An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy
D. Adén, K. Eriksson, S.Feltzing, E. K. Grebel, A. Koch, M. I. Wilkinson
aa r X i v : . [ a s t r o - ph . GA ] O c t Astronomy&Astrophysicsmanuscript no. herc˙hr˙vFinal2 c (cid:13)
ESO 2018September 25, 2018
An abundance study of red-giant-branch stars in the Herculesdwarf spheroidal galaxy
D. Ad´en , K. Eriksson , S. Feltzing , E. K. Grebel , A. Koch , and M. I. Wilkinson Lund Observatory, Box 43, SE-22100 Lund, Sweden Department of Physics and Astronomy, Uppsala University, Box 515, SE-751 20 Uppsala, Sweden Astronomisches Rechen-Institut, Zentrum f¨ur Astronomie der Universit¨at Heidelberg, M¨onchhofstr. 12-14, 69120 Heidelberg,Germany Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UKReceived 10 May 2010 / Accepted 24 October 2010
ABSTRACT
Context.
Dwarf spheroidal galaxies are some of the most metal-poor, and least luminous objects known. Detailed elemental abundanceanalysis of stars in these faint objects is key to our understanding of star formation and chemical enrichment in the early universe, andmay provide useful information on how larger galaxies form.
Aims.
Our aim is to provide a determination of [Fe / H] and [Ca / H] for confirmed red-giant branch member stars of the Hercules dwarfspheroidal galaxy. Based on this we explore the ages of the prevailing stellar populations in Hercules, and the enrichment history fromsupernovae. Additionally, we aim to provide a new simple metallicity calibration for Str¨omgren photometry for metal-poor, red giantbranch stars.
Methods.
High-resolution, multi-fibre spectroscopy and Str¨omgren photometry are combined to provide as much information on thestars as possible. From this we derive abundances by solving the radiative transfer equations through marcs model atmospheres.
Results.
We find that the red-giant branch stars of the Hercules dSph galaxy are more metal-poor than estimated in our previous studythat was based on photometry alone. From this, we derive a new metallicity calibration for the Str¨omgren photometry. Additionally,we find an abundance trend such that [Ca / Fe] is higher for more metal-poor stars, and lower for more metal-rich stars, with a spreadof about 0.8 dex. The [Ca / Fe] trend suggests an early rapid chemical enrichment through supernovae of type II, followed by a phaseof slow star formation dominated by enrichment through supernovae of type Ia. A comparison with isochrones indicates that the redgiants in Hercules are older than 10 Gyr.
Key words.
Galaxies:dwarf – Galaxies: evolution – Galaxies: individual: Hercules – Stars: abundances
1. Introduction
Over the past few years, the number of known dwarf spheroidal(dSph) galaxies orbiting the Milky Way has more than dou-bled through systematic searches in large photometric surveyssuch as the Sloan Digital Sky Survey (e.g., Zucker et al. 2006;Belokurov et al. 2007). These recently discovered dSph galaxieshave much lower surface brightness than the previously knowndSph galaxies. Typically, these systems have total luminosities M V > − / H] ≤ − Send o ff print requests to : D. Ad´en [email protected] mation of large galaxies (Sch¨orck et al. 2009). However, recentstudies of the ultra-faint (e.g., Kirby et al. 2008b; Frebel et al.2010b; Norris et al. 2010; Simon et al. 2010) and the classical(e.g., Starkenburg et al. 2010; Frebel et al. 2010a) dSph galax-ies have discovered stars with [Fe / H] ≤ −
3, thus reigniting thediscussion of the origin of the Galactic halo. Whether the metal-licity distribution functions of the halo and of the dSph galaxiesagree still remain to be determined. Additional abundance stud-ies are needed for both halo and dSph stars, in order to rule outselection biases due to low number statistics.Studies of [ α/ Fe] in the stars in the more luminous dSphgalaxies suggest that stars more metal-rich than [Fe / H] > − α/ Fe] ratios, whilst more metal-poor stars (fromnow taken to be stars with [Fe / H] < −
2) have about the sameenhancement in the α -elements relative to iron as the stars inthe halo and disk of the Milky Way (see, e.g., Shetrone et al.2001; Geisler et al. 2007; Tolstoy et al. 2009). This could be in-terpreted as support for an early accretion of dSphs. The discrep-ancy is poorly constrained for the recently discovered ultra-faintdSph galaxies, with notable exceptions for a few stars in theseultra-faint objects (Feltzing et al. 2009; Frebel et al. 2010b).The Hercules dSph galaxy lies at a distance of ∼ V -band sur-face brightness of only 27 . ± . − (Martin et al.2008). Previous studies, based on photometry and the measure-ments of the near-infrared Ca ii triplet lines in red giant branch Ad´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy
Table 1.
Properties of the Hercules dSph galaxy
Parameter Footnote α J2000 16 31 05.2 ± δ J2000 +
12 47 18 ±
17 a r h arcmin 8 . + . − . a M V − . ± . + − b E ( B − V ) 0.062 b M M ⊙ . + . − . · ca The centroid, α and δ , half-light radius, r h , and absolute magni-tude are taken from Martin et al. (2008).b The distance, D , and reddening, E ( B − V ), are taken from Ad´en et al.(2009a)c The mass within the central 300 pc is taken from Ad´en et al.(2009b). (RGB) stars, have found a mean metallicity of [Fe / H] ∼ − . i lines (Kirby et al.2008b) found a lower mean metallicity of − . ± .
51 dex.Koch et al. (2008b) found, using high-resolution spectroscopy oftwo Hercules RGB stars, that the hydrostatic burning α -elements(e.g., Mg, O) are strongly enhanced, while the heavy (mainly)s-process elements (e.g., Y, Sr, Ba, La) are largely depleted.The low [Fe / H] observed for the Hercules dSph galaxy suggeststhat star formation ceased relatively early after the formation ofthis galaxy. Thus, detailed elemental abundances for stars in theultra-faint dSph galaxies are key to our understanding of star for-mation and chemical enrichment in the early universe.In this study we will determine some of the elemental abun-dance trends in the ultra-faint Hercules dSph galaxy.This paper is organised as follows: in Sect. 2 we describe theobservations and the reduction of our spectra. In Sect. 3 we de-scribe the determination of the stellar parameters for each star.Section 4 deals with the abundance analysis. In Sect. 5 we pro-vide a comparison with abundances determined in other studies,in Sect. 6 we show and discuss our results and Sect. 7 concludesthe article.
2. Observations, data reduction, and measurementof equivalent widths
Some of the new ultra-faint dSph galaxies are seen through asignificant portion of the Milky Way disk. Moreover, sometimesthey have systemic velocities very similar to the bulk motion ofthe stars in the Milky Way disk. This is the case for the HerculesdSph galaxy (Ad´en et al. 2009a). Thus, when studying systemslike Hercules it is very important that the stars are confirmedmembers of the galaxy, and not foreground contaminating starsthat belong to the Milky Way. In Ad´en et al. (2009a) we showedthat the mean velocity of the Hercules dSph is very similar tothe velocity distribution of the foreground dwarf stars, making itdi ffi cult to disentangle the dSph galaxy stars from the foregrounddwarf stars using radial velocity measurements alone. We usedthe Str¨omgren c index to identify the RGB stars that belongto the dSph galaxy and showed that a proper cleaning of thesample results in a smaller value for the velocity dispersion ofthe system. This has implications for galaxy properties derivedfrom such velocity dispersions, e.g., resulting in a lower mass Table 2.
Data for the RGB stars in the Hercules dSph galaxyobserved with FLAMES.
ID RA DEC V ( b − y ) S / N UsedJ2000.0 J2000.12175 247.81591 12.58238 18.72 0.83 35 *42241 247.73849 12.78898 18.72 0.82 36 *41082 247.84564 12.74666 19.05 0.78 2342149 247.74718 12.79045 19.21 0.70 25 *41743 247.78386 12.80170 19.44 0.70 24 *42795 247.68541 12.82996 19.51 0.67 23 *40789 247.87404 12.74030 19.52 0.67 20 *41460 247.80860 12.75741 19.60 0.69 21 *42096 247.75261 12.82550 19.59 0.66 20 *40993 247.85432 12.75811 19.73 0.67 20 *42324 247.73111 12.76968 19.72 0.62 13 *12729 247.78123 12.52606 19.84 0.67 12 *40222 247.93108 12.78307 20.01 0.62 1142692 247.69607 12.75570 20.02 0.63 1243688 247.59341 12.86022 20.04 0.61 843428 247.61721 12.75078 20.09 0.60 1111239 247.87333 12.58958 20.11 0.61 941912 247.76877 12.77069 20.15 0.64 842008 247.76005 12.80071 20.21 0.61 941371 247.81831 12.83070 20.23 0.63 10Column 1 lists the RGB star ID (Ad´en et al. 2009a). Columns 2 and3 list the coordinates. Column 4 lists the V magnitude and column5 lists the ( b − y ) colour. Column 6 lists estimates of the S / N in thefinal spectra and column 7 indicates whether the star was analysedin this work, compare Sect. 4. (Ad´en et al. 2009b; Walker et al. 2009). In this study, we revisitthe previously identified RGB stars of the Hercules dSph galaxywith high-resolution spectroscopy.The RGB stars for this study were taken from the list ofHercules dSph galaxy members in Ad´en et al. (2009a). We se-lected RGB stars brighter than V ∼
20 (see Fig. 1). Stars fainterthan V ∼
20 were not considered since the signal-to-noise ratio,per pixel, (S / N) would be too low for equivalent width measure-ments. In total, 20 RGB stars were selected (see Table 2).
Our spectroscopy was carried out using the multiobjectspectrograph Fibre Large Array Multi Element Spectrograph(FLAMES) at the Very Large Telescope (VLT) on Paranal. Theobservations, 18 observing blocks of 60 minutes each made inservice mode, are summarised in Table 3. Operated in Medusafibre mode, this instrument allows for the observation of up to130 targets at the same time (Pasquini et al. 2002). 23 fibres werededicated to observing blank sky. We used the GIRAFFE / HR13grating, which provides a nominal spectral resolution of R ∼
20 000 and a wavelength coverage from 6100 Å to 6400 Å. Weverified the spectral resolution by measuring the full-width-halfmaximum of telluric emission lines in the combined sky spec-trum.
The FLAMES observations were reduced with the standardGIRAFFE pipeline, version 2.8.1 (Blecha et al. 2000). Thispipeline provides bias subtraction, flat fielding, dark-current sub-traction, and accurate wavelength calibration from a ThAr lamp. d´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy 3
Table 3.
Summary of the spectroscopic observations withFLAMES.
Date Exp. time [ min ]17 May 2009 18020 May 2009 12022 May 2009 12023 May 2009 12024 May 2009 6025 May 2009 18026 May 2009 6013 June 2009 18018 June 2009 60Total Exp. Time 1080Column 1 lists the date of observation and column 2 the exposuretime.
The 23 sky spectra were combined and subtracted from theobject spectra with the task SKYSUB in the SPECRED packagein IRAF .Next, the object spectra from the individual frames wereDoppler-shifted to the heliocentric rest frame and median-combined into the final one-dimensional spectrum. When com-bining the object spectra we used an average sigma clipping al-gorithm, rejecting measurements deviating by more than 3 σ , inorder to remove cosmic rays.Finally, we normalised the spectra with the taskCONTINUUM in the ONEDSPEC package in IRAF. Weused a Spline1 function of the 1st order. We note that thenomalisation was not optimal over the entire wavelength range.To accomodate for this, we set the continuum for each lineindividually when measuring the equivalent widths, W λ .The W λ for the absorption lines were measured by fittinga Gaussian profile to each of the lines using the IRAF taskSPLOT. However, for some of the weak lines with low S / N itwas better to determine the W λ by integration of the pixel val-ues using the ”e” option in SPLOT. The W λ s are listed in Table 4.We were not able to identify any absorption lines in the con-tinuum for stars fainter than V = .
80. The S / N for the spectrafor these stars are about 10. Thus, 8 stars were discarded from theabundance analysis (compare Table 2). Additionally, we werenot able to remove the sky emission for RGB star 41082 to a sat-isfying level, and the S / N was lower than expected from the starsmagnitude, indicating that something may have gone wrong withthe positioning of the fibre. Therefore, the spectrum for this starwas discarded also, leaving us with spectra for 11 usable RGBtargets.
3. Stellar parameters
The e ff ective temperature ( T e f f ) is often determined by requir-ing that the abundances derived from individual Fe lines are in-dependent of the excitation potential for the lines. This was notan option for us due to the small number of Fe i lines for eachstar. Instead, we calculated T e f f from Str¨omgren photometry us-ing the calibration in Alonso et al. (1999). The photometry isfrom Ad´en et al. (2009a) and has been corrected for interstellar IRAF is distributed by the National Optical AstronomyObservatories, which are operated by the Association of Universitiesfor Research in Astronomy, Inc., under cooperative agreement with theNational Science Foundation. extinction using the dust maps by (Schlegel et al. 1998). Thesemaps give a reddening of E ( B − V ) = . T e f f using the uncertainties for the Str¨omgren photom-etry. Since we are using deep photometry, and are only usingstars at the brighter end of the luminosity function, the errors areessentially the same for the stars in the sample. We find a typicalerror of about 100 K for all stars.Surface gravities, log g , were estimated using an isochroneby VandenBerg et al. (2006) with [Fe / H] = − .
31 (most metal-poor isochrone available), an age of 12 Gyr, colour transfor-mations by Clem et al. (2004), and no α -enhancement. Figure1 shows the colour-magnitude diagram for the Hercules dSphgalaxy with log g values indicated. The isochrone was shiftedusing the distance modulus derived in Ad´en et al. (2009a), ( m − M ) = . ± . g is to thechoice of the age for the isochrone, we repeated the abovederivation for isochrones with an age of 8 and 18 Gyr, and[Fe / H] = − .
31. We find that the estimated value of log g de-viated by a maximum of ∼ . g whenthe age was changed. Additionally, for comparison with anisochrone based on a di ff erent stellar evolutionary model, wecompared with values of log g derived using the Darthmouthisochrones (Dotter et al. 2008) with colour transformations byClem et al. (2004), and similar age and metallicity as for theisochrone by VandenBerg et al. (2006). We find that the valuesof log g estimated using the two sets of isochrones di ff er by about0.1 dex.Finally, we estimated the contribution to the error in log g from the uncertainty in the distance modulus and magnitude us-ing 10 Monte Carlo realisations of the distance modulus andmagnitude drawn from within the individual error bars on eachparameter. We find that the values of log g deviated by ∼ . g . Based on these three error estimates, wedefine an upper limit to the error in log g of 0.35 dex to makesure that the error is not under-estimated.In Sect. 4 we investigate how di ff erent values of log g a ff ectthe abundance analysis.We estimated the microturbulence, ξ t , using the ξ t and log g for metal-poor halo stars from Andrievsky et al. (2010). Thesestars have about the same metallicity and log g as our HerculesRGB stars. A least-square fit to their data, in ξ t vs. log g space(Fig. 2), of 35 giant stars yields ξ t = − . ± . · log g + . ± . . (1)We estimated the errors in ξ t using the uncertainties for theleast-square fit (Eq. 1) and an uncertainty in log g of 0.3 dex. Wefind a typical error in ξ t of ∼ . − .The final stellar parameters used in the abundance analysisare summarised in Table 5.
4. Abundance analysis
Model atmospheres were calculated for the programme starswith the code marcs according to the procedures described inGustafsson et al. (2008) and using the fundamental parametersin Table 5. Next a line list was compiled in the wavelength re-gion 6120 – 6400 Å with spectral lines from neutral and singlyionised atoms from the VALD database (Piskunov et al. 1995;Ryabchikova et al. 1997; Kupka et al. 1999, 2000). Equivalentwidths or synthetic spectra were then computed from radiativetransfer calculations in spherical geometry in the model atmo-spheres using the Eqwi / Bsyn codes that share many subrou-
Ad´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy
Table 4.
Equivalent width measurements.
RGB 12175 42241 42149 41743 42795 40789 41460 42096 40993 42324 12729Ion λ log g f EP W λ W λ W λ W λ W λ W λ W λ W λ W λ W λ W λ (Å) (dex) eV (mÅ) (mÅ) (mÅ) (mÅ) (mÅ) (mÅ) (mÅ) (mÅ) (mÅ) (mÅ) (mÅ)Ca i i i i i i i i i i i i i i i i i i i i i ii ii Table 5.
Photometry and model parameters used in the abundance analysis of the stars.
ID Other ID V ( b − y ) [Fe / H] T ef f log g ξ t S / Ndex K dex km s − V magnitude andcolumn 4 lists the ( b − y ) colour. Column 5 lists the metallicity as determined in Sect. 4.2. Column 6 to 8 list the stellar parameters asdetermined in Sect. 3. Column 9 lists an estimate of the S / N. tines and data files with marcs making the analysis largely self-consistent.For stars with at least two lines measurable, we adopt themean of the abundances derived from the individual W λ for eachelement as the final elemental abundances. For stars more di ffi -cult, in terms of identifying absorption lines, the final elementalabundances are determined using a χ -test (see Sect. 4.2.3) For elements with more than four lines measured, the randomerrors in the elemental abundance ratios were calculated as ǫ rand , [X / H] = σ X √ N (2) where X is the element, σ is the standard deviation of the abun-dances derived from the individual W λ , and N the number oflines for that element. For elements with two to four lines mea-sured, the uncertainty in the measurement of W λ , ǫ W λ , was esti-mated using the relation in Cayrel (1988). The random errors inthe elemental abundances were then estimated using 10 MonteCarlo realisations of W λ , drawn from within the probability dis-tribution of W λ given ǫ W λ . For each value of W λ , we recalcu-late an elemental abundance using the relation log( A ) ∝ log( W λ )where A is the elemental abundance. We note that the probabilitydistribution of log( A ) is asymmetric. Thus, we adopt the standarddeviation based on the sextiles (which is equivalent to 1 σ in thecase of a Gaussian distribution) as our final random error. Forelements with less than two lines measured we performed a χ - d´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy 5 Fig. 1.
Colour-magnitude diagram for the Hercules dSph galaxy(Ad´en et al. 2009a). • are RGB stars selected for this study. ◦ indicate RGB stars too faint for this study and open trian-gles are horizontal-branch stars. The solid line indicates theisochrone by VandenBerg et al. (2006) with colour transforma-tions by Clem et al. (2004). log g values for di ff erent magnitudesas indicated. Note that there are two stars at V ∼ . Fig. 2. ξ t vs. log g for metal-poor giant stars fromAndrievsky et al. (2010). The solid line indicates a least-squarefit to the data.test between the stellar spectrum and a grid of synthetic spectra,to estimate the random errors in the elemental abundances (seeSect. 4.2 and 4.3). Note that none of the Ca abundances are esti-mated using more than two lines. Thus, the errors in [Ca / H] arederived using either a χ -test or by propagating ǫ W λ as derivedusing the relation in Cayrel (1988).The systematic errors, ǫ sys , [X / H] , were estimated from the er-rors in the stellar parameters (Sect. 3) as follows: two stars wereselected randomly, RGB star 40789 and 42241. For these twostars, we study the final elemental abundances for several modelatmospheres. The model atmospheres were chosen so that wehad two values of log g , separated by 0.5 dex, three values of T e f f , separated by 100 K, and three values of ξ t , separated by 0.2 km s − . The separation between the T e f f and ξ t values cor-responds to the estimated errors in the parameters (see Sect. 3).The centre value for T e f f and ξ t corresponds to the values as de-termined in Sect. 3. Since the error in log g was more di ffi cult todetermine (see Sect. 3), we chose a separation in log g of 0.5 dexto make sure that we got an upper limit of the contribution fromthis stellar parameter. The elemental abundances varies with lessthan 0.05 dex when the value of log g is separated by 0.5 dex.However, we note that this is based on Fe i lines. Fe ii lines aremore sensitive to changes in log g .Thus, we have 18 model atmospheres for which we deter-mine the final elemental abundances of iron and calcium. Thestandard deviation of the 18 final elemental abundances, foriron and calcium, is then adopted as ǫ sys , [X / H] . We find a typi-cal ǫ sys , [X / H] of ∼ .
12 dex.The total errors in the elemental abundance ratios were cal-culated as ǫ [X / H] = q ǫ , [X / H] + ǫ , [X / H] (3)The final total errors are summarised in Table 6. The mean [Fe / H] is determined on the scale where log ǫ H = .
00. The solar iron abundance of 7.45 is adopted fromGrevesse et al. (2007).Due to the variation in the S / N, and the number of measur-able lines in the spectra, we analyse these stars individually or asgroups with spectra of similar quality (Sections 4.2.1, 4.2.2 and4.2.3). The result from the analysis is summarised in Table 6.
RGB star 12175, with V = .
5, is one of the two brightestRGB stars discovered in the Hercules dSph galaxy. However,due to its low metallicity, only 4 Fe i lines were distinguish-able from the continuum in the spectral range covered by ourobservation. These four iron lines give [Fe / H] = − . ± . i lines. Close to these two lines there are two additional Fe i lines that we could not measure quantitatively, but that we wereable to identify with the help of a synthetic spectrum. The syn-thetic spectrum shown in Fig. 3b supports the result that this is avery metal-poor star with [Fe / H] = − . / N as12175. However, due to its higher iron abundance, about fourtimes as many lines were measurable in this spectrum (compareTable 4). We find an [Fe / H] of − . ± .
14 dex. Additionally,for this star, we were able to measure two Fe ii lines. These linesgive an iron abundance of − . ± .
20 dex. Thus, the [Fe / H]as derived from Fe i lines do not agree within the error barswith [Fe / H] as derived from Fe ii lines. This discrepancy in thedetermination of the iron abundance could partially be causedby over-ionisation in Fe i . Ivans et al. (2001) argue that over-ionisation could cause an under-estimate of about 0.1 dex forRGB stars if Fe i lines are used.Figure 3d shows the stellar spectrum of 42241 around four ofthe measured Fe i lines. As can be seen, [Fe / H] derived from the W λ agrees well with a synthetic spectrum with an iron abundanceclose to the –2 dex value derived from the W λ s. Ad´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy
Fig. 3. Left panels:
Portions of stellar spectra around four Fe i (b) and two Ca i (a) lines for RGB star 12175. • indicate theobserved spectrum. The solid line indicates a synthetic spectrum with [Fe / H] = − . / H] = − .
8. The dotted lines in (a) indicate synthetic spectra with [Ca / H] ± . Right panels:
Portions of stellar spectraaround four Fe i (d) and two Ca i (c) lines for star 42241. • indicate the observed spectrum. The solid line indicates a syntheticspectrum with [Fe / H] = − . / H] = − . RGB stars 42149, 41743, 42795, 40789, 42096, 40993 and12729 have a lower S / N than 12175 and 42241. However, at leasttwo Fe i lines were measurable for each of the stars.Since the S / N is much lower for these stars, we did the fol-lowing test to ensure that the [Fe / H] derived from the equivalentwidths are reasonable. For each of the stars, we generated a setof synthetic spectra with five di ff erent [Fe / H] values, separatedby 0.2 dex, centred on the [Fe / H] derived from the equivalentwidths. A plot of the stellar spectrum, with the synthetic spectraover-plotted, enabled us to verify that the [Fe / H] derived fromthe W λ s is a good estimate of the iron abundance of the star. Wefound that none of the stellar spectra deviated significantly froma synthetic spectrum with a similar [Fe / H] abundance.Figure 4 shows an example, for 41743. As can be seen, an[Fe / H] of ∼ − . RGB stars 41460 and 42324 have low S / N (21 and 13, respec-tively) and are very metal-poor. Thus, it was di ffi cult to identifythe Fe i absorption lines in the spectra. However, we did see faintabsorption signatures but the low S / N made it virtually impossi-ble to measure the lines. Instead, we performed a χ -test betweenthe observed spectrum and a grid of synthetic spectra with 17di ff erent [Fe / H] values, separated by 0.05 dex. Each syntheticspectrum yields a χ value, and the best fit is found when χ isminimised ( χ min ). We used a width of 3 σ , which covers about99.7 per cent of the absorption feature, for each iron line in theline list (see Table 4). We investigated the sensitivity of the χ -test region by varying it between 2 σ and 4 σ and found that Fig. 4.
Portions of stellar spectra around three Fe i lines for RGBstar 41743. • indicate the observed spectra. The solid lines indi-cate synthetic spectra with [Fe / H] from − .
85 to − .
05 dex, topto bottom, separated by 0.2 dex each.it had negligible impact on the result. The continuum for eachline was adjusted, as the average of the signal on each side ofthe absorption feature over 0.6 Å, to accommodate for the localdeviations from the continuum normalisation in Sect. 2.3. Theerror for each pixel in the observed spectrum was approximatedby the variance in the spectrum. The distribution enclosed by χ min + σ for a normal distribution (Press et al.1992). We used this as the measurement error. The mean [Ca / H] is determined on the scale where log ǫ H = .
00 The solar calcium abundance of 6.34 is adopted fromAsplund et al. (2009). There are two Ca i lines, at 6122.22 Å and d´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy 7 For RGB star 12175 both Ca i lines were measured and theygive [Ca / H] = − . ± .
1. Figure 3a shows the stellar spectrumaround the Ca i lines. As can be seen, [Ca / H] as measured fromthe W λ agree well with a synthetic spectrum with similar [Ca / H].Additionally, Fig. 3a shows an example of two synthetic spectrawith [Ca / H] ± . / H] of − . ± .
2. This issignificantly higher than [Ca / H] for RGB star 12175. Figure 3cshows the stellar spectrum of 42241 around the two Ca i lines.As can be seen, [Ca / H] as derived from the W λ agree well witha synthetic spectrum with a similar abundance. RGB stars 42149, 41743, 40789, 42096 and 42324 have a lowerS / N than RGB stars 12175 and 42241. However, both of the Ca i lines were measurable in all four stars.Since the S / N is lower we repeated the same test done forthe iron abundance analysis (compare Sect. 4.2.2), generating agrid of synthetic spectra for each star, to see if the [Ca / H] as de-rived from the W λ were reasonable. We found that the syntheticspectrum of RGB star 40789, in comparison with the observedspectrum, indicates that the [Ca / H] determined from the mea-surements of the W λ was slightly, about 0.1 dex, over-estimated.Thus, we estimated the Ca i abundance for RGB star 40789 us-ing the same method as for the spectra identified as di ffi cult forthe measurement of the Fe i lines (see Sect. 4.2.3). For all otherstars in this category, the abundances from the measured W λ andthose from the χ -comparison of synthetic spectra showed goodagreement. For RGB star 42795, 41460, and 40993 only one or none ofthe Ca i lines were measurable. However we did see a generaldecrease in the continuum at the wavelengths for the Ca i linesindicating the presence of Ca in the atmospheres of these metal-poor stars. Thus, we estimated the Ca i abundance using the samemethod as for the spectra identified as di ffi cult for the measure-ment of the Fe i lines (see Sect. 4.2.3). The results from the anal-ysis are summarised in Table 6.We were not able to identify any Ca i absorption features forRGB star 12729. Thus, [Ca / H] remains unknown for this star.
5. A comparison with abundances determined inother studies
Lind et al. (2009) obtained high S / N spectroscopy of severalbright RGB stars in the Milky Way. They used the same instru-ment and grating (GIRAFFE / HR13) as in this study. Throughprivate communication they provided us with a spectrum of oneof their bright targets, star 17691, that has a S / N of about 300.We measured the W λ for the lines in Table 4 and performed an Table 6.
Derived elemental abundances for the RGB stars in theHercules dSph galaxy.
Star [Fe / H] N [Ca / H] N [Ca / Fe]12175 − . ± .
14 4 − . ± .
15 2 0 . ± . − . ± .
14 20 − . ± .
15 2 − . ± . − . ± .
15 2 − . ± .
16 2 − . ± . − . ± .
15 11 − . ± .
16 2 − . ± . − . ± .
15 2 − . ± . χ . ± . − . ± .
17 3 − . ± . χ − . ± . − . ± . χ − . ± . χ . ± . − . ± .
17 4 − . ± .
18 2 0 . ± . − . ± .
19 8 − . ± . χ − . ± . − . ± . χ − . ± .
28 2 0 . ± . − . ± .
17 5 ... ...Column 1 lists the RGB star ID. Column 2 and 4 list the [Fe / H]and [Ca / H], respectively, with total errors in the abundances as in-dicated. N indicates the number of lines measured for the deter-mination of [Fe / H] and [Ca / H], as indicated. χ indicates that thecorresponding abundance was determined through a χ / Fe]. abundance analysis for this star as described in Sect. 2.3 and 4.The stellar parameters was adopted from Lind et al. (2009). Wefind an Fe abundance that is 0.01 dex more metal poor, and a Caabundance 0.04 dex lower than given in Lind et al. (2009). Thus,our determinations of the abundances of Ca and Fe in star 17691are in agreement with Lind et al. (2009). Additionally, we findthat none of the elemental abundances as derived from individ-ual measurements of the W λ deviate significantly. This suggeststhat the e ff ect of atomic parameters should not contribute to ourelemental abundance errors. Koch et al. (2008b) obtained high resolution spectroscopy ( R ∼ / N and resolution as in this study, oftwo stars in the Hercules dSph galaxy, Her-2 and Her-3.These stars correspond to our RGB stars 42241 and 41082.However, RGB star 41082 was discarded from our sample (seeSect. 4). Koch et al. (2008b) find [Fe / H] = − . ± .
20 and[Ca / Fe] = − . ± .
05 for RGB star 42241. Note, however,that Koch et al. (2008b) measured W λ values of lines over abroader wavelength range from 5500–8900 Å. Our estimates of[Fe / H] are in very good agreement, but [Ca / Fe] as derived byKoch et al. (2008b) is 0.4 dex higher.Figure 5 shows our spectrum and the spectrum fromKoch et al. (2008b) for RGB star 42241. In Table. 7 we providea comparison between W λ s as measured from our observedspectrum, and W λ s as measured by us from the spectrumobtained by Koch et al. (2008b). We note that, for the Ca i lines,the spectrum from Koch et al. (2008b) has deeper absorption.However, the overall absorption for the Fe i and blendedlines are in good agreement, except for one weak Fe i line at λ = .
31 Å that is more prominent in our observed spectrum.We note that the S / N at this line in the spectrum from Koch et al.(2008b) is low, making it di ffi cult to distinguish such a weakline in the spectrum. There is a much brighter star, SDSSJ163056.63 + ∼
12 arcsec from 42241.Thus, we investigate the possibility that the fibre allocated for42241 has collected a significant amount of flux from SDSSJ163056.63 + + Ad´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy
Table 7.
Equivalent width measurements for RGB star42241 / Her-2.
Ion λ W λ, A W λ, K W λ, A W λ, K (Å) (mÅ) (mÅ)Ca i i i i i i i i ∼ ∼ W λ as measured from our observed spectrum and thespectrum obtained by Koch et al. (2008b), respectively. Column 5lists the ratio between the measurements. magnitudes brighter in the SDDS r -filter, which is centredon our wavelength region of interest. The seeing for ourobservations was ∼ + ff erences in the reduction procedure.Kirby et al. (2008b) studied 20 stars in the direction of theHercules dSph galaxy. Their metallicities are based on a recentlydeveloped automated spectrum synthesis method that takes theinformation in the whole spectrum into account (Kirby et al.2008a). The method was originally developed for globular clus-ters in the Milky Way and was then applied to ultra-faint dSphgalaxies in Kirby et al. (2008b). We have 7 stars in common be-tween our samples. Figure 6b shows the di ff erence between ourrespective determinations of [Fe / H]. We find that our [Fe / H] ison average 0.07 dex more metal-rich, with a scatter of 0.09 dex.In conclusion, the agreement between the [Fe / H] determinationsis very good.
In a previous study of the Hercules dSph galaxy (Ad´en et al.2009a) we estimated [Fe / H] using the Str¨omgren m index us-ing the calibration from Calamida et al. (2007). Figure 6a showsa comparison between the photometric [Fe / H] as estimated inAd´en et al. (2009a), [M / H] phot , and [Fe / H] as determined fromhigh-resolution spectroscopy in this study. We note that there isa strong trend such that [M / H] appears to be over-estimated inAd´en et al. (2009a) for metal-poor stars.
Fig. 6. a)
A comparison between our [Fe / H] and [M / H] fromAd´en et al. (2009a) ([M / H] Phot ). The error-bars represent theerror in [Fe / H] − [M / H] Phot and [Fe / H], respectively. b) Acomparison between our [Fe / H] and [Fe / H] from Kirby et al.(2008b) ([Fe / H] Kirby ). The error-bars represent the error in[Fe / H] − [Fe / H] Kirby and [Fe / H], respectively.
Given the excellent agreement between all three spectroscopicstudies it must be concluded that the metallicity calibration byCalamida et al. (2007) severely over-estimates the metallicity forvery metal-poor stars. A check shows that also their updated cal-ibration (Calamida et al. 2009) has the same problem. This is anunfortunate situation since the photometry allows us in principleto determine the metallicity of RGB stars with good accuracyalso for the fainter stars (compare errors in Ad´en et al. 2009a)and thus allowing the study of much more complete stellar sam-ples in the ultra-faint dSph galaxies.Here we present an attempt to deal with the situation. Sofar this is a very simplistic relation and only formally valid forstars with 0 . < m , < . − . < [Fe / H] < .
58 and1 . < ( v − y ) < . / H] derivedfrom high-resolution spectra available for stars in Draco(Cohen & Huang 2009; Shetrone et al. 2001), Sextans(Shetrone et al. 2001), UMaII (Frebel et al. 2010b) andHercules (this study), and combined these data with our ownStr¨omgren photometry where available. Fig. 7a shows thespectroscopic [Fe / H] as a function of m , for the stars. Aleast-squares fit yields[M / H] phot , new = . ± . · m , − . ± .
10) (4)Fig. 7b and 7c show [M / H] phot , new − [Fe / H] as a functionof m , and ( v − y ) , respectively. No strong trends are seen.For comparison Fig. 7d shows [M / H] CA07 − [Fe / H] vs. ( v − y ) ,where [M / H] CA07 is [Fe / H] as determined using the calibra-tion in Calamida et al. (2007). Here we can note a significant d´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy 9
Fig. 5.
A comparison betweenour spectrum and the spectrumfrom Koch et al. (2008b) , inthe region where they overlap,for RGB star 42241. • indi-cate our stellar spectrum. Thesolid line indicates the spec-trum from Koch et al. (2008b). di ff erence of both metallicity scales such that [M / H] CA07 > [Fe / H] spec . Taking into account the uncertainties of the least-squares fit and the correlation between the fitting parameters (Eq.4), and the error in m , from Ad´en et al. (2009a) we find a typi-cal error in [M / H] phot , new of 0.17 dex.
6. Results and discussion
The RGB stars analysed in this paper span a large range of ironabundances, from about –3.2 dex to –2 dex, indicating an ex-tended period of chemical enrichment. It is somewhat fortuitousthat the two brightest stars in our sample, RGB stars 12175 and42241, bracket the full range of metallicities. Thus there is nodoubt that the range of metallicities derived from high-resolutionspectroscopy is real.In Sect. 5.4 we provide a new Str¨omgren metallicity calibra-tion. This calibration is valid for stars with 0 . < m , < . − . < [Fe / H] < .
58. Two of the 28 RGB stars fromAd´en et al. (2009a) have an m , less than the range for whichthe new metallicity calibration is valid. However, with an m , of0.01, these stars are included in the sample as a slight extrapola-tion. In Fig. 8a we show the resulting histogram of [M / H] phot , new for all the 28 RGB stars identified in (Ad´en et al. 2009a). The binsize of 0.2 dex represents the typical error in [M / H] phot , new (see Sect. 5.4). Figure 8b shows the corresponding error-weightedmetallicity distribution. For this plot, each stars was assigneda Gaussian distribution with a mean of [M / H] phot , new and a dis-persion equal to the typical error in [M / H] phot , new (0.17 dex).The Gaussians, one for each star, were then added to create themetallicity distribution function. We note that the distribution of[M / H] phot , new is shifted towards lower metallicities when the newcalibration is applied, and that there is an abundance spread inthe metallicity distribution for the RGB stars of at least 1.0 dex.Additionally, we note a more concentrated distribution.Figure 9a and 9b show V vs. ( v − y ) for the stars with [Fe / H]derived from high resolution spectroscopy. Additionally, in theseplots, we show two isochrones with [Fe / H] = − .
31 (most metal-poor isochrone available) and − .
14 dex. As can be seen, theisochrones of a given metallicity become redder with increasingage. Since the isochrone with [Fe / H] = − .
31 is too metal-rich,compared to [Fe / H] as derived from the spectroscopy, an evenmore metal-poor isochrone at the age of 8 Gyr would be evenbluer, excluding an age of about 10 Gyr or younger. At an age of14 Gyr, the isochrone with [Fe / H] = − .
31 is slightly redder thanmost of the stars more metal-poor than [Fe / H] = − .
7. Hencea more metal-poor isochrone would presumably represent thelocus of these stars very well, arguing for an age older than about10 Gyr for the Hercules dSph galaxy.Figure 9c shows V vs. ( v − y ) for all the 28 RGB starsidentified in (Ad´en et al. 2009a). Fig. 7. a)
Spectroscopic [Fe / H] vs. m , for Draco ( • and ◦ ),Sextans (open stars), UMaII (filled triangles) and Hercules(filled squares). b) , [M / H] phot , new − [Fe / H] vs. m , using Eq. (4)to derive [M / H]. c) , [M / H] phot , new − [Fe / H] vs. ( v − y ) using Eq.(4) to derive [M / H]. d) [M / H] CA07 − [Fe / H] vs. ( v − y ) usingthe calibration by Calamida et al. (2007) to derive [M / H].
Figure 10 shows [Ca / Fe] as a function of [Fe / H]. We find a trendsuch that [Ca / Fe] is higher for more metal-poor stars, and lowerfor more metal-rich stars. Fortuitously, the most metal-rich andthe most metal-poor star in the sample are both bright and havespectra with high S / N (see discussion in Sect. 4 and also Table 2).Thus we can be certain that the trend actually has this shape andwe are not misinterpreting spectra of lower quality.The production of alpha ( α )-elements, such as Ca, Si, Ti, Mg,and O, is correlated with the end stage of massive stars. Mg andO are created during the hydrostatic He burning in massive stars,and Si, Ca, and Ti are primarily produced during core-collapsesupernovae (Woosley & Weaver 1995). On the other hand, lessmassive stars are able to produce significant amounts of Fe inSNe Ia. Thus, the ratio of α -elements to iron is used to trace thetime scale of the star formation in a stellar system. If the starformation rate is high, then the gas will be able to reach a higher[Fe / H] before the first SNe Ia occur. This can be observed in aplot of [Ca / Fe] vs. [Fe / H] as a ”knee”, where [Ca / Fe] decreaseas [Fe / H] increase (McWilliam 1997). The fraction of stars at[Fe / H] less than the ”knee” gives information on the star forma-tion timescale.The observed continuous downward trend, without a ”knee”,for [Ca / Fe] vs. [Fe / H] in Hercules can thus be interpreted as a
Fig. 8. a)
Metallicity histogram for RGB stars in the HerculesdSph galaxy. The shaded histogram shows the distribution of[M / H] phot , new . For comparison, the dashed histogram shows thedistribution of [M / H] phot (Ad´en et al. 2009a). b) Correspondingerror-weighted metallicity distribution.brief initial burst of short-lived SNe II that enhanced the produc-tion of α -elements. Since there are no stars at [Fe / H] less thanthe ”knee”, the star formation rate was very low. The subsequentcontinuous decline would be expected if contributions fromlong-lived SNe Ia were the dominant factor, decreasing [ α / Fe]while increasing [Fe / H]. This means that essentially no massivestars formed after the initial burst. Additionally, we interpret therelatively short range in [Fe / H] (no stars with [Fe / H] > − ffi ciency star formation (for a discussion of contin-uous and bursty star formation histories and the role of SNe Iasee, e.g., Gilmore & Wyse 1991; Matteucci 2009). The classi-cal dSph galaxies, such as Carina, Sculptor and Fornax, alsoshow these types of trends for the α -elements (e.g., Venn et al.2004; Koch et al. 2008a; Tolstoy et al. 2009; Kirby et al. 2009).However, these dSph galaxies are more metal-rich and moremassive than, e.g., Hercules. Only a few other ultra-faint dSphshave chemical element abundances published for only a handfulof stars each.Frebel et al. (2010b), Feltzing et al. (2009), Norris et al.(2010) and Simon et al. (2010) studied Coma Berenices, UrsaMajor II, Bo¨otes I, and Leo IV, all recently discovered ultra-faintand metal-poor systems. Figure 11 summarises our data andtheir data. Additionally, recent studies have analysed very metal-poor stars in the classical systems Draco, Sextans and Sculptor(Cohen & Huang 2009; Aoki et al. 2009; Frebel et al. 2010a).We add these new data to the plot in addition to the abundancesfrom other studies of Fornax, Carina, Sculptor, Sextans, UrsaMinor and Draco (Shetrone et al. 2001, 2003; Sadakane et al.2004; Letarte et al. 2007; Koch et al. 2008a).Overall, there is a faster declining [Ca / Fe] with [Fe / H] for thedSph galaxies as compared with the halo stars in the solar neigh-bourhood (from the compilation by Venn et al. 2004, including d´en et al.: An abundance study of red-giant-branch stars in the Hercules dwarf spheroidal galaxy 11
Fig. 11.
A comparison of [Ca / Fe] as a function of [Fe / H] for stars in several dSph galaxies. • indicate Hercules (this study).Filled squares represent the ultra-faint dSph galaxies Ursa Major II, Coma Berenices, Bo¨otes I and Leo IV (Feltzing et al. 2009;Frebel et al. 2010b; Norris et al. 2010; Simon et al. 2010). Open squares represent the classical dSph galaxies Draco, Sextans, UrsaMinor, Fornax, Carina and Sculptor (Shetrone et al. 2001, 2003; Sadakane et al. 2004; Koch et al. 2008a; Cohen & Huang 2009;Aoki et al. 2009; Frebel et al. 2010a). The solid ellipses outline RGB stars in the classical dSph galaxy Fornax from Letarte et al.(2007).data from Fulbright (2002, 2000); Stephens & Boesgaard(2002); Bensby et al. (2003); Nissen & Schuster (1997);Hanson et al. (1998); Prochaska et al. (2000); Reddy et al.(2003); Edvardsson et al. (1993); McWilliam (1998);McWilliam et al. (1995); Johnson (2002); Burris et al. (2000);Ivans et al. (2003); Ryan et al. (1996); Gratton & Sneden (1991,1994, 1988)). Thus, for example, the trend seen from our datain Hercules is the same as the overall trend seen for Draco.This is interesting and could be interpreted as that the Fecontribution from SNe Ia were the dominant factor for bothHercules and Draco. However, since Draco has many morestars with [Fe / H] > −
7. Conclusions
We have studied confirmed RGB stars in the ultra-faintHercules dSph galaxy with FLAMES high-resolution spec-troscopy. Abundances were determined by solving the radiativetransfer calculations using the codes Eqwi / Bsyn in marcs modelatmospheres.We find that the RGB stars of the Hercules dSph galaxyincluded in this study are more metal-poor than estimatedin Ad´en et al. (2009a), however in good agreement withKirby et al. (2008b), with a metallicity spread of at least 1 dex.Based on the position of the RGB stars in colour-magnitude dia-grams, in comparison with isochrones, we conclude that there isno clear indication of a population younger than about 10 Gyr.Additionally, we provide a first attempt at a new metallicitycalibration for Str¨omgren photometry based on high-resolution spectroscopy for several dSph galaxies. With this new calibra-tion, we find several RGB stars in the Hercules dSph galaxy thatare more metal-poor than [Fe / H] = –3.0 dex.Finally, we have determined the [Ca / Fe] for the RGB starsin this study. We found a trend such that [Ca / Fe] is higher formore metal-poor stars, and lower for more metal-rich stars. Thistrend is supported by our two brightest stars in the sample and isinterpreted as a brief initial burst of SNe II during a very low starformation rate, followed by the enrichment of [Fe / H] by SNe Ia.
Acknowledgements.
We acknowledge Karin Lind for providing us with a spec-trum of one of their RGB stars. S.F. is a Royal Swedish Academy of SciencesResearch Fellow supported by a grant from the Knut and Alice WallenbergFoundation. K.E is gratefully acknowledging support from the Swedish researchcouncil. M.I.W. is supported by a Royal Society University Research Fellowship.AK acknowledges support by an STFC postdoctoral fellowship.
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