive as the V –band magnitude becomes brighter.This trend is not significant, as indicated by the Pearson cor-relation coe ffi cients of − − − − ffi -cult. This results in an inability of the photometric metallicitiesto reproduce the Ca T spectroscopic metal–poor tail of the MDF(cf. Koch et al. 2008b). On the other hand, the Ca T method hasits largest sensitivity at the metal–poor end.The shaded histograms in Fig. 5 show the MRS–based MDFsof the common stars. Again, only stars with photometric metal-licities within the range of − − (V − I) M I dashed: 12.5Gyrsolid: 7Gyr [Fe/H] from left to right: −2.1 −1.7, −1.3, −0.9, −0.5 Fig. 7.
Dartmouth isochrones for an age of 12.5 Gyr (blackdashed) and 7 Gyr (red solid). The intermediate–age isochronelies bluewards from the older isochrone at a fixed metallicity.Note that for a constant age and di ff erent values of [Fe / H] theslope of the RGB changes, while for a varying age and a con-stant [Fe / H] the slope of the RGB changes very little.The number of the common stars for each dSph is listed inTable 5.
4. Discussion
In a stellar system with a complex SFH where both old andintermediate–age stellar populations are present, its RGB con-tains stars belonging to the full age range of approximately1.5 Gyr and older ages (Salaris, Cassisi & Weiss 2002), depend-ing on the details of the stellar system’s SFH. Thus the assump-tion of a single old age for the stellar populations and there-fore for the isochrones used in the interpolation holds only inthe case of a negligible intermediate–age population. In dSphs,the initial star formation may have lasted as long as 3 Gyr oreven longer (Marcolini et al. 2008; Ikuta & Arimoto 2002), thusleading to large metallicity dispersions (Grebel, Gallagher &Harbeck 2003). In the case of dSphs dominated by old popula-tions with ages larger than 10 Gyr, this extended star formationdoes not substantially a ff ect their photometric metallicities andcan lead to photometric metallicity di ff erences of individual starsof only approximately 0.1 dex, as demonstrated in Lianou etal. (2010) using isochrone grids of two di ff erent ages (12.5 Gyrand 10.5 Gyr) and a range in metallicities in M 81 group dSphs.Here we explore the e ff ects of the presence of intermediate–age populations on deriving photometric metallicities under theassumption of a single old age. For that purpose, we comparethe photometric metallicities with spectroscopic metallicities de-rived through the Ca T method and through the MRS method, ona star–by–star basis.It is clear that in the presence of intermediate–age popula-tions we do not expect a priori that there will be an agreementbetween the photometric and spectroscopic metallicities. Theexistence of mixed–age populations is expected to lead to anoverestimate of the photometric metallicities towards the metal–poor part. At fixed metallicities, an intermediate–age popula-tion would lie bluewards in color on the RGB as compared toan old population. Thus, intermediate–age populations wouldbe assigned more metal–poor metallicities than their true value,if they were erroneously assumed to be old. This photometric“metal–poor bias” is demonstrated in Fig. 7, where isochrones
8. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case of two fixed ages of 12.5 Gyr and 7 Gyr are overplotted withmetallicities ranging from − − We list the mean photometric and mean spectroscopic metallic-ity properties for the five studied dSphs in Table 3, where boththe mean and median metallicity values are listed, as well as thestandard deviation. For the Ca T spectroscopic metallicities welist the mean metallicity properties both on the CG97 metallic-ity scale and on the isoscale. The mean properties were derivedfrom the full available data sets, corresponding to the white his-tograms shown in Fig. 2 and Fig. 5. Therefore they do not corre-spond to the common stars.
In the case of Sculptor and Sextans, the di ff erence between theirmedian photometric and median Ca T spectroscopic metallici-ties on the isoscale is 0.08 dex. The typical photometric metal-licity uncertainties have a median of 0.13 dex and 0.06 dex forSculptor and Sextans, respectively, while the typical spectro-scopic uncertainties have a median of 0.11 dex and 0.15 dexfor Sculptor and Sextans, respectively. Sculptor and Sextans aredominated by old populations. The fraction of the old popula-tions is more than 86% in Sculptor and 100% in Sextans (Orbanet al. 2008). It is therefore reassuring that the photometric andCa T spectroscopic metallicities on the isoscale are in such agood agreement.There is good agreement also between the median photo-metric metallicity of Sculptor and its median Ca T spectroscopicmetallicity on the CG97 metallicity scale, with a di ff erence of0.2 dex, while typical spectroscopic metallicity uncertainties onthe CG97 metallicity scale have a median of 0.05 dex. This is notthe case for Sextans, where the di ff erence of the median spec-troscopic and the photometric metallicity amounts to 0.48 dex,based on 173 stars (Battaglia et al. 2011) (white histogram inthe middle panel of Fig. 2). This mismatch between the twomedian metallicity values for Sextans can be explained if oneconsiders that the individual Ca T spectroscopic metallicities onthe CG97 metallicity scale include metallicity values as metal–poor as − − ff erent selection criteria in terms ofmetallicity ranges used for the metallicities on the CG97 metal-licity scale and the photometric metallicities may account forthis large di ff erence, which further suggests that such a compar-ison may not be appropriate for a galaxy with as metal–poor starsas in Sextans.Finally, the agreement between the medians of the photomet-ric and MRS metallicities is quite good in the case of Sculptorwhere their di ff erence amounts to only 0.03 dex, whereas forSextans their di ff erence amounts to 0.19 dex. Typical MRSmetallicity uncertainties have a median of 0.12 dex and 0.19 dexfor Sculptor and Sextans, respectively. Carina, Fornax, and Leo II have complex star formationand chemical enrichment histories that produced substantialintermediate–age populations, each in di ff erent amounts. Thedi ff erence of their median photometric metallicity from their me- Table 4.
Mean metallicity properties corresponding to the mix-ture of stellar fractions as described in Section 4.1.2.
Galaxy [Fe / H] mixture mean ± σ median(dex) (dex)Carina − . ± . − . − . ± . − . − . ± . − . dian spectroscopic metallicity is indeed non–zero, with the ten-dency of the median photometric metallicities to be more metal–poor than the spectroscopic ones.We can qualitatively estimate the expected metal–poor biasby comparing the median metallicity derived assuming a purelyold population with the median metallicity derived assuming amixture of the stellar populations. In order to find the medianmetallicity of a mixture of stellar populations, we use the frac-tion of the total stellar mass formed within the last 10 Gyr and1 Gyr ( f G , f G , respectively; Orban et al. 2008, their Table 1;reproduced in Table 5) in conjuction with the mean mass–weighted age ( τ ; Orban et al. 2008, their Table 1; reproduced inTable 5) for Carina, Fornax, and Leo II. For that purpose, we runthe interpolation code with a constant age of the isochrones equalto τ . Then, we randomly assign f inter = ( f G − f G )% of the starswithin our RGB sample metallicities as derived using isochroneswith constant ages equal to τ . The remaining 100 − f inter of thestars are assigned their original metallicities, assuming that theyare of a constant, old age of 12.5 Gyr. In all cases, the range inmetallicities is varied from − − − − − ff erence of the median metallicitieswhen assuming a purely old stellar population and when assum-ing a mixture of stellar populations results in 0.17 dex, 0.16 dex,and 0.15 dex, respectively, for the aforementioned dSphs makingthem more metal–rich in the case of mixed–age populations. Thedi ff erences of the median photometric from the median spectro-scopic (on the isoscale) metallicities in the case of Carina andLeo II are consistent with such mixtures of the stellar popula-tions, while in the case of Fornax the di ff erence is larger thanthat computed using its respective admixture. This suggests thateither a higher fraction f inter and / or a younger age τ is requiredin order to produce such a di ff erence. The age τ of Fornax is7.4 Gyr (Orban et al. 2008). If we assume 100% of the starswithin our RGB sample to have formed with this age we derivea median photometric metallicity of − ff erence as thatbetween the photometric and spectroscopic (on the isoscale) me-dians. Therefore, an age τ much younger than 7.4 Gyr is requiredin order to justify the di ff erence between the median photomet-ric and spectroscopic (on the isoscale) metallicities. It turns outthat all the stars in our RGB sample would need to have an ageof ∼ f inter from 55% to 100%and with ages from 2 Gyr to 4 Gyr, respectively, are required inorder to produce the observed di ff erence between the medianphotometric metallicity and the median spectroscopic metallic-ity on the isoscale for Fornax. These age ranges are consistent
9. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case
Table 3.
Mean metallicity properties corresponding to the white histograms of Fig. 2 and Fig. 5.
Galaxy [Fe / H] phot [Fe / H] CG [Fe / H] isoscale [Fe / H] MRS mean ± σ median mean ± σ median mean ± σ median mean ± σ median(dex) (dex) (dex) (dex) (dex) (dex) (dex) (dex)Sculptor − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − .
74 ... ...Fornax − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . − . ± . − . with the findings of Coleman & de Jong (2008), i.e., that Fornaxexperienced a strong burst of star formation during the last 3–4 Gyr. We also note that Fornax has the largest age spread everfound in any Galactic dSph, extending to ages as young as 100–200 Myr (Grebel & Stetson 1999). For those stars with both spectroscopic and photometric mea-surements, we show the photometric versus the Ca T metal-licities in the upper panels of Fig. 8, separately on the CG97metallicity scale and on the isoscale for Carina, Fornax, Leo II,and Sculptor. For those stars with both MRS and photometricmeasurements, the photometric versus the MRS metallicities isshown in Fig. 9 for Sculptor, Sextans, Fornax, and Leo II. In allcases, the lower panels each show the residuals of the compari-son. ∆ [Fe / H] is always the di ff erence between the spectroscopicmetallicities minus the photometric metallicities.A positive di ff erence ∆ [Fe / H] means that the spectroscopicmetallicities are more metal–rich than the photometric metallic-ities. The photometric systematic uncertainty that can contributeto a positive di ff erence ∆ [Fe / H] is the photometric metal–poorbias due to the presence of an intermediate–age population. Thismetal–poor bias has been estimated to amount to up to 0.4 dexfor a star–by–star comparison when deriving photometric metal-licities assuming a single old age of 12.5 Gyr for the underly-ing population as compared to assuming a single age of 8.5 Gyr(Lianou et al. 2010), with the maximum di ff erence occurring atthe metal–poor end.Possible sources of uncertainties that can contribute to thephotometric metallicities are the distance modulus and redden-ing. In the case of Sculptor, a variation of the distance modulusby ± ff erence of photometric metallicities of10%, where an increase of the distance modulus by 0.14 magleads to more metal–poor metallicities. A variation of the red-dening by ± ff erence of the photomet-ric metallicities of 12%, where an increase in the reddening by0.02 mag leads again to more metal–poor metallicities.Another source of uncertainty originates from the assump-tion of a scaled–solar composition of the [ α / Fe] chosen for theDartmouth isochrones. Again, using Sculptor as a test case, wechoose an [ α / Fe] equal to + ff erences, while the median photomet-ric metallicity gets more metal–poor by 0.1 dex (see also Kaliraiet al. 2006). Individual α –element ratios for Sculptor indicatethat [ α / Fe] has an average value of approximately zero (Venn etal. 2004; their Figure 2 and Figure 7), across the range of metal-licities we consider here for the isoscale of − . ≤ [Fe / H] CG ≤ − . α / Fe] of zero is further justified by the range ofages of the stars present, where their [ α / Fe] tends to approachsolar values, as discussed in Koch et al. (2008b). Furthermore,for Carina and for the metallicity ranges we consider here, the[ α / Fe] ratio has an average value of approximately zero (Koch etal. 2008a; their Figure 2, left bottom panel), and the same holdsfor Fornax (Letarte et al. 2010; Venn et al. 2004; their Figure 2).The motivation of keeping the α –element enhancement con-stant through the whole metallicity range, in contrast to whathigh–resolution α –element abundances indicate (e.g., Koch etal. 2008a, Cohen & Huang 2009, 2010; and references therein),stems from the fact that the exact position of the “knee”, formedby a plateau of constant [ α / Fe] as a function of [Fe / H] andby the declining values of [ α / Fe] towards the metal–rich enddue to the SN Ia contribution, depends on the star formationand chemical evolution history of each dSph (e.g., Marcolini etal. 2008). In more distant galaxies it is not possible to obtainhigh–resolution measurements or to measure individual stellar[ α / Fe] ratios. Therefore one cannot infer the location of the knee,whose position could be used to fit [ α / Fe] as a function of the[Fe / H] range (Cohen & Huang 2009, 2010) and then use such afunction as an input for the [ α / Fe] in the isochrones. Thus, oneneeds to choose a constant [ α / Fe] value for the whole metallicityrange used in the isochrones. We note that the present day high–resolution spectroscopic measurements of metallicities of thedSphs studied here permit the determination of the location ofthe knee in conjuction with detailed chemical evolution modelsin the cases of Sculptor and Carina (Geisler et al. 2007; Koch etal. 2008a; Lanfranchi, Matteucci & Cescutti 2006), while in theremaining dSphs only limits on the position of the knee can beplaced (e.g., Koch 2009; Tolstoy, Hill & Tosi 2009; Lanfranchi& Matteucci 2010; and references therein).
In the case of an old–age dominated population such as inSculptor, one would expect the photometric metallicities tomatch the spectroscopic metallicities once everything has beenplaced on the same metallicity scale. This is not what is observedin Fig. 8 for Sculptor, where there is an excess of stars withpositive ∆ [Fe / H] that increases towards the Ca T spectroscopicmetal–rich end. On the isoscale, the median value of the di ff er-ence ∆ [Fe / H] is equal to 0.08 dex with a full range of 0.82 dex,while typical metallicity uncertainties have a median of 0.05 dex(photometric) and 0.11 dex (Ca T). The minimum ∆ [Fe / H] isequal to − ff erence in metallicities ∆ [Fe / H] versus the spec-troscopic metallicity is listed in Table 5. On the CG97 metallic-ity scale, the median value of ∆ [Fe / H] is equal to 0.28 dex witha full range of 1.01 dex.
10. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case [ F e / H ] pho t Carina−2.5−2−1.5−1 [Fe/H]
CG97 ∆ [ F e / H ] −2.5 −2 −1.5 −1−101 [ F e / H ] pho t Fornax−2.5−2−1.5−1−0.50 [Fe/H]
CG97 ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5 0−1012 [ F e / H ] pho t Leo II−2.5−2−1.5−1−0.5 [Fe/H]
CG97 ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5−0.500.51 [ F e / H ] pho t Carina−2.5−2−1.5−1 [Fe/H] isoscale ∆ [ F e / H ] −2.5 −2 −1.5 −1−101 [ F e / H ] pho t Fornax−2.5−2−1.5−1−0.50 [Fe/H] isoscale ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5 0−1012 [ F e / H ] pho t Leo II−2.5−2−1.5−1−0.5 [Fe/H] isoscale ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5−101 [ F e / H ] pho t Sculptor−2.5−2−1.5−1−0.5 [Fe/H]
CG97 ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5−0.500.51 [ F e / H ] pho t Sculptor−2.5−2−1.5−1−0.5 [Fe/H] isoscale ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5−0.500.51 Fig. 8.
The first two rows show, from left to right, the photometric versus the Ca T spectroscopic metallicities (upper panels), aswell as the residuals of the comparison (lower panels), on the CG97 metallicity scale and on the isoscale for Carina, Fornax, andLeo II. The last row shows the same for Sculptor. The error–weighted contours range from 0.5 to 2.5 σ in steps of 0.5. The dashedline indicates unity. [ F e / H ] pho t Sculptor −3−2.5−2−1.5−1−0.5 [Fe/H]
MRS ∆ [ F e / H ] −3 −2.5 −2 −1.5 −1 −0.5−101 [ F e / H ] pho t Sextans −3−2.5−2−1.5−1 [Fe/H]
MRS ∆ [ F e / H ] −3 −2.5 −2 −1.5 −1−101 [ F e / H ] pho t Fornax −3−2.5−2−1.5−1−0.5 [Fe/H]
MRS ∆ [ F e / H ] −3 −2.5 −2 −1.5 −1 −0.5−101 [ F e / H ] pho t Leo II −3−2.5−2−1.5−1−0.5 [Fe/H]
MRS ∆ [ F e / H ] −3 −2.5 −2 −1.5 −1 −0.5−101 Fig. 9.
Photometric metallicities versus MRS metallicities (upper panels), as well as their residuals (lower panels), in the sense ofMRS metallicities minus photometric metallicities versus MRS metallicities, for Sculptor, Sextans, Fornax and Leo II. The error–weighted contours range from 0.5 to 2.5 σ in steps of 0.5. The dashed line indicates unity.
11. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case [ F e / H ] pho t Sculptor −2.5−2−1.5−1−0.5 [Fe/H] HR ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5−0.500.51 Fig. 10.
Photometric metallicity, as well as the residuals, as afunction of the high–resolution spectroscopic metallicity. Theerror–weighted contours range from 0.5 to 2.5 σ in steps of 0.5.The dashed line indicates unity.There is a very good agreement between the metallicitiesof the two methods within the metallicity range from − − ff erence of the spec-troscopic metallicity minus the photometric metallicity in thismetallicity range is 0.01 dex, while the full range of the di ff er-ence in metallicities remains the same, equal to 0.82 dex. The spectroscopic metallicities in our samples may be as metal–poor as − − − − − − ff ects a ff ecting the metallicities. We note thatin Fig. 10 (upper panel), there exist some stars towards thephotometric metal–poor end that have more metal–rich high–resolution metallicities, which could be indicative of a metal–poor bias or may be due to the decreased metallicity sensitivityof the photometric method for bluer RGB colors. Again, there isthe tendency of ∆ [Fe / H] to increase towards the high–resolutionspectroscopic metal–rich end. The median of the di ff erences is0.23 dex, while the relative di ff erences ∆ [Fe / H] / [Fe / H] HR in thiscase are approximately 16%. Typical high–resolution metallic-ity uncertainties have a median of 0.1 dex. The full range ofthe di ff erences is equal to 1.17 dex, with minimum di ff efenceof − ff erence of 0.81 dex. [ F e / H ] C a T Sculptor −3−2.5−2−1.5−1−0.5 [Fe/H]
MRS ∆ [ F e / H ] −3 −2.5 −2 −1.5 −1 −0.5−1.5−1−0.500.5 [ F e / H ] C a T Sextans −3.5−3−2.5−2−1.5−1 [Fe/H]
MRS ∆ [ F e / H ] −3.5 −3 −2.5 −2 −1.5 −1−101 [ F e / H ] C a T Fornax −1.5−1−0.50 [Fe/H]
MRS ∆ [ F e / H ] −1.5 −1 −0.5 0−1−0.500.5 [ F e / H ] C a T Leo II −2.5−2−1.5−1−0.5 [Fe/H]
MRS ∆ [ F e / H ] −2.5 −2 −1.5 −1 −0.5−101 Fig. 11.
From left to right, the upper panels show the Ca T spec-troscopic metallicities versus the MRS metallicities for Sculptor,Sextans, Fornax, and Leo II, while the lower panels show theirresiduals. The error–weighted contours range from 0.5 to 2.5 σ in steps of 0.5. The dashed line indicates unity. The same trend of an excess of stars with positive ∆ [Fe / H] is ob-served in Fig. 9, where we compare the MRS metallicities withthe photometric metallicities. In addition, in some cases there isalso an excess of stars with negative ∆ [Fe / H], indicative of starswith spectroscopic metallicities more metal–poor than the pho-tometric ones. In any case, the discrepancy between the MRSmetallicities and the photometric metallicities is higher thanin the case of the Ca T–based spectroscopic metallicities. Themedian of the di ff erences between the photometric and MRSmetallicities is 0.1 dex, while the full range of the di ff erencesis 1.62 dex, which is double the full range in the case of the Ca Ton the isoscale versus photometric metallicities. Typical MRSmetallicity uncertainties have a median of 0.11 dex. The mini-mum ∆ [Fe / H] is equal to − ff erence in metallicities ∆ [Fe / H]versus the MRS metallicity is listed in Table 5.
The Ca T and MRS metallicities of a given star di ff er fromeach other (Fig. 11), and from high–resolution measurements(Battaglia et al. 2008b for Ca T; Kirby et al. 2009 for MRS).Shetrone et al. (2009) discuss that the discrepancy between theCa T–based and MRS metallicities for Leo II may be due tothe di ff erent metallicity scales, among other factors. It wouldbe thus interesting to compare the Ca T and MRS metallicitieswhen both are placed to a common metallicity scale, such as theisoscale. Such a comparison needs to be postponed until moreGalactic GC metallicities on the MRS scale are observed thatare in common with the Dotter et al. (2010) GC sample.In the case of Sculptor, the Ca T versus the MRS metallic-ities are shown in the upper left panel of Fig. 11. The median
12. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case of the di ff erences between the Ca T and MRS metallicities is0.09 dex, while the full range of the di ff erences is 1.69 dex. Wenote that the latter full range of the di ff erence in metallicities istwice the full range as compared to the Ca T versus photomet-ric metallicities, for Sculptor, but of the same order as comparedto the MRS versus the photometric metallicities case. Typicalmetallicity uncertainties have a median of 0.06 dex (Ca T) and0.11 dex (MRS). The minimum ∆ [Fe / H] is equal to − − − ff erences is equal to 0.2 dex, with a full rangeof the di ff erences of 0.69 dex, while the minimum value of thedi ff erence is − ff erenceis 0.15 dex. In this metallicity range, the median of the metallic-ity di ff erences is double the one in the case of the Ca T on theisoscale versus the photometric metallicities. In the metallicityrange where the Ca T is the most sensitive, there seems to besimilarly highly discrepant to the MRS metallicities. Sculptor is an old–age dominated system, with more than 86%of its stars having ages larger than 10 Gyr (Orban et al. 2008).The presence of old, low–luminosity AGB stars may contributeto the ∆ [Fe / H] becoming positive due to the photometric metal–poor bias, but the overall mean metallicity properties are un-a ff ected (e.g. Lianou et al. 2010). Hurley–Keller et al. (1999)discuss that Sculptor may contain two old stellar populations,based on its horizontal branch morphology, while Harbeck etal. (2001) find a population gradient and Tolstoy et al. (2004)identify two kinematically distinct ancient components. De Boeret al. (2011) suggest that star formation in Sculptor ceased 7 Gyrago. Furthermore, Menzies et al. (2011) identify two AGB vari-ables, one of which suggests that stars as recent as 1–2 Gyr agomay have formed, consistent with the age distribution modellingthat Revaz et al. (2009) derive.Motivated by the recent findings of de Boer et al. (2011),we use an isochrone of 7 Gyr to derive the photometric metal-licities of Sculptor. The new median metallicity becomes moremetal–rich by 0.28 dex, which would place a metal–rich limiton the median metallicity of Sculptor assuming that 100% ofthe stars have an age of 7 Gyr. We further use the fractions ofthe total stellar mass of Sculptor given in Orban et al. (2008)to derive the intermediate–age stellar fraction, which is equal to f G − f G . Then, we randomly assign a corresponding fractionof the stars in our RGB sample to this intermediate–age popula-tion with metallicities derived using the 7 Gyr isoschrones, whilethe remaining fraction of stars is assigned metallicities based onthe 12.5 Gyr isochrones. The derived median metallicity of thismixture becomes more–metal rich by 0.02 dex. If we ask insteadwhat the fraction of the intermediate–age stars (with an age of7 Gyr) is that would produce a metallicity di ff erence of the or-der of that between the Ca T (placed on the isoscale) and pho-tometric median metallicities of 0.08 dex, we find a fraction of24%. That is, 24% intermediate–age stars with ages of 7 Gyr areneeded in order to result in a di ff erence of the median photomet-ric metallicity of the mixed–age population and the median pho-tometric metallicity assuming a purely old system of 0.08 dex. Sextans is the only dSph in our sample that consists of purelyold stellar populations (Orban et al. 2008; Lee et al. 2009). As described earlier, we do not perform a comparison of individ-ual common stars between the Ca T and photometric metalliciessince we do not have enough stars in common. Here, we onlycompare the MRS versus the photometric metallicities, as wellas the Ca T–based versus the MRS metallicities.
The second panel from the left in Fig. 9 shows the MRS metal-licity versus the photometric metallicity, as well as the residuals.Since Sextans is a purely old system, one would again expect avery good agreement between the MRS and photometric metal-licities. As shown in Fig. 9, this is not the case. The median ofthe di ff erences between the photometric and MRS metallicitiesis 0.07 dex, while the full range of the di ff erences is 1.48 dex.The relative di ff erences are 11%. The slope of the di ff erencein metallicities ∆ [Fe / H] versus the MRS metallicity is listed inTable 5. Typical spectroscopic uncertainties have a median of0.12 dex.
In the upper right panel of Fig. 11 we show the Ca T ver-sus the MRS metallicities for Sextans. In this case, again ahigh scatter is observed between the two spectroscopic meth-ods. The median of the di ff erences between the Ca T and MRSmetallicities is 0.12 dex, while the full range of the di ff erencesis 0.83 dex. Typical metallicity uncertainties have a median of0.15 dex (Ca T) and 0.12 dex (MRS). The spectroscopic mea-surements are assumed to be independent of age. Carina, Leo II and Fornax have a significant fraction ofintermediate–age stars that lead to an age–metallicity degener-acy along the RGB, as shown in Fig. 10 of Koch et al. (2006) forCarina, in Fig. 8 of Koch et al. (2007) for Leo II, and in Fig. 22 ofBattaglia et al. (2006) for Fornax. These complex SFHs will af-fect the photometric metallicities in the sense of the photometricmetal–poor bias discussed earlier.
In all cases, just as with Sculptor, Fig. 8 shows a trend of increas-ingly positive ∆ [Fe / H] with increasing [Fe / H]. The same trend isobserved in the study of Gullieuszik et al. (2007; their Figure 13)for Fornax, where they compare their photometric metallicities,derived from near–IR colors, with the Ca T spectroscopic mea-surements of Battaglia et al. (2006) and Pont et al. (2004). In ourstudy, the positive di ff erences of the metallicities are attributedto the presence of intermediate–age stars, which have bluer col-ors than old stars at a given metallicity, as demonstrated in Fig. 7.The negative di ff erences can be attributed to the poorer resolu-tion of the isochrones towards the metal–poor end. The median ∆ [Fe / H] is 0.18 dex, 0.13 dex, and 0.52 dex for Carina, Leo IIand Fornax, respectively, while the full range of ∆ [Fe / H] is ap-proximately 0.58 dex, 1.17 dex, and 2.37 dex respectively. Thevalues quoted refer to the Ca T–based spectroscopic metallici-ties placed on the isoscale. Typical spectroscopic uncertaintieshave a median of 0.17 dex, 0.24 dex, and 0.16 dex, while typi-cal photometric metallicity uncertainties have a median value of0.05 dex, 0.02 dex, and 0.11 dex, for the above mentioned dSphs,respectively. If we focus on the metallicity range from −
13. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case − ∆ [Fe / H] of 0.21 dex,0.1 dex, and 0.13 dex for Carina, Leo II and Fornax, respectively,while the range of ∆ [Fe / H] is equal to 0.37 dex, 0.99 dex, and1.41 dex, for the above mentioned dwarfs, respectively.
In the case of Fornax, Tafelmeyer et al. (2010) find one ex-tremely metal–poor star in common to our photometric sam-ple, shown with the red asterisk in the CMD of Fornax(Fig. 1; Frx 05–42). This extremely metal–poor star has a high–resolution Fe I abundance of − − The same trends are observed when we compare the MRS metal-licities with the photometric metallicities as shown in Fig. 9. Thephotometric and MRS spectroscopic metallicities become simi-larly discrepant as in the case of the Ca T metallicities. The me-dian of the di ff erences between the photometric and MRS metal-licities is 0.45 dex for Fornax and 0.33 dex for Leo II, while thefull range of the di ff erences is 2.56 dex for Fornax and 2.11 dexfor Leo II. The relative di ff erences are 47% for Fornax and 24%for Leo II. The slopes of the di ff erence in metallicities ∆ [Fe / H]versus the MRS metallicity for Fornax and Leo II are listed inTable 5. The typical MRS metallicity uncertainties have a me-dian of 0.1 dex, and 0.11 dex for Fornax and Leo II, respectively.
The lower left and right panels of Fig. 11 show the Ca T ver-sus the MRS metallicities for Fornax and Leo II. Both these fig-ures show a similarly large scatter as in the case of Sculptorand Sextans. Shetrone et al. (2009) compare the Ca T–based andMRS metallicities for faint Leo II stars and also find them to bediscrepant in a similar way as we find them here. In our study, themedian of the di ff erences between the Ca T and MRS metallici-ties is 0.24 dex and 0.02 dex, respectively for Fornax and Leo II,while the full range of the metallicity di ff erences is 1.12 dex and1 dex, respectively. Typical metallicity uncertainties have a me-dian of 0.14 dex (Ca T) and 0.11 dex (MRS) for Fornax, whilefor Leo II these are 0.16 dex (Ca T) and 0.11 dex (MRS).In the case of Leo II and when we compare ∆ [Fe / H] inthe Ca T metallicity range from − − ∆ [Fe / H] is 0.07 dex while its range is 0.88 dex. Based on these S l ope f − f CG970 0.5 10.511.5 S l ope f − f Isoscale0 0.5 10.511.5 S l ope f − f MRS0 0.5 10.511.5 S l ope f − f CG970 0.5 10.511.5 S l ope f − f Isoscale0 0.5 10.511.5 S l ope f − f MRS0 0.5 10.511.5 S l ope τ [Gyr] CG976 8 10 120.511.5 S l ope τ [Gyr] Isoscale6 8 10 120.511.5 S l ope τ [Gyr] MRS6 8 10 120.511.5
Fig. 12.
Slopes of the error–weighted linear least squares fitto the datapoints of the lower panels of Fig. 8 and Fig. 9 asa function of the intermediate–age fractions ( f G − f G , upperpanels; f G − f G ; middle panels), as well as a function of themass–weighted mean age τ (lower panels), Sculptor, Sextans,for Carina, Fornax and Leo II. The red solid line corresponds toan error-weighted linear least squares fit to the data. The errorbars correspond to the error of the coe ffi cients of the fit to thedatapoints of Fig. 8 and Fig. 9.values, the agreement between the Ca T and MRS metallicitiesfor Leo II is slightly better than in the Ca T on the isoscale ver-sus photometric metallicities case. For Fornax, there are not anystars in common for metallicities less than − ∆ [Fe/H] dependenceon thedSph’sSFH An error–weighted linear least squares fit to the datapoints ofthe lower panels of Fig. 8 and Fig. 9, which show ∆ [Fe / H] as afunction of the spectroscopic metallicities, results in the slopeslisted in Table 5 for the CG97 metallicity scale, the isoscale, andthe MRS metallicity scale. In the case of a purely old population,one would expect that the slope is zero, as a result of ideally zerodi ff erences between the photometric and spectroscopic metallic-ities. The non–zero slopes of the ∆ [Fe / H] as a function of thespectroscopic [Fe / H] are shown in Fig. 12 which are now plot-ted against the f G − f G (upper panels), the f G − f G (middlepanels), as well as against the mass–weighted mean age, τ , ofeach dSph (lower panels), adopted from Orban et al. (2008; f G is the fraction of stars formed within the last 5 Gyr). The valuesof f G , f G , f G , and τ are reproduced in Table 5.In the upper panels of Fig. 12, there is a tendency of increas-ing the intermediate–age fraction to increase the slope of the ∆ [Fe / H] as a function of the [Fe / H] spec . This is demonstratedby the red solid line which is an error–weighted linear leastsquares fit to the data points in Fig. 12. The error bars corre-spond to the errors of the coe ffi cients of the fit to the datapointsof the lower panels of Fig. 8 and Fig. 9. The upper left panel ofFig. 12 suggests that the Ca T metallicities on the CG97 metallic-ity scale versus the photometric metallicities show the most pro-nounced dependence on increased intermediate–age fractions ofstars whereas the discrepancies between MRS and photometric
14. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case metallicities remain relatively low regardless of the admixtureof younger populations. The Pearson correlation coe ffi cients are0.95, 0.85, and 0.54 for the CG97, isoscale, and MRS cases re-spectively, while it is significant only in the case of the CG97metallicity scale within the 85% confidence level.In the middle panels of Fig. 12, the same tendency is ob-served when we plot the slopes of Fig. 8 and Fig. 9 against the f G − f G fractions. Here, the trend is significant within the 98%confidence level only in the case of the isoscale, with a Pearsoncorrelation coe ffi cients of 0.96, but it is not significant in the re-maining cases of the CG97 and MRS metallicity scales with aPearson correlation coe ffi cient of 0.87 and 0.24, respectively.In the lower panels of Fig. 12, there is a much less significanttrend of a decreasing mass–weighted mean age with an increas-ing slope of ∆ [Fe / H] as a function of [Fe / H] spec . Again, the redsolid line is an error–weighted linear least squares fit to the datapoints in Fig. 12, while the error bars correspond to the errorsof the coe ffi cients of the fit to the datapoints of the lower panelsof Fig. 8 and Fig. 9. The lower panels of Fig. 12 suggest thatthe trend is insignificant within the 99% confidence level, withPearson correlation coe ffi cients of 0.81, 0.64, and 0.78 for theCG97, isoscale, and MRS cases respectively. The presence of an intermediate–age population in a dSph leadsto a metal–poor bias in the photometric metallicities, in thesense that the stars are assigned with too metal–poor photomet-ric metallicities compared to their spectroscopic values. In thecase of the Galactic dSphs studied here, where some of themhave a pronounced or even dominant intermediate–age popula-tion, the individual stellar di ff erences of the spectroscopic mi-nus the photometric metallicities can reach a range in metallicityspanning up to 2.37 dex in the case of Fornax which has the mostextended star formation and chemical evolution history. In prac-tice, the photometric metallicities become more metal–poor ascompared to the Ca T spectroscopic or MRS metallicities whenintermediate–age populations contribute. In dSphs where thefraction of the intermediate–age population is small, the assump-tion of a single old age when deriving photometric metallicitiesappears to yield relatively good results. In the case of Sculptor,there is a systematic trend of increasing ∆ [Fe / H] with increasingCa T [Fe / H] that mimics the same trend observed in dSphs witha substantial fraction of intermediate–age stars present, consis-tent with the recent findings of de Boer et al. (2011) and Menzieset al. (2011) regarding the range of ages of the stellar content ofSculptor. We find that 24% of intermediate–age stars with an ageof 7 Gyr are needed in order to account for the di ff erence of themedian spectroscopic metallicity with the median photometricmetallicity.In more distant dSphs where the use of the Ca T method(or MRS) to derive spectroscopic metallicities is not avail-able due to the faintness of the stars to be targeted, one hasto rely on the photometric method in order to have an esti-mate of their metallicity. The mean metallicities derived fromthe photometric method in the case of dSphs dominated byold stars are biased towards the metal–poor end by approxi-mately 0.08 dex as compared to the Ca T metallicities placedon the isoscale (for Sculptor). The intrinsic scatter in this caseis 0.16 dex for the photometric metallicities and 0.20 dex forthe spectroscopic metallicities placed on the isoscale, whichleads to an intrinsic scatter of their di ff erence of approximately0.26 dex. The intrinsic scatter of the di ff erence of the spectro-scopic metallicity, on the isoscale, minus the photometric metal- licity is 0.09 dex, 0.32 dex, and 0.24 dex for Carina, Fornax, andLeo II, respectively, which are less or comparable with the me-dian of the ∆ [Fe / H]. Thus, depending on the size of the frac-tions of intermediate–age stars, using the photometric methodmay underestimate the mean metallicity by a few tenths of dexin [Fe / H].Given the fraction of the intermediate–age populations in adSph, one can derive an estimate of how much o ff set the pho-tometric metallicities may be as compared to the spectroscopicmetallicities. In more distant dSphs, the ability of deriving ac-curate SFHs is hampered by the same age–metallicity degener-acy examined here (Gallart, Zoccali & Aparicio 2005) on theRGB as well as by our inability to obtain CMDs that reachthe old main–sequence turn–o ff s. Therefore, one has to rely onthe presence of luminous AGB stars as a probe of the pres-ence of intermediate age populations. In a study of MDFs ofnine dSphs in the M81 group of galaxies, we detected luminousAGB stars in all of them, with fractions ranging from 3% to 14%(Lianou et al. 2010; see also Caldwell et al. 1998, Da Costa2004). Similarly, luminous AGB stars were detected in early–type dwarfs in other groups of galaxies (Rejkuba et al. 2006,Girardi et al. 2010, Crnojevic et al. 2011), as is also the casefor Local Group dwarf galaxies (e.g., Battinelli & Demers 2004;Davidge 2005; Groenewegen 2007; Whitelock, et al. 2009; andreferences therein).
5. Summary and Conclusions
We test the validity of the photometrically derived stellar metal-licities generally used under the assumption of a single old age,and we explore the e ff ect of the presence of intermediate–agestellar populations on photometrically derived stellar metallici-ties. We choose five Galactic dSphs, namely Sculptor, Sextans,Carina, Fornax, and Leo II, which have di ff erent SFHs and con-tain a di ff erent fraction of intermediate–age stars, ranging fromold ages in Sextans to very prominent intermediate–ages inFornax. We use their resolved RGBs and we derive their photo-metric metallicities using a linear interpolation method assuminga constant old age for the theoretical isochrones and a wide rangein metallicities, from − − ff ect of the presence of intermediate–age stellarpopulations on the derivation of photometric metallicities. Thecomparison between the photometric and spectroscopic metal-licities is performed both on the CG97 metallicity scale and onthe metallicity scale defined by the Dartmouth isochrones in thecase of the Ca T–based metallicities. Moreover, we simulate thee ff ect of intermediate–age populations on the photometric metal-licities via isochrone models of di ff erent ages.The comparison of the mean photometric metallicity proper-ties with the mean spectroscopic ones shows that we can safelytrust the photometrically derived stellar metallicities in the caseof old–dominated systems such as Sculptor and Sextans, wherethe comparison of the photometrically and spectroscopically de-rived median metallicity gives a di ff erence of 0.08 dex. In sys-tems such as Fornax, which has the most extended star formationand chemical enrichment history, the comparison between the mean metallicity properties derived from di ff erent methods giveshighly discrepant results that amount to 0.51 dex in the caseof the median MRS metallicity versus the median photometricmetallicity. In order to account for a di ff erence of 0.43 dex be-tween the median photometric metallicity and the median spec-
15. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case
Table 5.
Slopes of the ∆ [Fe / H] versus the spectroscopic [Fe / H], numbers of stars used in our comparisons (N), and populationfractions, adopted from Orban et al. (2008).
Galaxy Carina Fornax Leo II Sculptor Sextans τ (Gyr) 7.1 7.4 8.8 12.6 12.0 f G f G f G CG
24 131 25 60 ...N isoscale
19 114 17 47 ...N
MRS ... 90 127 131 31Slope CG . ± .
11 0 . ± .
06 0 . ± .
21 0 . ± .
08 ...Slope
Isoscale . ± .
15 0 . ± .
07 1 . ± .
20 0 . ± .
09 ...Slope
MRS ... 0 . ± .
12 0 . ± .
11 0 . ± .
03 0 . ± . troscopic metallicity on the isoscale, as observed in Fornax, itwould require that a fraction of stars between 100% to 55% onthe RGB formed from 4 to 2 Gyr ago, a finding that is also sup-ported by Coleman & de Jong (2008).For those stars that are in common in the spectroscopic andphotometric samples and for galaxies that formed the major-ity of their stellar populations within the last 10 Gyr, we findthe maximum di ff erence between the median Ca T metallicityand the median photometric metallicity, amounting to 0.52 dexfor Fornax, as well as the maximum range of the di ff erencesbetween the MRS and photometric metallicities (amounting to2.56 dex again for Fornax). These di ff erences become very smallfor almost purely old stellar populations, of the order of less than0.1 dex for Sculptor and Sextans when comparing both MRS andCa T metallicities with photometric metallicities.There is the trend of the di ff erences between the individualstellar metallicities derived from all methods to increase towardspositive ∆ [Fe / H], and this systematic deviation strongly dependson the particular SFH of each studied dSph. As compared toCa T–based metallicities, the photometric metallicities seem toshow the best agreement in the metallicty range from around − − ff ect of age on the di ff erences between MRS andphotometric metallicities is less pronounced, regardless of theintermediate–age stellar mass fraction, while for Ca T metallici-ties versus photometric metallicities there is a stronger manifes-tation of the age–metallicity degeneracy.Each spectroscopic method yields di ff erent results. Our com-parison between metallicities from di ff erent spectroscopic meth-ods shows di ff erences of a similar size as the comparison ofmetallicities between spectroscopic methods and photometry inthe case of the old–age dominated dSphs Sculptor and Sextans.Such di ff erences are of the order of 0.1 dex. In the case of Leo IIand Fornax, the comparison between di ff erent spectroscopicmethods show di ff erences smaller than those when compar-ing spectroscopic with photometric metallicities. As expected,we do find e ff ects of the age–metallicity degeneracy for galax-ies with high fractions of intermediate–age stellar populations.Therefore, we find that we are justified to use the photomet-ric method of deriving stellar metallicities in the case of old orintermediate–age dominated dSphs when we focus on the metal-licity range from − − Acknowledgements.
The authors thank an anonymous referee for the thought-full comments. We kindly thank Giuseppina Battaglia and Matthew Walker, theformer for sharing with us the full photometric datasets of Sculptor and the Ca Tspectroscopic dataset of Sextans, and the latter for sharing with us the full pho-tometric datasets of Sculptor, Fornax, and Carina. We also kindly thank AaronDotter for extremely useful discussions on Dartmouth isochrones. Katrin Jordiand Thorsten Lisker are also acknowledged for useful discussions. SL acknowl-edges an IAU travel grant to participate to the XXVII GA, during which this workwas motivated to initiate. SL and this research were supported within the frame-work of the Excellence Initiative by the German Research Foundation (DFG) viathe Heidelberg Graduate School of Fundamental Physics (HGSFP) (grant num-ber GSC 129 / / / IPAC ExtragalacticDatabase (NED) which is operated by the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under contract with the National Aeronautics and SpaceAdministration. This research has made use of NASA’s Astrophysics DataSystem Bibliographic Services.
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16. Lianou et al.: Spectroscopic versus Photometric Metallicities : Milky Way Dwarf Spheroidal Companions as a Test Case