Photometric Metallicities in Bootes I
aa r X i v : . [ a s t r o - ph . GA ] J a n Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 8 October 2018 (MN L A TEX style file v2.2)
Photometric Metallicities in Bo ¨otes I
J. Hughes, G. Wallerstein, A. Dotter, D. Geisler Physics Department, Seattle University, Seattle, WA 98122 Astronomy Department, University of Washington, Box 351580, Seattle, WA 98195-1580 Research School of Astronomy & Astrophysics, Australian National University, Weston, ACT 2611, Australia Grupo de Astronom´ıa, Departamento de Astronom´ıa, Universidad de Concepci´on, Casilla 160-C, Concepci´on, Chile
Accepted xxx. Received xxx.
ABSTRACT
We present new Str¨omgren and Washington data sets for the Bo¨otes I dwarf galaxy, andcombine them with the available SDSS photometry. The goal of this project is to refine aground-based, practical, accurate method to determine age and metallicity for individual starsin Bo¨otes I that can be selected in an unbiased imaging survey, without having to take spectra.With few bright upper-red-giant branch stars and distances of about − kpc, the ultra-faint dwarf galaxies present observational challenges in characterizing their stellar population.Other recent studies have produced spectra and proper motions, making Bo¨otes I an ideal testcase for our photometric methods. We produce photometric metallicities from Str¨omgren andWashington photometry, for stellar systems with a range of − . > [ F e/H ] > − . . Needingto avoid the collapse of the metallicity sensitivity of the Str¨omgren m -index on the lower-red-giant branch, we replace the Str¨omgren v -filter with the broader Washington C -filter tominimize observing time. We construct two indices: m ∗ = ( C − T ) − ( T − T ) , and m ∗∗ = ( C − b ) − ( b − y ) . We find that CT by is the most successful filter combination,for individual stars with [ F e/H ] < − . , to maintain ∼ . dex [Fe/H]-resolution over thewhole red-giant branch. The m ∗∗ -index would be the best choice for space-based observa-tions because the ( C − y ) color is not sufficient to fix metallicity alone in an understudiedsystem. Our photometric metallicites of stars in the central regions of Bo¨otes I confirm thatthat there is a metallicity spread of at least − . > [ F e/H ] > − . . The best-fit Dartmouthisochrones give a mean age, for all the Bo¨otes I stars in our data set, of . ± . Gyr. Fromground-based telescopes, we show that the optimal filter combination is CT by , avoiding the v -filter entirely. We demonstrate that we can break the isochrones’ age-metallicity degeneracywith the CT by filters, using stars with log g = 2 . − . , which have less than a 2 per centchange in their ( C − T ) -colour due to age, over a range of 10-14 Gyr. Key words: galaxies: dwarf; galaxies: individual – (Bo¨otes I) – Local Group.
The Sloan Digital Sky Survey (SDSS) survey (in ugriz bands)has been used to identify ∼ (see Willman & Strader 2012)new Milky Way satellites (for example, Willman et al. 2005a,b;Belokurov et al. 2006a,b; Zucker et al. 2006a,b; Willman 2010).This paper is the second in a series, describing our ongoing studiesof several of the recently discovered dwarf galaxies surrounding theMilky Way Galaxy (MWG), using the Apache Point Observatory(APO) 3.5-m telescope. We discuss new Str¨omgren photometry ofBo¨otes I and compare it with our previously-published Washing-ton photometry and other recent spectroscopic studies, particularlythose of Koposov et al. (2011) and Gilmore et al. (2013a,b). In thispaper we deduce the star formation history of the central region ofBo¨otes I from photometry, and determine the most effective and ef-ficient combination of broad-band and medium band filters to breakthe age/metallicity degeneracy of populations such as these. Willman (2010) wrote a review of the search methods, forthese “least luminous galaxies”, which can be as faint as − times the luminosity of the MWG. Ten years ago, the MWGonly had 11 known dwarf galaxy companions, which was atodds with cosmological simulations predicting hundreds of lowmass ( M ⊙ ) dark matter halos. Where were the “missing satel-lites”? The apparent mismatch between the number of observeddark matter halos, and those predicited by the Λ CDM cosmologi-cal models was partially explained by “simple” models (Willman2010) of how stellar populations form inside low-mass dark mat-ter halos (Bullock, Kravtsov & Weinberg 2000; Benson et al. 2002;Kravtsov, Gnedin & Klypin 2004; Simon & Geha 2007). The firstpart of the problem is finding the least luminous galaxies, and thesecond issue is to determine the most efficient method to studythese sparsely-populated systems. A recent review by Belokurov(2013) calls the pre-SDSS dwarf galaxy population “classical”dwarfs. c (cid:13) J. Hughes et al.
Willman’s (2010) review of the automated star-count anal-ysis shows how we have increased the completeness of unbi-ased sky surveys, and also describes the next generation of sur-veys planned for the next decade or so. Detailed descriptions ofhow the automated searches were carried out can be found inWillman et al. (2002) and Walsh, Willman, & Jerjen (2009, here-after, WWJ). Once the stellar-overdensities were found, observershave to separate the dwarf spheroidal (dSph) population from thatof the MWG’s halo stars in the field. The method used by WWJfirst selects a range of Girardi isochrones (see Girardi et al. 2005,and references therein), assuming that the dSphs have populationswhich are aged between 8 and 14 Gyr, with − . < [ F e/H ] < − . . This range of models was used to create a colour-magnitude(CM) filter, which was then moved to 16 values of the distancemodulus, between 16.5 and 24.0. The software then looked forstellar overdensities, above a certain detection threshold; WWJ de-scribe this in detail, along with how the data was simulated. Alongwith dwarf galaxies, the MWG’s halo has tidal debris and unboundstar clusters, which can also be picked up in this method. Fol-lowing up the detections with photometry and spectroscopy is es-sential to finding which of the detections are actual dwarf galax-ies. When these SDSS searches were performed, Willman (2010)notes that the least luminous galaxies can only be detected out toabout 50 kpc. The CM filter method (WWJ) can locate systemswith distances in the range of 20-600 kpc, but it is brightness lim-ited. Koposov et al. (2008) and Belokurov (2013) discuss the SDSScompleteness limits, where dwarf satellite of our Galaxy are com-plete out to a virial radius of 280 kpc at M V ∼ − (using SDSSDR5). For systems such as Segue 1 with M V ∼ − , only a fewpercent of the “virial volume” can be sampled. Thus, part of theproblem is the faintness of the “darker” satellites, and part of it isthe automated detection method uses filters which do not separatethe sparse dwarf populations from the foreground stars in colour-magnitude diagrams.Some of these lowest luminosity dSphs (discovered in theSDSS) do not look like the tidal debris of collisions (as discussedin Belokurov 2013), they look like the primordial leftovers fromgalaxy-assembly and Gilmore et al. (2013a) go as far as to identifyBo¨otes I as “surviving example of one of the first bound objects toform in the Universe.”Early star formation can progress in different ways, depend-ing on the star formation rate, but the pathway should be detectablein spectroscopic surveys (Gilmore et al. 2013a,b). Both papers dis-cuss two star formation channels for these extremely metal-poorsystems. Rapid-star-formation after Pop III core-collapse super-novae can produce carbon-rich (CEMP-no) stars. The “long-lived,low star-formation rate” would produce more carbon-normal abun-dances. Gilmore et al. (2013a,b) identify Bo¨otes I as the latter case.However, some authors have identified a few red giant stars in Boo Ias carbon-rich (Lai et al. 2011; Gilmore et al. 2013b). The . × r h distance of the radial-velocity-confirmed member, Boo-1137, fromthe center of Bo¨otes I might indicate that a much more massiveoriginal system is being stripped (see Figure 1). The half-light ra-dius of Bo¨otes I is about 240 pc (Gilmore et al. 2013a). At first ex-amination, Bo¨otes I appears to be a normal, if extended, dSph at aGalactocentric distance of about 60 kpc, with e ∼ . , and − . to(at least) − . in [Fe/H]. Any stellar system/dwarf galaxy found ataround 20 kpc would be contaminated by MWG thick disk and halostars, while those which lie beyond 100 kpc are mostly affected bythe MWG halo stars. However, the Sloan filters do not separate outthe dSph stars from the MWG stars very well on colour-magnitude Figure 1. (a)
Map of the stars on the Bo¨otes I region. Stars with radial ve-locity measurements and identified as members, from Martin et al. (2007)are shown as filled red triangles. Koposov et al.’s (2011) sample is shown asopen blue circles, and the stars having radial velocities consistent with thedSph are indicated as filled blue circles (74). In addition, the stars with ve-locities < V r < km/s are encircled by an outer blue ring (55), andthose with a greater dispersion (19), but within the range < V r < km/s are the filled blue squares. The stars with high resolution spectroscopydiscussed by Norris et al. (2009, 2010a,b) and Feltzing et al. (2009) arenumbered as Boo-1137 and Boo-127 as open red stars. The 7 RGB starsstudied by Gilmore et al. (2013b) are indicated by red 5-point-line stars.The small red open circles are the 165 stars from HWB, and show the . × . square-arcminute, APO SPIcam FOV. We also re-observed theoutlying RGB stars in vbyCT T ( RI ) . (b) Finding chart for HWB’s dataon a × pixel scale. The black filled circles are proportional to T -magnitudes, and the open circles around them signify stars statisticallylikely to be Boo I members from color-comparisons. (c) The central fieldco-added image of the same field as (b), with the RGB stars from HWB andthis paper identified. diagrams (CMDs) or colour-colour plots (Belokurov et al. 2006b;Hughes, Wallerstein & Bossi 2008, hereafter, HWB).Koposov et al. (2011) used an “enhanced” data reduction tech-nique to achieve velocity errors of better than 1 km/s with the fiber-fed VLT/FLAMES+GIRAFFE system, around the
CaII -triplet(hereafter CaT, 8498, 8542, and 8662 ˚A). Koposov et al.’s (2011)interpretation of their data prefers a two-component velocity distri-bution for Bo¨otes I, with 98% confidence. We plot the finding chartfor this survey, our photometric data and Martin et al.’s (2007) sur-vey in Figure 1. Koposov et al. (2011) state that it is less likely thatthere is a one-component Gaussian with a velocity dispersion of . +0 . − . km/s. About 70% of the stars in their data set have a veloc-ity dispersion of . +0 . − . km/s (the “colder” population) and a “hot-ter” population with a velocity dispersion of km/s. They give analternative explanation that Bo¨otes I could have a one componentvelocity distribution, but that the stars’ velocities are not distributedisotropically; we agree with Koposov et al. (2011) that this modelis hard to test without full spatial coverage. From Figure 1, it isclear that a much deeper survey needs to be made of the whole re-gion out to at least 3 half-light radii, as Koposov et al. (2011) assert, c (cid:13) , 000–000 hotometric Metallicities but that there is likely to be a very low density of “halo” objects be-longing to Bo¨otes I. The multiple short exposures around CaT, usedfor the Koposov et al. (2011) study, can’t resolve metallicities be-low [ F e/H ] ∼ − . . High-resolution spectroscopy of these starsrequire about 15 hours observation each with VLT FLAMES andGIRAFFE and FLAMES (Gilmore et al. 2013a,b).If we have any hope of mapping the full extent of Bo¨otes I andexamining the more distant systems which are likely to be found inthe future, we need a more efficient method to identify age andmetallicity spreads in sparsely populated systems, before selectingstars for spectroscopy. Martin et al. (2007) found only 30/96 starsidentified as having the appropriate SDSS colors had Bo¨otes I’s ra-dial velocity. SDSS ugriz -filters were not designed for this task.In this paper, we are using the relatively well-studied Bo¨otes I tofind an efficient photometric method of locating dSph-members andsolving for age and metallicity, with at least the . dex accuracyin [ F e/H ] given by the CaT spectra. Simply stated, our problemin studying the stellar populations in the dSphs/ultra-faint dwarfs(UFDs), is that some have few or no upper-red-giant branch stars.Without these bright stars, we require exposure-times of manythousands of seconds to achieve acceptable S/N, when observing inblue or UV filters. If we want to survey these objects spectroscop-ically, we should have an efficient way of identifying interestingstars by color, over and above the SDSS photometry. Traditionalgravity-sensitive and metallicity-sensitive colours and indices in-volve the use of filters which become impractical with red, faintstars on the subgiant branch (SGB). Which blue filter is best forbalancing metallicity sensitivity with achievable S/N? Our methodfor comparing spectroscopic and photometric metallicity measure-ments is set out in §
2, with the observations described in §
3. Thedetailed analysis is given in § § How do we characterize the stellar populations of a system withsimilar properties to Bo¨otes I?
Studies show (Willman 2010, andreferences therein) that the majority of these dSph and UFDs havevery few red-giant branch (RGB) stars, which are normally the onlystars bright enough for high-resolution spectroscopy.
We considered using some combination of the Washington,Str¨omgren, and SDSS filters, which are available at most obser-vatories (see Figure 2). We began this project in 2007, imagingseveral of the dwarf galaxies using the Washington CT T -filters(using R & I instead of T and T to reduce observing time; see § vby -filters. All the ob-servations used for the analysis in this paper are given in Table 1,and discussed in detail in § [ F e/H ] came from earlyspectroscopy (Martin et al. 2007), from our Washington observa-tions (HWB), and higher resolution spectroscopy by Norris et al.(2008, 2010a,b); Lai et al. (2011); Gilmore et al. (2013b).The Washington system was used to define theGeisler & Sarajedini (1999, hereafter, GS99) standard giantbranches. GS99 show that compared to Da Costa & Armandroff (1990), using the broad-band V - & I -filters, they can obtainthree times the precision in metallicity determinations, at about amagnitude below the tip of the RGB, at around M T = − . Martin et al. (2007) and HWB found evidence of metallicityspread in Bo¨otes I, which has been confirmed by higher resolu-tion spectroscopy (Norris et al. 2008; Ivans 2013 in preparation;Gilmore et al. 2013a,b). HWB’s estimate of the spread in [ F e/H ] for Bo¨otes I was calibrated to GS99’s standard giant branches,and is therefore tied to the metallicity-scale of globular clustersused in that paper. Siegel (2006) notes that Boo I’s stellar pop-ulation is similar to that of M92 HWB, and we note that M92and M15 are regarded as the most metal poor globular clus-ters at [ F e/H ] ∼ − . . GS99 discuss the metallicity scalesof Zinn (1985); Zinn & West (1984); Carretta & Gratton (1997),and also define a “HDS” scale of their own, which takes the un-weighted means of available high-dispersion spectroscopy (mostlyfrom Rutledge, Hesser & Stetson’s (1997) study of calcium-tripletstrengths). In GS99, the most metal-poor globular cluster intheir study, M15, has [ F e/H ] = − . on the HDS scale, [ F e/H ] = − . on the Zinn & West (1984) scale, but -2.02on the Carretta & Gratton (1997) calibration. Within the uncertain-ties, this magnitude of disagreement alone could explain the differ-ence in mean [Fe/H] between the Washington photometry and theSDSS data (also see discussion in Hughes & Wallerstein 2011a).The Washington filters and the GS99 standard giant branches aregenerally designed to return the CaT-matched metallicity scale ofZinn (1985). GS99 derive nine calibrations based on M T andmetallicity, and let the user decide which is appropriate for theircluster/galaxy.The HWB-average value of [ F e/H ] = − . +0 . − . dex wasdetermined from the 7 brightest members of Bo¨otes I in their dataset (detected in the CRI filters), with the smallest photometric un-certainties. Hughes & Wallerstein (2011a) discuss a recent paperby Lai et al. (2011) on Bo¨otes I, which used low resolution spectra,the SDSS bands and other available filters to characterize the stars.Lai et al. (2011) determined [Fe/H], [C/Fe], and [ α /Fe] for eachtarget star, utilizing a new version of the SEGUE Stellar ParameterPipeline (SSPP; Lee et al. 2008a,b) named the n-SSPP (the methodfor non-SEGUE data). The Lai et al. (2011) study found the [Fe/H]-range to be about . − . dex, and a mean [ F e/H ] = − . (with an uncertainty of . dex in each measurement). HWB, usingWashington photometry alone, find [ F e/H ] = − . , and a range > . dex in the central regions. Martin et al. (2007) studied 30 ob-jects in Bo¨otes I and found the same mean value as HWB with thecalcium triplet (CaT) method. It is known that the CaT-calibrationmay skew to higher [Fe/H]-values at the lower-metallicity end, be-low [ F e/H ] ∼ − . (Kirby et al. 2008). Koposov et al. (2011)comment that the inner regions of Bo¨otes I do seem to be moremetal-rich at the . σ level, than the outer regions (Figure 1a),which our photometry does not cover. Koposov et al. (2011) ex-amined 16 stars from Norris et al. (2010a) and showed that pro-gressing radially outwards from the center of Figure 1a, the inner 8stars have a mean [ F e/H ] = − . ± . and the outer 8 have [ F e/H ] = − . ± . . which we normally quote as ± . dex, but the error bars combined withthe calibrations make the metallicity determination slightly asymmetric.c (cid:13) , 000–000 J. Hughes et al.
Frebel, Simon & Kirby (2011), have amassed a high-resolution spectroscopic study of the chemical composition ofseveral UFDs, and a recent paper by Kirby et al. (2012) discusseshow supernovae (SN) enrich/pollute the gas in low-mass dSphs.In the latter paper, they comment that SN in systems like Bo¨otesI would be more effective at enrichment, on an individual basis,than early massive stars were at enriching the MW’s halo becausethere was less gas to contaminate. In addition, Kirby et al. (2012)note that a star in a dSph with [ F e/H ] ∼ − . is sampling theprevious generation of massive stars with [ F e/H ] << − . . Thisis a particularly important point when we consider that Norris et al.(2010b) have found that Boo-1137 has [ F e/H ] = − . , and thisis discussed at length in Gilmore et al. (2013a,b). Hughes & Wallerstein (2011a, a summary of a conference presen-tation) discussed recent papers that explored the optimal colour-pairs to use for age and metallicity studies (e.g. Li & Han 2008;Holtzman et al. 2011). However, much of the rhetoric is theoreticaland involves testing on nearby, densely populated globular clusters.The search for practical colour-pairs also challenges the observerto use filters that can be employed on the same instrument, on thesame night (if possible), to minimize zero-point offsets and seeingdifferences.Ross et al. (2014) calibrated the Dartmouth isochrones forHubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) us-ing 5 globular clusters in the metallicity range − . < [ F e/H ] < +0 . . They found that clusters with known distances, reddeningand ages could have their metallicities determined to ∼ . dex(overall). Otherwise, non-pre-judged results on the globulars’ dom-inant metallicity showed the best colors to be: F W − F W (SDSS-u combined with Johnson-V) yields the cluster metallicityto ∼ . to . dex (high to low metallicity), F M − F W ( Ca II Cont. combined with Johnson-V) gives ∼ . to . dex,and F W − F W (Washington-C and Johnson-V) gives ∼ . to . dex. In this paper, we did not test F M , but ( C − y ) is equivalent to ( C − V ) . With the dSphs, the systems are not verywell-studied, and we require the best color for individual stars, notthe whole RGB.Calamida et al. (2012) have produced a metallicity calibrationfor dwarf stars based on the Str¨omgren m -index and near-infraredcolours, but their calibration works better for populations whichare more metal-rich than the UFDs. In this section, we comparethe various filter-combinations and note some pitfalls which maybe unique to UFD populations. Figure 2a shows the transmissioncurves for the filters given in Table 2 (Bessell 2005), taken fromthe CTIO website , with the ATLAS9 model flux density for astar with T eff = 4750 K , [ F e/H ] = − . , [ α/F e ] = +0 . , log g = 1 . .Overall, the best photometric system designed for separat-ing stars by metallicity is considered to be the intermediate-bandStr¨omgren photometry (Str¨omgren 1966). The distant RGB starsin the dSphs are very faint at Str¨omgren-u, and only the 8 bright-est proper-motion members are detected at SDSS-u (6 from HWBand the 2 extra RGB stars with high-resolution spectra, including Figure 2. (a)
Transmission curves for the filters given in Table 2, fromthe CTIO website. We also show the ATLAS9 model flux density for T eff = 4750 K , [ F e/H ] = − . , [ α/F e ] = +0 . , log g = 1 . .Str¨omgren filters (including u ) are shown as shaded black curves. Wash-ington filters are shown in shaded red, with the R − and I -filters as dashedred lines. SDSS filters are shown in blue. (b) Normalized flux plots forHE1523-0901 (black) and CS22892-052 (red), from 3800-4800 ˚A. We showthe filter transmission curves for C (red), v (black), b (black), and g (blue)filters; we note the major CN and CH features. The original resolution hasbeen smoothed to show the carbon-sensitive absorption. (c) The normalizedflux curves for HE1523-0901 (black) and CS22892-052 (red), from 4200-4400 ˚A, with major CN & CH spectral features marked.
Boo-1137). Without the u -band, we are unable to obtain the surfacegravity-sensitive, c -index, where c = ( u − v ) − ( v − b ) , (1)which measures the Balmer jump.The metallicity of the stars ( F e plus light elements) is sensi-tive to the m -index, where m = ( v − b ) − ( b − y ) . (2)The ( b − y ) -colour is a measure of the temperature and ( v − b ) is a measure of metallic line blanketing (see Figure2a). Many papers have mapped the Str¨omgren metallicity indexto [Fe/H] (e.g Hilker 2000; Calamida et al. 2007, 2009) and findthat calibrations fail for the RGB stars at ( b − y ) < . forall schemes. Faria et al. (2007) commented that the loci of metal-rich and metal-poor stars overlap on the lower-RGB, which theysay is likely due to the larger photometric errors. Although thisstatement is not false, it is not the only reason for the issue (Fig-ure 2). The m -index loses sensitivity as the difference in lineabsorption between b and v becomes equal to the difference in c (cid:13) , 000–000 hotometric Metallicities line absorption between b and y (Hughes & Wallerstein 2011a). Asstars become fainter lower down the RGB, the surface tempera-ture rises and the lines get weaker (also see: ¨Onehag et al. 2009;´Arnad´ottir, Feltzing & Lundstr¨om 2010, and references therin).The latter paper discusses the VandenBerg, Bergbusch & Dowler(2006) isochrones and the temperature-colour transformation byClem et al. (2004), and makes a point that their classificationscheme can only be used for giants with ( b − y ) > . .Also from Figure 2, we can see the advantages that the Wash-ington filters provide over the Str¨omgren and SDSS filters. Thebroad C -filter includes the metallicity-defining lines contained inthe narrower v -filter and part of the b -filter, and also surface-gravitysensitive Str¨omgren- u and SDSS- u . Thus, the colour ( C − T ) should be sensitive to T eff , [ F e/H ] , [ α/F e ] , and log g (GS99).The Str¨omgren filters are more effective than Washington bands ina system with a well-populated upper RGB, or if the stellar systemis close enough to have ∼ per cent photometry below the sub-giant branch (SGB), where the isochrones separate. As discussedin HWB, Geisler (1996) and Geisler, Claria & Minniti (1991), themore-commonly used broadband R − and I -filters can be convertedlinearly to Washington T and T , but with less observing timeneeded (also see the filter profiles in Figure 2a). The C -filter isbroader than the Johnson B -band, and is more sensitive to line-blanketing. Washington- C is a better filter choice than Johnson- B or Str¨omgren- v for determining metallicity in faint, distant galax-ies. Table 2 includes estimates for the total exposure times requiredto reach the main-sequence turn-off (MSTO) of dSphs with theWFPC3 on HST (also see Ross et al. 2014).Summarizing comments by Sneden et al. (2003), metallicityis usually synonymous with [Fe/H], but other elements may beinhomogeneously-variable in dSphs as well as the Milky Way’shalo. [ F e/H ] = log ( N F e /N H ) ∗ − log ( N F e /N H ) ⊙ . (3)The metallicity is normally taken to be: Z = Z (0 . f α + 0 . , (4)where f α ≡ [ α/F e ] , the α -enhancement factor, and Z is the“heavy element abundance by mass for the solar mixture with thesame [ F e/H ] ” (Kim et al. 2002).In Figure 2b and 2c, we use 2 metal-poor RGB stars to illus-trate the sensitivity of the Str¨omgren, Washington and SDSS filtersto carbon-enhancement. HE 1523-0901 (black line: Frebel et al.2007) is a r-process-enhanced metal-poor star with [ F e/H ] ≈− . , [ C/F e ] = − . , log T eff = 4650 K , and log g = 1 . . CS22892-052 (red line) is also an r-process rich object (Sneden et al.2003, 2009; Cowan et al. 2011) with [ F e/H ] ≈ − . , [ C/F e ] ≈ . , log T eff = 4800 K , log g = 1 . , and [ α/F e ] ≈ +0 . .The change in the CH-caused G-band is apparent in Figure 2c, andCN/CH features affect the C (in particular), v − , and b -filters, butthe SDSS g -band is relatively clear of contamination, but g is notvery sensitive to metallicity either. The spectra shown in Figure 2were provided by Anna Frebel (private communication).Carretta et al. (2011) reports a study of globular cluster starswith CN/CH variations. They discuss other ways to constructStr¨omgren-indices, finding a filter combination that will sepa-rate the first and second generations of globular cluster stars.Carretta et al. (2011) settled on c y = c − ( b − y ) (5) δ = ( u − v ) − ( b − y ) , (6) with c y being defined by Yong et al. (2008), and is an index whichis sensitive to gravity and N . Both of these indices have lim-ited use in our study, since they require high precision photome-try at the Str¨omgren- u − and v − bands. Carretta et al. (2011) pointout that m and c y have a “complicated,” degenerate dependenceon metallicity (involving [ F e/H ] and N ), and show that δ ismuch more effective at estimating the N − abundance, and remains CNO -sensitive over a much broader range of stellar temperatures,metallicities and surface gravities, since the temperature depen-dence is weak. Carretta et al. (2011) are more concerned with sep-arating the N-poor, Na-poor, O-rich first generation globular popu-lation, from the N-rich, Na-rich, O-poor, second generation stars (ifpresent). We note that there is a particular problem which involvesthe carbon-rich stars in the dSphs, because their colours alwaysmake a metal-poor star mimic those of a much more metal-richobject.
As in HWB, we observed the same central field (see Table 1) inBo¨otes I ( RA = 14 h m s , Dec = 14 . ◦ J2000) with theApache Point Observatory’s 3.5-m telescope, using the direct imag-ing SPIcam system. The detector is a backside-illuminated SITeTK2048E × pixel CCD with 24 micron pixels, whichwe binned ( × ), giving a plate scale of 0.28 arc seconds perpixel, and a field of view (FOV) of . × . square arcminutes.The HWB data set for Bo¨otes I was taken on 2007 March 19 (witha comparison field in M92 taken on 2007 May 24). We took 21frames in Washington C, and Cousins R and I filters, with exposuretime ranging from 1 seconds to 1000 seconds. The readout noisewas 5.7e- with a gain of 3.4 e-/ADU. The images were flat-fieldedusing dome or night-sky flats, along with with a sequence of zeros.We then processed the frames using the image-processing softwarein IRAF. The vby -observations used in this paper are detailed in Ta-ble 1, along with the Washington filter data from HWB (whenthe seeing, and most airmass-values, were noticeably better). TheStr¨omgren data was taken on 2009 January 17-18, 2009 May 1, and2011 April 5. The January 2009 data used the × in Str¨omgrenfilter set, which had vignetted the images. The 3-inch square uvby filters arrived from the manufacturer (Custom Scientific, Inc., ofPheonix, AZ) after the January 2009 observing run. We comparedthe Bo¨otes I stars observed in January and May 2009 and found thatthere was no appreciable difference in the instrumental magnitudesat the same airmass. The photometric quality of the January datawas better than the May data, but the January 2009 images weretaken with the smaller filters. After some questions about recordedexposure times in the image headers were resolved, more frameswere taken in April, 2011, to ensure stability of the zero-points. Wealso took some additional images in June, 2012 in C and R , but theseeing was never better than . ′′ so they are not included. The fi-nal weighted mean-magnitude program rejected the latter observa-tions because of poor image quality compared to the earlier frames.In addition to the Bo¨otes I central field chosen in 2007, we also IRAF is distributed by the National Optical Astronomy Observatory,which is operated by the Association of Universities for Research in As-tronomy (AURA) under cooperative agreement with the National ScienceFoundation.c (cid:13) , 000–000
J. Hughes et al. observed two RGB stars, in separate fields, which had high resolu-tion spectra in the literature: Boo-1137 and Boo-127 (Norris et al.2010a,b; Frebel, Kirby & Simon 2010; Feltzing et al. 2009).Table 1 lists the data taken at APO. The images taken on 2007March 19 had sub-arcsecond seeing, and enabled us to make thebest possible master source list for DAOPHOT. For conversion tothe standard Washington system, we used the Geisler (1996) Wash-ington standard frames, containing at least 5 stars in each frame, forat least 30 standards per half-night (the APO 3.5-m is scheduled inthat manner). For the Str¨omgren data, this was more of an issue,since the Str¨omgren system was calibrated with single stars. To re-duce observing overheads, we used M92 as a cluster standard. Weused the M92 fiducial lines to assist in matching the APO data tothe standard system. To supplement the HWB Washington data, wetook C and R images of the Bo¨otes I central field in 2009 (not I ), tomake sure that there was no calibration issue with the earlier data.No problems were detected.Employing the same data reduction method as HWB, we usedtwo iterations of (DAOPHOT-PHOT-ALLSTAR), with the first it-eration having a detection threshold of 4 σ , and the second pass hada 5 σ detection limit. We used ∼ stars in each frame to constructthe point spread functions (PSFs), and assume that it do not varyover the chip. The chip had been found to be very stable and therehas been no evidence that the PSF varies over the image. ALLSTAR(Stetson 1987) was further constrained to only detect objects with aCHI-value < . , and almost all sources had CHI (the DAOPHOTgoodness-of-fit statistic) between 0.5 and 1.5 (to remove cosmicrays and non-stellar, extended objects). We found the aperture cor-rection between the small (4 pixel) aperture used by ALLSTAR inthe Bo¨otes I field, and the larger (10-15 pixel) aperture used forthe standards, by using the best point spread function (PSF) starsin each images. We used the IMMATCH task to match the sources ineach image, making several datasets in each filter combination. We then puttogether the final source list as follows: requiring that each star be detectedin at east one image in each filter, and the final magnitude and colours werecalculated as the weighted (airmass, FWHM, DAOPHOT uncertainty) meanof each individual detection.We later tested the final photometry using the standalone version ofALLFRAME (Stetson 1994), and found that the results were consistentwith our method. When we used DAOPHOT III/ALLFRAME, this methodproduced almost identical results to those obtained by manually shiftingall the images to the same positions, median-filtering them all and pro-ducing a source list from that. When we used that master-list to feed intothe IRAF version of ALLSTAR, it produced 166 total detections seen at vbyCT T ( RI ) , but the v-band data is noticeably noisier, as expected.Compared to the HWB list, 117 objects were detected, and we use thisgroup of objects in the comparison to M92. We find that there are 34 ob-jects having a v -band uncertainty less than 0.10 dex, which were detectedin multiple frames in each band (on more than one night), and had a loweroverall standard-deviation-of-the-mean uncertainty; these objects are listedin Table 3. However, we plot the full-dataset in Figure 3, to show the uncer-tainty in magnitudes and colors, for comparison with models in § T and V ( y ) . This is the bestmeasure of how well DAOPHOT is working, and it is correlated with air-mass and seeing. The images are not crowded, we have a factor of 10 fewerobjets than we would detect in M92. With the artificial star experiments,the completeness of the data set is controlled by the v -band magnitude. Theonly completeness issue involves the 2 bright foreground stars seen in Fig-ure 1c, but the source density is too low for many objects to be missed. Atthis point, we are not constructing luminosity functions below the MSTO,so completeness is less of a concern than the photometric uncertainties foreach star. Using M92 as a cluster standard, we reduced the frames usingIRAF’s DAOPHOT, with 20-30 stars to fit the PSF. We then selected starson the outer parts of the globular cluster for testing; our photometry yielded matches to the standard system used for ∼ randomly selected stars incommon with the Frank Grundahl M92’s data set (private communication,F. Grundahl; Grundahl et al. 2000) of σ rms = 0 . in V ( y ) , σ rms =0 . in ( b − y ) , and σ rms = 0 . in m . Our confirmation framesfrom 2011 were only deep enough to detect the bright RGB stars in Bo¨otesI, so those stars have more observations and hence lower uncertainties in vbyCT . In Figure 4, we show colour-magnitude diagrams used for cali-bration of Boo I to M92 (cyan points: Grundahl et al. 2000). The dark blueline is the Dartmouth isochrone (Dotter et al. 2008) which fits well with arecent study by di Cecco et al. (2010), DM = 14 . , [ F e/H ] = − . , [ α/F e ] = 0 . and Y = 0 . , and Age = 11 ± . Gyr. Bo¨otes I is takento have E ( B − V ) = 0 . and DM = 19 . , as used in HWB.We solved for each filter, rather than the Str¨omgren indices, for eachnight. The transformation equations on 2009 May 1 are as follows: V = y i − . − . b i − y i ) − . X, σ rms = 0 . (7) b = b i − .
217 + 0 . b i − y i ) + 0 . X, σ rms = 0 . (8) v = v i − . − . v i − b i ) − . X, σ rms = 0 . (9)Here, X denotes the effective airmass and the subscript i indicates the instru-mental magnitude. The σ rms values are the comparison with the standards.HWB’s photometry from 2007 March 19 yielded matches to the GS99standard system of σ rms = 0 . in T , σ rms = 0 . in ( C − T ) ,and σ rms = 0 . in ( T − T ) . In T , the average uncertainties in thefinal CMD were σ rms = 0 . at the level of the horizontal branch, and σ rms = 0 . at the MSTO. The transformation equations are as follows: T = R i − .
461 + 0 . C i − R i ) − . X, σ rms = 0 . (10) ( C − T ) = 1 . C i − R i ) − . − . X, σ rms = 0 . (11) ( T − T ) = 1 . R i − I i ) + 0 . − . X, σ rms = 0 . (12)As before, X denotes the airmass and the subscript i indicates the instru-mental magnitude.The final calculated uncertainties for each individual star in eachimage were found by taking the uncertainties from photon statistics,DAOPHOT’s uncertainties, the aperture corrections, and the standard pho-tometric errors in quadrature. We then took the weighted means of multipleobservations, which reduced uncertainties internal to the data set. Thus, weachieved better uncertainties in for each star by taking the weighted means,with the weighting being dependent on the DAOPHOT uncertainties andthe airmass, which was found to be equivalent to the seeing. We constructedimage sets comparing short and long exposures, keeping to similar airmassand seeing between frames, to achieve multiple, independent observationsof each star and improved the final (standard-deviation-of-the-mean) uncer-tainty for the objects above T ∼ mag. We were able to detect 166objects in the field in the vbyCT T ( RI ) -filters. A finding chart for theobjects in Table 3 (117 objects) is given in HWB, and is shown in Figure 1band 1c here. Also, from Table 3, the 19 brightest stars were detected in theSDSS survey , and we include them in Table 4.An independent, external test on how well we have calibrated the datais discussed in § The process used by HWB to remove non-dSph stars from our final dataset was modified from that used on the globular clusters, NGC 6388 and ω Cen (Hughes et al. 2007; Hughes & Wallerstein 2000, respectively). Dueto observing-time constraints, we did not observe an off-galaxy field, but in-stead generated artificial field stars with the TRILEGAL code (Girardi et al.2005), calibrated for the SPIcam FOV and the appropriate magnitude lim-its. Briefly, we can statistically compare CMD of the off-galaxy region (orthe simulated field) to the Bo¨otes I field. The method was adapted from (cid:13) , 000–000 hotometric Metallicities Table 1.
APO 3.5-m CCD Frames taken in 2007-2011Field UT Filter τ ( s ) Airmass FWHM( ′′ ) Boo-127 09-01-18 y 300 1.19 1.0Boo-127 09-01-18 b 600 1.17 1.8Boo-127 09-01-18 v 1200 1.14 1.6Boo-1137 09-01-18 y 300 1.10 1.0Boo-1137 09-01-18 b 600 1.09 1.3Boo-1137 09-01-18 v 1200 1.08 0.9Boo Ic C -magnitudes (HWB) within max (2.0, 0.2)mag. of the C and C − T colours of the supposed dwarf-population starsin the CMD. We call this number N on . Now, we also count the number ofc (cid:13) , 000–000 J. Hughes et al.
Table 2.
Filters ConsideredFilter λ ( ˚A) ∆ λ ( ˚A) System HST/WFC3 τ ( s ) u 3520 314 Str¨omgren F390M 18,980v 4100 170 Str¨omgren F410M 10,214b 4688 185 Str¨omgren F461M 5318y 5480 226 Str¨omgren F547M 1,494C 3980 1100 Washington F390W 2,612 T R C F625W 605 T I C F775W 390 R R C F625W 605 I I C F775W 390u 3596 570 SDSS F336W 6,336g 4639 1280 SDSS F475W 835r 6122 1150 SDSS F625W 605i 7439 1230 SDSS F775W 988(1) Filter data from Bessell (2005).(2) HST/WFC3 filter best equivalent to ground-based choice.(3) Estimated exposure time for a G2V star at V ∼ mag. at the distanceof Bo¨otes I for S/N = 50 .field stars, in the off-dwarf image or image sub-section (or simulated field),that fall within the same ranges in the CMD, and call this number N off .We calculate the probability that the star in the on-dwarf field CMD isa member of the dwarf galaxy population as: p ≈ − min αN UL off N LL on , . ! (13)Where α is the ratio of the area of the dSph galaxy region to the areaof the (simulated) field region and N UL off ≈ ( N off + 1) " − N off + 1) + 1 . p N off + 1 (14)The equations are taken from the Appendix of Hughes & Wallerstein(2000), and corresponding to eq. [2] of Mighell, Sarajedini & French(1998) and eq. [9] of Gehrels (1986). Here, eq.[14] is the estimated upper(84 per cent ) confidence limit of N off , using Gaussian statistics. N LL on ≈ N on × (cid:20) − N on − . √ N on + 0 . N − . on (cid:21) (15)Then, eq.[15] is then the lower 95 per cent confidence limit for N on (eq. [3] of Mighell, Sarajedini & French (1998), and eq. [14] of Gehrels(1986)). For a large, relatively nearby cluster like ω Cen, we assumed thatthe whole on-cluster field is part of the system (a fairly safe assumption), sothat α is assumed to be 1, in that case. Here, we generated a population ofMWG stars with the TRILEGAL code for the same sky area as the SPIcamFOV, so that α = 1 for Bo¨otes I, also. Then, in order to estimate if anyparticular star is a cluster/dwarf member, we generate a uniform randomnumber, < p ′ < , and if (eq.[13]’s) p > p ′ , we accept the star as amember of the cluster or dwarf galaxy. This method works best if there isa colour/metallicity difference between the foreground and Bo¨otes I dwarfpopulations, which means it is less effective at removing field stars if weuse the SDSS-filters.Figure 3a–c shows the final photometric uncertainties from the Wash-ington filter data. We re-reduced the data, and made a median-filtered im-ages for each vbyCT T ( RI ) -filter, shifted the images, and made a masterlist of objected detected in a summed master-median-filtered image. Theopen circles are the 166 objects detected in all the median-filters images.Figure 3d–f shows the uncertainty distribution for the 166 detections in the vby -filters as open circles. The Washington-filter images had fainter mag-nitude limits than the Str¨omgren images, so we continue to use the statis-tical cleaning results from HWB, but we can use the Str¨omgren indices toestimate photometric metallicities and compare with the statistical results.Observing time in the v-filter is controlling our limiting magnitude. We Figure 3.
Uncertainty vs. magnitude plots for the Boo I data sets,from HWB and this paper. Open circles are 166 stars with CT T -measurements. These are the DAOPHOT uncertainties from the master-median-filtered images in each of the 6 filters. (a) Uncertainty in T vs. T . (b) Uncertainty in ( C − T ) vs. T . (c) Uncertainty in ( T − T ) vs. T . (d) Uncertainty in V y vs. V y , which is Johnson- V calculated fromStr¨omgren- y . (e) Uncertainty in ( b − y ) vs. V y . (f) Uncertainty in m vs. V y .compared the 166 objects detected in the median-filtered images in all 6bands, compared them with the 165 objects from HWB, and 117 objectspassed the DAOPHOT CHI-value < . in the v -band, and we merged thetwo lists. Table 3 contains the 34 objects which were observed on more thanone night in all filters and had uncertainties < . in the v -band. The anal-ysis from this point onwards requires that all objects have at least vbyCT -magnitudes. c (cid:13) , 000–000 hotometric Metallicities Table 3.
Objects in Bo¨otes I with Washington & Str¨omgren PhotometryID X R Y R RA DEC Class T ( C − T ) ( T − T ) V ( b − y ) m Boo-1137 − − − − ID from HWB, proper motion-confirmed members listed first.(2) Positions from the Figure 1b.(3) HWB’s object classes:A - If sources passed the statistical cleaning process, had the correct colours and had photometry in all filters with uncertainties less than 0.05.B - Objects passed the cleaning program, but had uncertainties in all filters not less than 0.05.C - Passed the statistical cleaning process, had the correct colours and A-type good photometry, but failed the comparison with the randomly generatedprobability.D - Objects failed the statistical cleaning process (also had the right colours but poor photometry).E - Passed statistical cleaning but failed colour selection (according to HWB).F - These objects failed both statistical cleaning and colour selection, and tended to be well outside the CMD area of a metal-poor dwarf. Usually brightforeground stars. Following on from the discussion in §
2, several authors have generated pho-tometric calibrations on the Str¨omgren [Fe/H]-scale, amongst them, Hilker(2000) and Calamida et al. (2007). In this section, we select several calibra-tions from those papers, where m is the dereddened m -index and [ m ] isthe reddening-free version: Hilker (2000) :[
F e/H ] Hil = m − . b − y ) + 0 . . b − y ) − . . (16) Calamida et al. (2007) :[
F e/H ] m = m + 0 . − . v − y ) . v − y ) − . . (17) Calamida et al. (2007) :[
F e/H ] [ m ] = [ m ] + 0 . − . v − y ) . v − y ) − . . (18)These methods of calculating photometric metallicities are used forcolumns 2–4 of Table 5.In Figure 5a and 5b, we show colour-colour plots and [Fe/H]-calibrations for M92 (cyan points). The blue points are the M92 RGB starsabove the horizontal branch (HB). Having the same type of cool, metal-poor RGB as the expected dSph population, these plots illustrate the loss ofmetallicity resolution on the lower-RGB in the Str¨omgren system. We usedthe TRILEGAL code to generate a field of artificial stars at the correctgalactic latitude, for the same magnitude limits as our dSph field. Figure5c and 5d show our Bo¨otes I data from Table 3 (black points with error http://stev.oapd.inaf.it/cgi-bin/trilegal (Vanhollebeke, Groenewegen & Girardi2009)c (cid:13) , 000–000 J. Hughes et al.
Figure 4. (a) M V vs. ( b − y ) Str¨omgren CMD for M92 (cyan points;data provided by F. Grundahl), Boo I Str¨omgren data only (black points),Str¨omgren and Washington objects (black filled circles), and proper-motionmembers with Str¨omgren, Washington and SDSS magnitudes (red filledtriangles). The dark blue line is the Dartmouth isochrone correspondingto [ F e/H ] = − . , [ α/F e ] = 0 . and an age of 11 Gyr. M92 has E ( B − V ) = 0 . and DM = 14 . . Boo I has E ( B − V ) = 0 . and DM = 19 . . (b) M V vs. m , the Str¨omgren CMD for M92(cyan points), Boo I Str¨omgren data only (black points), Str¨omgren andWashington objects (black filled circles), and proper-motion members withStr¨omgren, Washington and SDSS magnitudes (red filled triangles). Thedark blue line is the Dartmouth isochrone corresponding to [ F e/H ] = − . , [ α/F e ] = +0 . , and an age of 11.0 Gyr.bars) and the TRILEGAL-generated artificial stars (blue circles). The redtriangles are the bright RGB stars with SDSS-colours. The Str¨omgren fil-ters are well-suited to separate the dSph population from the foregroundstars. We note that the TRILEGAL artificial stars have the same colors asthe foreground RGB stars, and are separate from the upper-RGB proper-motion members Figure 5c and 5d; all data points overlap for stars whichlikely have log g > . , which is not a function of photometric uncertainty,it is the Str¨omgren bands losing sensitivity to metallicity. We confirm thatthe Str¨omgren indices are only useful for upper RGB stars from these plotsalone.We use the usual Str¨omgren relationships: E ( b − y ) = 0 . E ( B − V ); (19) E ( v − y ) = 1 . E ( B − V ); (20) E ( m ) = − . E ( b − y ); (21) [ m ] = m + 0 . b − y ) . (22)The reddening-free metallicity index is [ m ] , as used by Calamida et al.(2007); the reddening law is taken from Cardelli, Clayton & Mathis (1989)and Crawford (1975).Calamida et al. (2007) generated several versions of the Str¨omgren- [ F e/H ] calibration, which we tested with our Table 3 data; their cal-ibration equations that best fit our data are given in equations [17] & Figure 5. (a)
Plot of m = ( v − b ) − ( b − y ) vs. ( b − y ) for M92 RGBstars (blue points, F.Grundahl, private communication), and the rest of theglobular cluster’s stars (cyan). The calibration lines of constant [Fe/H] aretaken from Hilker (2000). (b) For the same M92 sample, we show [ m ] = m +0 . b − y ) , the reddening-free index, plotted against ( v − y ) . Calibra-tion from Calamida et al. (2007). (c) m = ( v − b ) − ( b − y ) vs. ( b − y ) for our sample (from the median filtered images), with the Hilker (2000)calibration. In total, 117 objects were detected in vby filters, shown as blackpoints. The TRILEGAL code was used to generate a sample of foregroundstars, shown as blue filled circles. The RGB proper-motion members areshown as red triangles. (d) [ m ] = m + 0 . b − y ) vs. ( v − y ) for thesame sample of Bo¨otes I stars, with the Calamida et al. (2007) calibration.[18]. These calibrations were chosen because they best matched the spec-troscopy available in 2010 (Feltzing et al. 2009; Norris et al. 2008; Ivans2009; Martin et al. 2007). The Calamida et al. (2007) equations are basedon “semiempirical” calibrations of Clem et al. (2004), and have differencesbetween the [ F e/H ] phot and [ F e/H ] spec values of − . ± . dexand − . ± . dex, respectively.When Calamida et al. (2007) tested the Hilker (2000) calibration on73 field RGB stars, the difference between the schemes was found to be . ± . dex. Hughes et al. (2004) used the Hilker (2000) calibration fortheir study of ω Cen, which Calamida et al. (2009) found to be in agreementwith their work. For stellar populations in dSph galaxies, it is impracticalto use any calibration involving the u -band, both because the RGB and MSstars are too faint in the near-UV, but Str¨omgren- u is more sensitive to red-dening than v or C . In practice, half of all observing time would have to bededicated to u -band imaging, to have a chance of obtaining c -indices, sowe do not consider these here. Figure 5a shows an interesting characteristicof the Hilker (2000) calibration, in that the RGB (dark blue points) of M92is skewed with respect to the semi-empirical lines of constant [ F e/H ] , andthe tip of the RGB would appear more metal poor than the lower part ofthe RGB. Figure 5b confirms that Calamida et al. (2007)’s [ m ] vs. ( v − y ) calibration fits well with M92 having [ F e/H ] ≈ − . . When we apply thecalibrations to our data in Table 5, this skewing is observed (comparing col-umn 2 to columns 3 & 4). Again, we notice that the fainter RGB stars havelarge uncertainties, resulting from the loss of sensitivity of the m -indexand the increasing photometric uncertainties, particularly at Str¨omgren- v .c (cid:13) , 000–000 hotometric Metallicities For the Washington filters, we use: E ( C − T ) = 1 . E ( B − V ); (23) E ( T − T ) = 0 . E ( B − V ); (24) M T = T + 0 . E ( B − V ) − ( m − M ) V ; (25)from Geisler, Claria & Minniti (1991) and GS99. HWB used equations(23)–(25) and the GS99 standard giant branches to find the [ F e/H ] -valuesfor the Bo¨otes I RGB stars. Note that GS99 use A V = 3 . E ( B − V ) ;not setting R V = 3 . does not transform into an appreciable difference forBo¨otes I, as E ( B − V ) = 0 . .In Table 6, we show the preliminary results fromHughes & Wallerstein (2011b), where the stellar parameters were es-timated from χ fits to the [ α/F e ] = 0 . to +0 . Dartmouth isochrones(Dotter et al. 2008). We found that the best fits gave [ α/F e ] = +0 . ± . dex. The early results presented in Hughes & Wallerstein’s (2011b)conference paper were consistent with the Martin et al. (2007), CaT-basedspectroscopy, available at the time. However, the model grid was not fineenough for our goals, and we ran extensive, finer-grid models, based on theDartmouth isochrones.We expect that the dSph stars are α -enhanced in the same wayas the MWG halo population (see discussion in Cohen & Huang 2009;Norris et al. 2008, and our § ). We use both the α -enhanced andsolar-scaled models from the Dartmouth Stellar Evolution Database (Dotter et al. 2008; Chaboyer et al. 2001; Guenther et al. 1992) to comparewith our data. From Figure 6b, we see that ( C − T ) widens the separation of the giantbranches of different metallicities, giving a resolution for the GS99 RGBfiducial lines of ∼ . dex. One of us (GW) suggested the Washingtonsystem, which was developed by Canterna (1976); Geisler (1996) definedCCD standard fields for the system. In HWB, we found that Washingtonfilters spread out the stars at the MSTO, and we have found that ( C − T ) is more effective than the SDSS-colours ( g − r ) , as shown in Figure 6a.The SDSS photometry is not sensitive enough to this difference in coloursto distinguish Boo I’s level of metallicity spread. The subset of 19 objectswith ugriz magnitudes (Table 4) contains most of the bright objects fromHWB and this paper’s Str¨omgren data set. These are the objects which haveStr¨omgren and Washington colours falling in the appropriate ranges whichenable us to calculate the photometric values of [ F e/H ] . Table 3 containsforeground stars and Bo¨otes I members, and intersects with the spectro-scopic data set of Martin et al. (2007). We have radial velocities and inde-pendent metallicities for 8 of the objects in Table 3, and Str¨omgren andWashington [ F e/H ] phot -values for many of them. We added the 2 giantsoutside the central Bo¨otes I field, Boo-1137 and Boo-127, as additional cal-ibrators, because Boo-1137 (Norris et al. 2010b) is very metal poor, andboth have had a number of spectra taken (see Table 5).We considered the effect of replacing the g -filter with the muchbroader C -band (Hughes & Wallerstein 2011a). As we can see from Figure6b and 6c, the colour, ( C − r ) works well for the upper RGB ( log g < . )in Bo¨otes I, but that the lower-RGB stars ( . < log g < . ) are not well-separated in this colour. The reasons for this discrepancy are filter-width andtransmission, which are shown in Figure 2a and Table 2. While the Sloan r -filter has a greater overall transmission than the Washington T -filter, ithas become standard practice to substitute the broadband R -filter for T ,since it has ∆ λ R = 1580 ˚A, compared to ∆ λ T = 770 ˚A (Geisler 1996,also see Table 2).As with the Lai et al. (2011) method, there are merits in combiningall the available photometry, but we are searching for the minimum usefulnumber of filters that can break the age-metallicity degeneracy. In Figure 7,we compare the Str¨omgren and Washington filters, and construct two new http://stellar.dartmouth.edu/ ∼ models/ Figure 6.
CMDs and colour-colour plots using a mixture of SDSS andWashington filters to show the [Fe/H]-sensitivity (HWD). In all diagrams,the red triangles are the 8 RGB stars, known to be proper-motion mem-bers. All isochrones shown are solar-scaled and have an age of 12 Gyr. (a) M r vs. ( g − r ) with Dartmouth models, α -enhanced to +0.3. (b) M T vs. ( C − T ) with Dartmouth models, also α -enhanced to +0.3. (c) M r vs. ( C − r ) (d) ( r − i ) vs. ( g − r ) SDSS colour-colour plot,with the Dartmouth isochrones. (e)
Washington colours with GS99 standardgiant branches (HWB).indices: m ∗ = ( C − T ) − ( T − T ) (26)and m ∗∗ = ( C − b ) − ( b − y ) . (27)Our motivation in defining these indices is to avoid the collapse of themetallicity sensitivity of the m -index on the lower RGB, and to attempt toreplace the v -filter with the broader C -filter (also see Hughes & Wallerstein2011a). Figure 7h shows m ∗∗ vs. ( C − T ) , and allows us to use 4filters, CT by , which reduces observing time and keeps ∼ . dex [Fe/H]-resolution for stars with − . > [ F e/H ] > − . . Figure 7i shows thatwe could use Cby for metallicity estimates − . > [ F e/H ] > − . .These colour-colour plots are not sensitive to age on the RGB, recoveringage-resolution at the MSTO. However, reaching the MSTO with Cby ismuch faster than with vby (see Table 2). Figs.7a, b & c show that m maybe preferred for systems with − . > [ F e/H ] > − . , but we note that ( C − T ) would also be more useful there, with much shorter exposuretimes.c (cid:13) , 000–000 J. Hughes et al.
Table 4.
SDSS Magnitudes for Stars in Bo¨otes I Central FieldID SDSS u g r i z
ClassBoo-1137 19.77(03) 18.11(01) 17.37(01) 17.04(01) 16.86(01) Member Boo-127 20.01(05) 18.16(01) 17.37(01) 17.02(01) 16.85(01) Member HWB-3 20.10(05) 17.73(01) 16.28(01) 14.77(01) 13.98(01) FHWB-4 20.47(05) 18.00(01) 16.57(00) 15.65(01) 15.16(01) FHWB-6 23.37(74) 22.43(12) 20.96(04) 19.47(02) 18.76(04) EBoo-117/HWB-8 19.98(05) 18.21(01) 17.44(01) 17.10(01) 16.92(01) CBoo-119/HWB-9 20.21(04) 18.43(01) 17.69(01) 17.38(01) 17.21(01) AHWB-11 21.74(20) 19.49(01) 18.05(01) 17.23(01) 16.77(01) EHWB-15 24.46(13) 20.63(03) 19.22(01) 18.18(01) 17.63(02) EHWB-16 21.08(11) 19.70(02) 19.13(01) 18.87(01) 18.72(04) AHWB-18 22.48(36) 20.42(02) 19.54(02) 19.16(02) 19.01(05) EHWB-20 23.47(80) 20.90(03) 19.62(02) 19.03(02) 18.70(04) EHWB-21 24.50(67) 21.22(03) 19.86(02) 19.18(02) 18.77(03) EHWB-22 21.63(11) 20.35(02) 19.85(02) 19.63(02) 19.55(06) AHWB-23 24.11(61) 21.92(06) 20.31(02) 19.00(01) 18.24(02) EHWB-24 21.69(11) 20.74(02) 20.21(02) 20.02(03) 19.99(08) CHWB-26 25.01(12) 21.82(07) 20.59(03) 19.94(03) 19.64(08) EHWB-28 22.51(38) 21.04(04) 20.63(03) 20.42(04) 20.40(15) AHWB-29 22.24(29) 21.00(04) 20.69(03) 20.50(05) 20.27(13) AHWB-31 21.71(19) 21.27(05) 20.87(04) 20.77(06) 20.55(17) CHWB-34 22.67(43) 21.47(05) 21.00(05) 20.81(06) 20.44(15) A(1) Confirmed Boo I members outside central field.
Figure 7.
Colour-colour plots using a mixture of Str¨omgren and Washing-ton filters to show the [Fe/H]-sensitivity. In all plots, the red triangles are the8 RGB stars from proper-motion studies (Martin et al. 2007), and we showthe Dartmouth models in the range, − . > [ F e/H ] > − . . We define: m ∗ = ( C − T ) − ( T − T ) and m ∗∗ = ( C − b ) − ( b − y ) , withdereddened- m written as m = ( v − b ) − ( b − y ) . (a) m vs. ( b − y ) . (b) m vs. ( C − T ) . (c) m vs. ( C − y ) . (d) m ∗ vs. ( b − y ) . (e) m ∗ vs. ( C − T ) . (f) m ∗ vs. ( C − y ) . (g) m ∗∗ vs. ( b − y ) . (h) m ∗∗ vs. ( C − T ) . (i) m ∗∗ vs. ( C − y ) . When crossing the boundaries between photometric systems, we found itinstructive to construct SEDs for our sample, as a independent and exter-nal check on our photometry and to make sure all the magnitudes were ontheir standard systems (Bessell 2005). This process enabled us to comparethe Dartmouth models and the ATLAS9 synthetic stars to the real data, andunderstand better the constraints placed by the observational uncertaintiesand the relationship between each stars’ temperature and metallicity. Fig-ures 8–15 display SEDs for the 8 RGB proper-motion confirmed membersof Bo¨otes I shown with the best-fitting (employing a simple χ fit) AT-LAS9 model fluxes, appropriately scaled to pass through the majority ofthe photometry data points. If there is a wide discrepancy between the fitsto the ATLAS9 models in Washington, Str¨omgren, and SDSS filters, weshow 2 fits. The y-axes are always flux density, log( νF ν ), in ergs/s/cm, andthe x-axes are wavelength in microns. We used the conversions from mag-nitudes to fluxes from the HST ACS website. The Washington system andthe Str¨omgren data are VEGAmag and the SDSS system is ABmag, andwe determined that the 8 RGB stars had the fluxes transformed to the samescale for Washington, Str¨omgren, and SDSS magnitudes, without any fur-ther shifting, except for HWB-22, where the SDSS fluxes are consistentlyhigher. Since the Washington and Str¨omgren data appeared to be consistentwith the same T eff for HWB-22, we did not shift any of our zero-pointscales. As expected, our photometry uncertainties produce smaller errorbars than the SDSS data, and these stars also suffer from large uncertaintiesin SDSS-u. Where available, we include the JHK measurements.In all diagrams, the SDSS data is shown as open squares, theStr¨omgren measurements are shown as small filled triangles, Washingtonmagnitudes are the larger filled triangles, and 2MASS data (if available) isshown as open stars. The error bars are the σ uncertainties in the data. Ifthere was a Johnson-V observation, it is shown as an open circle. Boo-1137 (Figure 8) is the brightest object in this sample, and themost metal-poor, reported to be [ F e/H ] = − . , by Norris et al. (2010b),who obtained high-resolution spectroscopy of from VLT/UVES. This starwas not originally in our data set because it is 24 ′ from the center of thedSph. Norris et al. (2010b) pronounced it the most metal-poor giant ob-served (to-date) in one of the ultra-faint SDSS dSphs, and show that Boo-1137’s elemental abundances are similar to those seen in metal-poor Milky (cid:13) , 000–000 hotometric Metallicities Figure 8.
Spectral-energy distribution of Boo-1137 shown with the best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled. TheSDSS data is shown as open squares, the Str¨omgren measurements areshown as filled triangles, Washington magnitudes are the larger filled tri-angles, and 2MASS data is the open stars. The error bars are the σ uncer-tainties in the data. (a) SED for the range in wavelength, . µm < λ < . µm . (b) SED for the range in wavelength, . µm < λ < . µm .Way halo stars. Given the range in fits from Table 5, we show the ATLAS9model-range which fit the data best, i.e. very metal-poor, T eff = 4750 K , [ F e/H ] = − . , [ α/F e ] = +0 . , and log g = 1 . . Boo-127 (Figure 9) was found to have an unusual [Mg/Ca] abundanceratio, similar to the Hercules dSph (Feltzing et al. 2009). Feltzing et al.(2009) found [ F e/H ] = − . , while Norris et al. (2008) found [ F e/H ] = − . . From the spectroscopy in Table 5 and isochrone fits inTable 9, we find that [ F e/H ] = − . across all the filter-systems and thatthe best ATLAS9 fits are models, with T eff = 4750 K , [ F e/H ] = − . , [ α/F e ] = +0 . , and log g = 1 . . However, Norris et al. (2010a) later ob-tained UVES/FLAMES data for Boo-127, where they reported, [ F e/H ] = − . ; with a mean error of about 0.27 dex. Gilmore et al. (2013b) con-curs, so we can conclude that the spectroscopic [ F e/H ] -values are now inagreement. Boo-117/HWB-8 (Figure 10) has the most independent observations.Norris et al. (2008) measured [ F e/H ] = − . , using the calibration fromthe strength of the Ca II K line, and found [ Ca/F e ] ∼ . . This value wasmore metal-rich than the [ F e/H ] = − . noted by Martin et al. (2007),and is at least 0.4 dex more metal-rich than any of our other photometricestimates. Feltzing et al. (2009) reported a value of [ F e/H ] = − . forBoo-117 (HIRES; using the Fe lines, amongst others), that is more consis-tent with our Str¨omgren data. As discussed in Feltzing et al. (2009), evendifferent spectroscopic surveys can vary from . to . dex, so we shouldnot be surprised by this. We show the ATLAS9 models/interpolations, with T eff = 4625 K , [ F e/H ] = − . & [ α/F e ] = +0 . & log g = 1 . .We note that the bluer photometry points are more consistent with a slightly Figure 9.
Spectral-energy distribution of Boo-127 shown with the best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled. TheSDSS data is shown as open squares, the Str¨omgren measurements areshown as filled triangles, Washington magnitudes are the larger filled tri-angles, and 2MASS data is the open stars. The error bars are the σ un-certainties in the data. The Johnson- V observation is is shown as an opencircle. (a) SED for the range in wavelength, . µm < λ < . µm . (b) SED for the range in wavelength, . µm < λ < . µm .more metal-rich spectrum, but that all the fits are well-within the uncer-tainties stated in the spectroscopic studies. Also, Lai et al. (2011) derive [ F e/H ] = − . and [ C/F e ] = − . , from their low resolution spectra,SDSS and other filters with the n-SSPP code. Boo-119/HWB-9 (Figure 11) is a star we expected to have incon-sistent photometric estimates, since Martin et al. (2007, Boo-119) derived [ F e/H ] = − . , and the isochrone fits to each filter set range into themore metal-rich regime: [ F e/H ] = − . for the SDSS filters, The Wash-ington filters give [ F e/H ] = − . , and we find [ F e/H ] = − . from theStr¨omgren isochrones. We expected this discrepancy to be a characteristicof a CN- or carbon-rich star, and Lai et al. (2011) report [ F e/H ] = − . and [ C/F e ] = +2 . . The best-fit ATLAS9 models indicate an inter-polation in the range T eff = 4625 K − K , [ F e/H ] = − . to − . , [ α/F e ] = +0 . to +0 . , and log g = 1 . . The model with T eff = 4750 K and [ F e/H ] = − . , has the smallest residuals, and isconsistent with the CaT-measurement from Martin et al. (2007). We showthe range of models with T eff = 4600 − K , [ F e/H ] = − . to − . , [ α/F e ] = +0 . to +0 . , and log g = 1 . . HWB-22 (Figure 12) may be variable. There is no clear offset inthe photometry points between the different filter systems for any of theother RGB stars, but it does seem be the case here. Martin et al. (2007)give [ F e/H ] = − . , Lai et al. (2011) give [ F e/H ] = − . and [ C/F e ] < . , and our isochrone fits give [ F e/H ] = − . to − . . TheATLAS9 models indicate the best fit is: T eff = 5250 K , [ F e/H ] = − . , [ α/F e ] = +0 . , and log g = 2 . . The difference in photometry couldc (cid:13) , 000–000 J. Hughes et al.
Figure 10.
Spectral-energy distribution of Boo-117/HWB-8 shown withthe best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled.The SDSS data is shown as open squares, the Str¨omgren measurements areshown as filled triangles, Washington magnitudes are the larger filled trian-gles, and 2MASS data is the open stars. The error bars are the σ uncer-tainties in the data. The Johnson- V observation is shown as an open circle. (a) SED for the range in wavelength, . µm < λ < . µm . (b) SED forthe range in wavelength, . µm < λ < . µm .be caused by a temperature difference, but that the metallicity and surfacegravity measurements are all consistent with each other. We chose to showthe fit to the Str¨omgren and Washington colours. HWB-24 (Figure 13) The GS99 calibration gives − . ± . dex,and adds no further information. The GS99 standard RGB’s (and theDotter et al. 2008 models in Washington filters) become insensitive to verylow metallicities amongst the brighter RGB stars much more rapidly thanthe Str¨omgren calibrations. For Washington data on low-metallicity sys-tems, it is better to use the CMDs than the colour-colour plots, sincethe models separate better in luminosity and ( C − T ) than they do in ( T − T ) . At this level on the RGB, the Str¨omgren calibration starts tolose sensitivity. HWB-28 (Figure 14) fits the SDSS isochrones and the Lai et al.(2011) models both with [ F e/H ] > − . , but the Str¨omgren-fit gives [ F e/H ] = − . . The fit from the Washington filters gives [ F e/H ] = − . , closer to the Martin et al. (2007) estimate [ F e/H ] = − . from theCaT-method. From the ATLAS9 models, we can see the why the SDSSfilters can indicate a much more metal-poor model than the Str¨omgrenfilters and the C-band. Note that the g-band error bars encompass bothmodel SEDs, T eff = 5250 K − K , [ F e/H ] = − . and − . , [ α/F e ] = +0 . and +0 . , and log g = 3 . . This temperature rangemakes the dashed line fit the SDSS photometry with smaller residuals thanthe more metal-rich case. HWB-34 (Figure 15) has a consistent ATLAS9 model temperature,with T eff = 5375 K , and we show [ F e/H ] = − . and − . , Figure 11.
Spectral-energy distribution of Boo-119/HWB-9 shown withthe best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled.The SDSS data is shown as open squares, the Str¨omgren measurementsare shown as filled triangles, Washington magnitudes are the larger filledtriangles, and 2MASS data is the open stars. The error bars are the σ un-certainties in the data. (a) SED for the range in wavelength, . µm < λ < . µm . (b) SED for the range in wavelength, . µm < λ < . µm . [ α/F e ] = +0 . and +0 . , and log g = 3 . . Lai et al. (2011) fit [ F e/H ] = − . , Martin et al. (2007) find [ F e/H ] = − . . TheStr¨omgren system isochrones yield [ F e/H ] = − . and the CT T -photometry gives [ F e/H ] = − . . This star is at the exactly the right (orin this case, wrong) part of the temperature/metallicity distribution to makeit very difficult to discern where this star falls within [ F e/H ] = − . ± . dex, and the deciding factor would be the C - or v -magnitude. For the 8 Bo¨otes I radial-velocity-confirmed members (Table 5), thephotometric metallicities that were most discrepant were for the fainterobjects on the lower RGB, as we expected. However, Boo-119/HWB-9’s (Figure 11) discrepancies are likely due to carbon-enhancement. Wenow compare the spectroscopic metallicities to those found from dif-ferent filter sets and hybrid methods. Table 5 shows a clear offsetfrom the [Fe/H]-values from the spectroscopy-alone studies (Gilmore et al.2013b; Norris et al. 2010b; Feltzing et al. 2009; Martin et al. 2007;Hughes, Wallerstein & Bossi 2008), but that shift to lower [ F e/H ] was dis-cussed in §
2, and is partly to do with scaling changes over time and cali-bration of CaT-measurements. Apparently, no photometric system can copewith Boo-119’s carbon-iron abundance ratio, [ C/F e ] = +2 . , exceptfor Lai et al.’s (2011) modified n-SSPP method, which skews all [Fe/H]-estimates lower than any scale based on CaT alone (Koposov et al. (2011)notes that their scale is not calibrated below [ F e/H ] = − . )c (cid:13) , 000–000 hotometric Metallicities Figure 12.
Spectral-energy distribution of HWB-22 shown with the best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled. TheSDSS data is shown as open squares, the Str¨omgren measurements areshown as filled triangles, Washington magnitudes are the larger filled tri-angles. The error bars are the σ uncertainties in the data. (a) SED for therange in wavelength, . µm < λ < . µm . (b) SED for the range inwavelength, . µm < λ < . µm .Feltzing et al. (2009) discuss their spectroscopy of Bo¨otes I, in light ofwork by Koch et al. (2008) on the Hercules dSph. In these dark-matter dom-inated dSphs, the very low density of baryons should mean that the chemicalenrichment history is dominated by only a “few supernovae”, which meansthat the element abundances of the stellar population might show star-to-starchemical inhomogeneities, tracing individual SNe II events (Gilmore et al.2013a,b). In studying the Hercules system, Koch et al. (2008) estimate thatonly 10 SN were needed to give the “atypical abundance ratios” (andmore should have contributed). Bo¨otes I is less massive than Hercules, butFeltzing et al. (2009) only report one star, Boo-127, (and possibly Boo-094,also not observed here), has unusual variations in Mg and Ca. Expectingmore individuality, Feltzing et al. (2009) conclude that Bo¨otes I is surpris-ingly well-mixed. Norris et al. (2009) beg to differ, and they take issue withFeltzing et al.’s (2009) [ Mg/Ca ] value as being too high for one of theirseven Bo¨otes I stars, the aforementioned, Boo-127. We agree with Norris’sgroup, and also Gilmore et al. (2013b).Norris et al. (2009) obtained high-resolution spectroscopy of Boo-1137 from VLT/UVES (not included in HWB’s data set because it is ′ from the center of the dSph), pronouncing it the most metal-poor giant ob-served (to-date) in one of the ultra-faint SDSS dSphs, with [ F e/H ] = − . . Norris et al. (2009) find that Boo-1137’s elemental abundances aresimilar to those seen in metal-poor MWG halo stars. They also discussBo¨otes I’s SF history, surmising that it most likely underwent an early,short period of star formation, cleared by SN II which enriched it’s inter-stellar medium inhomogeneously. In Boo-1137, Norris et al. (2009) find α -enhancement (compared to Fe) of ∆[ α/F e ] ∼ . , “relative to the mean Figure 13.
Spectral-energy distribution of HWB-24 shown with the best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled. TheSDSS data is shown as open squares, the Str¨omgren measurements areshown as filled triangles, Washington magnitudes are the larger filled tri-angles. The error bars are the σ uncertainties in the data. (a) SED for therange in wavelength, . µm < λ < . µm . (b) SED for the range inwavelength, . µm < λ < . µm .of the metal-poor halo stars.” Even though the spectroscopy studies we havementioned have tried to cover as much of the Bo¨otes I dSph as possible (andBoo-1137 is almost two half-light radii from the center), all groups havecollected medium resolution spectra of less than 30 members, with high-resolution spectra of only a handful of stars. As Tolstoy, Hill & Tosi (2009)and Gilmore et al. (2013a) say, SNe Ia start to contribute to the chemicalcomposition − years after the first stars form. There is a widerange in [ F e/H ] , but not in the α -elements. So, if the massive stars inBo¨otes I cleared the interstellar medium quickly, star formation lasted lessthan 1 Gyr. Can we detect an age spread that small? What kind of metallicity or age spread would we expect to see inBo¨otes I?
Age estimates cannot usually be made for individual RGB stars,but the GS99 standard giant branches do have an age-metallicity degen-eracy, compared to the Dartmouth isochrones. Is the separation of RGBstars with Bo¨otes I’s range in chemical composition, large enough to dif-ferentiate between RGB-isochrones in any colour? Our normal practice isto use the RGB to find the metallicity and the MSTO to find ages, wherethe isochrones separate. Brown et al. (2012) and Kirby et al. (2012) studiedthe metallicity distributions and star formation histories (SFHs) of severaldSphs. Isochrone fits to these populations, as noted by Kirby, have to beperformed at the upper-RGB, the SGB and the MSTO, in order to breakthe age-metallicity degeneracy. In many dSphs, we do not have sufficientupper-RGB stars to make this fit (Willman 2010).To improve the resolution of our grid of Dartmouth isochrones, weran a simple closed-box chemical evolution mode. We used the Dartmouth(solar-scaled) isochrones to produce populations of stars with a similarc (cid:13) , 000–000 J. Hughes et al.
Table 5.
Metallicities of Possible Bo¨otes I StarsID [ F e/H ] Hil [ F e/H ] m [ F e/H ] m ] [ F e/H ] GS [ F e/H ] spec [ α/F e ] Gil [ F e/H ] Lai [ C/F e ] Lai
Boo-1137 − . . -2.4 -2.3 − . . -3.7 − -3.66 y 0.44 − − Boo-127 − . . -2.2 -2.2 − . . -1.49 − -2.01 y 0.18 − − Boo-117/HWB-8 − . . -1.9 -1.8 − . . -1.72 -2.2 -2.18 y 0.18 -2.3 -0.50Boo-119/HWB-9 − . . -1.7 -1.7 − . . − -2.7 -3.33 y 0.77 -3.8 +2.20HWB-16 − . . -2.2 -2.2 − . . − − − u − − − HWB-19 − . . -0.5 -0.6 − . . − − − n − − − HWB-22 − . . -2.3 -2.3 − . . − -2.0 − y − -2.9 < . HWB-24 − . . -2.0 -2.0 − . . − -1.9 − y − -2.3 +0.40HWB-28 − . . -1.6 -1.6 − . . − -1.5 − y − -2.5 +0.39HWB-29 − . . -1.8 -1.7 − . . − − − u − − − HWB-31 − . . -3.8 -3.6 − . . − − − u − − − HWB-34 − . . -2.3 -2.3 − . . − -1.3 − y − -2.4 +0.34HWB-40 − . . -2.1 -2.1 − . . − − − u − − − (1) From photometry: Str¨omgren- [ F e/H ] calibration from Hilker (2000).(2) From photometry: Str¨omgren- [ F e/H ] :– m calibrations from Calamida et al. (2007), uncertainties are ∼ greater than the Hilker(2000) calibration.(3) From photometry: Str¨omgren- [ F e/H ] :– [m] calibrations from Calamida et al. (2007).(4) From photometry: averaging GS99’s standard RGB-calibrations, since there is a spread in metallicity.(5) From spectroscopy, respectively: Norris et al. (2008); Martin et al. (2007); Gilmore et al. (2013b). Proper motion membership desig-nated: yes=y; no=n; unknown=u.(6) Gilmore et al. (2013b)(7) From photometry and spectroscopy Lai et al. (2011) n-SSPP method.(8) Boo-117 appears in Martin et al. (2007); Norris et al. (2008); Feltzing et al. (2009). Gilmore et al. (2013b) prefers [ F e/H ] ∼ − . . Table 6.
Fitted Parameters for Bo¨otes I Stars from Hughes & Wallerstein (2011b)ID [ F e/H ] Spec [ F e/H ] phot T eff ( K ) log g Age (Gyr) Boo-117/HWB-8 -2.25 -2.4 4700 1.4 11Boo-119/HWB-9 -2.7 -2.7 4750 1.5 12HWB-22 -2.2 -2.2 5250 2.6 12HWB-24 -1.9 -1.8 5300 2.7 12HWB-28 -1.5 -1.2 5350 2.9 11HWB-34 -1.3 -1.1 5400 3.1 12(1) From Martin et al. (2007).(2) Means found from fitting Washington and Str¨omgren photometry separately to the α -enhancedDartmouth isochrones, then taking weighted means, dependent on error bars. Uncertainties arethen ± . dex.(3) Weighted mean from Dartmouth isochrones, uncertainties are ± K .(4) Weighted mean from Dartmouth isochrones, uncertainties are ± . dex.(5) Weighted mean from Dartmouth isochrones, uncertainties are ± . Gyr.
Table 7.
Model Fits for − . > [ F e/H ] > − . and Constant Ageof 11.5 Gyr, [ α/F e ] = 0 . colour/Index MSTO RGB rRGB(mag.) M T ∼ M T − . > M T > C − T ) ( T − T ) ( b − y ) m [ m ] m ∗ m ∗∗ ( C − y ) ( u − g ) ( g − r ) ( r − i ) ( B − V ) † ( V − R ) † ( V − I ) † α -enhanced models generated from the Dartmouth isochrones(Dotter et al. 2008). † From Table 4 of Geisler (1996), converting ( C − T ) to BVRI colours. c (cid:13) , 000–000 hotometric Metallicities Table 8. colour Change/Gyr for Model Fits for Constant [ F e/H ] = − . , [ α/F e ] = 0 . , and Age Range of 10-14 Gyr ∆ colour/Index MSTO RGB rRGB(mag.) M T ∼ M T − . > M T > C − T ) ( T − T ) ( b − y ) m [ m ] m ∗ m ∗∗ ( C − y ) ( u − g ) ( g − r ) ( r − i ) ( B − V ) † ( V − R ) † ( V − I ) † α -enhanced models generated from the Dartmouth isochrones(Dotter et al. 2008). † From Table 4 of Geisler (1996), converting ( C − T ) to BVRI colours. Figure 14.
Spectral-energy distribution of HWB-28 shown with the best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled. TheSDSS data is shown as open squares, the Str¨omgren measurements areshown as filled triangles, Washington magnitudes are the larger filled tri-angles. The error bars are the σ uncertainties in the data. (a) SED for therange in wavelength, . µm < λ < . µm . (b) SED for the range inwavelength, . µm < λ < . µm . Figure 15.
Spectral-energy distribution of HWB-34 shown with the best-fitting ATLAS9 (interpolated) model fluxes, appropriately scaled. TheSDSS data is shown as open squares, the Str¨omgren measurements areshown as filled triangles, Washington magnitudes are the larger filled tri-angles. The error bars are the σ uncertainties in the data. (a) SED for therange in wavelength, . µm < λ < . µm . (b) SED for the range inwavelength, . µm < λ < . µm .c (cid:13) , 000–000 J. Hughes et al. physical size, mass, and metallicity spread to Bo¨otes I, but with ages of10–14 Gyr over the approximate metallicity range − . > F e/H > − . . We obtained over 50,000 artificial stars (binary fraction of 0.5) withStr¨omgren, Washington and SDSS magnitudes. We compared model starswith our objects having vbyCT T measurements.From these model runs, we chose 3 simple cases. Firstly, there is asingle-age (11.5 Gyr) population (1216 stars), with a conservative spreadin metallicity from [ F e/H ] = − . up to − . . We call this Case I. Thesecond population (Case II: 9133) was designed to be enriched in situ, with − . < [ F e/H ] < − . . The metallicity distribution terminated afterstar formation lasting at least 4 Gyr. We added Case III, an alternative long-duration population with a few “starbursts,” to determine if we could tell itapart from Case II. In Case III, there are 1374 stars born 12 Gyr ago, with − . < [ F e/H ] < − . , 6375 stars with − . < [ F e/H ] < − . ,which are 0.5 Gyr younger, and 1363 stars with − . < [ F e/H ] < − . , with SF extending up to 10 Gyr ago, and then terminating. Using theKolmogorov-Smirnov Test for Two Populations, where the null-hypothesis( H ) is that the populations are the same, we can tell the difference betweenthe age spreads in Cases I, II and III, but not the metallicity ranges.In order to make the models more realistic, we use the photometric un-certainties from Figure 3. From tests, we found that we required at least 2%photometry at the MSTO to determine if there are age spreads present, sincethe isochrones exhibit a change of ∼ . mag. in ( C − T ) for each Gyrin age. There would have to be much deeper Str¨omgren photometry for anyage spread less than 1.5 Gyr to be distinguished. In the Washington systemalone, with [ F e/H ] ∼ − . , 2 per cent photometric uncertainty at theMSTO would reveal an age spread of > Gyr.We selected models with log g of 1.0-2.0 for the RGB stars, 2.0-3.0for the rising-RGB (rRGB), below the level of the HB, and log g ∼ . for the MSTO. We examined the colours in the Str¨omgren, Washingtonand SDSS systems, at fixed age and fixed-[Fe/H]. Our goal was to quan-tify the filter systems sensitivity and break the age-metallicity degeneracyas cleanly as possible, avoiding the upper-RGB. The results of the artifi-cial star experiments are given in Tables 7 and 8, and Figure 16. Figure16a shows colours and indices for the stars in all the models with an age of11.5 Gyr, and examines a range of − . < [ F e/H ] < − . . The RGBstars’ range is shown in orange, the rRGB in gold, and the MSTO in violet.Figure 7b takes stars at a constant [ F e/H ] = − . . We know that the realstars are α -enhanced at the +0.2 to +0.4 dex level, (Norris et al. 2010b andGilmore et al. 2013b; see Table 5) which would make a metal-poor star lookmore metal rich in the broad-band colors. In Figure 16b, we let the modelstars have a fixed metallicity value of [ F e/H ] = − . (more like a realsample of [ F e/H ] > − . ) and let the age vary from 10-14 Gyr.Even though these models cannot be considered well-calibrated be-low [ F e/H ] = − . , we show the lower end of the [ F e/H ] -range, from − . < [ F e/H ] < − . , at a constant age of 11.5 Gyr, but we hatch thebar-chart to recognize this factor. If we were fortunate to collect so many [ F e/H ] -values of enough real stars in dSphs at this low range in [ F e/H ] ,the stars may be α -enhanced and may not appear so metal-poor broadbandcolors (CN- or C-enhanced). However, this is the parameter-space wherethe SDSS-colors recover their usefulness. For our sample, that the SDSS-colors are very uncertain here, as the u − and g − magnitudes have largeuncertainties (see Table 4) returned are too low for the MSTO-stars, at thesensitive TO-value of log g . If we had detections down to the MSTO stars,they would have a spread in ( u − g ) > . . Here, the SDSS filters lackof sensitivity to α -elements lets us recover a star’s metal-poor nature, evenif it was an extreme example, e.g. Boo-119. However, for this color to beeffective, the stars have to be detected at SDSS − u , which takes more thantwice as long as the C -band (see Table 2). For stars just above the MSTOto the upper-RGB, ( C − T ) is most effective for all evolutionary stagesin both age and metallicity. The ( C − T ) calibration loses is sensitivitybelow [ F e/H ] ∼ − . on this scale, which is why we have to supplementit with ( b − y ) . The filter combination CT by , or even Cby , maintains itssensitivity to metallicity below [ F e/H ] ∼ − . , as can be seen in Figures7g–i. Also note that the rRGB colours are hardly sensitive to age at all, andcan be used to break the age-metallicity degeneracy. We want to avoid usingSloan-u or Str¨omgren-u, and the v -band, as both consume observing time(see Table 2). However, many searches for closer and brighter extremely metal-poor stars (Spite et al. 2013), this color could be vital, but even theyuse ( g − z ) to avoid SDSS-u.From the models, we find that the ( C − T ) -colour is best for oursample above the MSTO; the ( C − y ) -colour is shown to be useful (inagreement with Ross et al. 2014), m ∗ is better than m ∗∗ , and all these arebetter than the SDSS colours. However, constructing indices involves 3 or4 filters, which increases the uncertainty in an parameters derived from acolour-colour or color-index calibration. The method of deriving age and [ F e/H ] will the smallest uncertainty is to use a color sensitive to tempera-ture and one sensitive to chemical composition, but we need to combine theWashington and Str¨omgren filters.We considered that Bo¨otes I might resemble ω Cen, the core of acaptured dE, with extended enrichment and a long period of star forma-tion (Gratton et al. 2011; Hughes et al. 2004). Due to its lack of H I or re-cent star formation (SF) (Bailin & Ford 2007), we might expect Bo¨otes Ito have a simple history, similar to most globular clusters (Milone et al.2012), with a short burst of star formation, terminated by supernovae (SNe)II events, or tidal stripping (Fellhauer et al. 2008) removing the ISM. Thisscenario should give rise to almost a single-age fit to the CMD, and a verynarrow ( ∆[ F e/H ] < . ) dex metallicity range. Marcolini & D’Ercole(2008) discussed the model of Marcolini et al. (2006) which describes thechemical evolution of dSphs (particularly Draco, but it can be general-ized). Marcolini & D’Ercole (2008) argue that the SNe II ejecta from thestar formation event in a Draco-like dSph (actually about “50 instanta-neous bursts” over 60 Myr) should be retained, due to the extra mass fromthe dark matter halo, and because “efficient radiative losses” keep the en-riched ISM flowing back to the central regions of the dSph, mixing thegas. Cohen & Huang (2009) obtained high-resolution spectra of 8 stars inDraco, adding to 14 they had observed previously, which had a metallicityrange of − . > [ F e/H ] > − . dex, similar to Bo¨otes I; their age-metallicity relationship indicated that SF in Draco lasted about 5 Gyrs. Anage spread even half this large should have been obvious for Bo¨otes I, evenwith the uncertainties in Figure 3. The modeling of Draco’s enrichment his-tory (Marcolini & D’Ercole 2008), showed a star formation process lastingabout 2 Gyr, with most of the initial Fe-enrichment coming from SNe II,with chemical inhomogeneities appearing later, caused by SNe Ia “pockets”of material, with higher [ F e/H ] and lower [ α/F e ] , which take 2–3 Gyr tomix in with the rest of the gas, the dynamics of which is driven by the SNeII effects. The discussion of possible star formation histories for this systemis also illustrated by Gilmore et al. (2013a).At the very least, the real Bo¨otes I stars have [ α/F e ] = +0 . ± . dex, but this value seems to be unchanging; it is likely that SF terminatedbefore the onset of SN Ia contamination. We assume this can be quanti-fied as a colour-shift. When we examined the Dartmouth isochrones, for [ α/F e ] = 0 . and +0 . , in the Str¨omgren system only the y-filter seemedto be sensitive to [ α/F e ] , making stars brighter by 0.046 mag. at 12 Gyrand [ F e/H ] = − . . We saw that the model stars with low metallicitieslost sensitivity in the v - and b -filters, making those magnitudes insensitiveto α -abundances. In the Washington filters, T was shifted by -0.057 mag.and ( C − T ) by +0.035, with a variation of less than 1 per cent .Setting [ α/F e ] ∼ +0 . for Bo¨otes I, we compare our Class A–C stars’ CT by -magnitudes with the whole data set of over 50,000 ar-tificial stars, and the results are listed in Table 9. We performed χ fitsto the stars generated from the [ α/F e ] = 0 . Dartmouth isochrones(Dotter et al. 2008), using the colour-shifts determined for the CT by -filters. With the possible inclusion of two blue stragglers (HWB-45 andHWB-51), and HWB-9 being carbon-rich (and CN-strong), the average ageis . ± . Gyr, and the range in metallicity is − . > [ F e/H ] > − . ,which would be shifted to around − . > [ F e/H ] > − . with α -enhancement added back (in agreement with Gilmore et al. 2013b). We notethat Boo-1137 does not appear as metal poor as it should, also, likely be-cause the C-filter also loses sensitivity for very metal-poor stars. Our testsof the recovery of the artificial stars where we added typical photometricuncertainties found that the ( C − T ) -colour started to become insensitivewhen [ F e/H ] < − . . We also found it necessary to use ( b − y ) as thetemperature-sensitive colour instead of ( T − T ) : otherwise, the tempera-tures of the real stars became at least 500K too hot compared to the SEDsshown in Figures 8–15. Using m ∗∗ and ( b − y ) or ( C − y ) did not improvec (cid:13) , 000–000 hotometric Metallicities Table 9.
Final Model Fits to Bo¨otes I StarsID Age(Gyr) [ F e/H ] T eff ( K ) log g ± . Gyr ± . dex ± K ± . dexBoo-1137 12.0 -2.6 4775 1.34Boo-127 10.8 -2.2 4743 1.38Boo-117/HWB-8 10.6 -2.0 4684 1.42Boo-119/HWB-9 10.8 -1.8 4705 1.49HWB-16 11.5 -1.6 5022 2.21HWB-19 11.5 -3.4 5292 2.91HWB-22 11.5 -1.9 5184 2.60HWB-24 11.5 -2.4 5314 2.77HWB-28 11.5 -1.6 5288 2.89HWB-29 11.5 -1.6 5298 2.92HWB-31 12.0 -2.5 5422 3.03HWB-34 11.5 -1.7 5365 3.10HWB-40 11.6 -1.6 5411 3.49HWB-45 12.0 -3.0 6919 4.07HWB-47 11.9 -1.7 5574 3.51HWB-48 11.5 -3.5 7022 4.17HWB-50 11.5 -1.8 5709 3.62HWB-51 11.5 -3.5 6948 3.91 χ fits to artificial stars generated from the [ α/F e ] = 0 . Dartmouth isochrones (Dotter et al. 2008), using the CT by -filters. Light cyan rows are confirmed members and the lightgray row is a star that was ruled out by Martin et al. (2007)using its radial velocity.the fit. ( C − y ) or ( C − T ) alone are not sufficient for individual stars,unlike whole giant branches (Ross et al. 2014).We conclude that the fewest number of filters we can use for these old,metal-poor populations, is 4, and those are CT by . We preserve the ∼ dexrange in [Fe/H] from the spectra, but we estimate Table 9’s [ F e/H ] -valuesare, on average, 0.5 dex more metal-rich than Lai et al. (2011). Our resultsare more consistent with the CaT-calibrations, and the other spectroscopicstudies (see Gilmore et al. 2012).To display the observational uncertainties in derived parameters forTable 9, Figure 17 shows the CMDs in Str¨omgren, Washington, and SDSSfilters for the model stars to match the real data shown in Figures 4 & 18.Starting with the black circles for Case II, with − . < [ F e/H ] < − . and ages, 10–14 Gyr. We then restrict the age range to 11-12 Gyr (greencircles), and then to 11.3-11.7 Gyr (yellow). The green and yellow pointshave the same metallicity spread. Figure 17a–c are the models with nophotometric scatter, and Figures 17d–f introduce the photometric uncer-tainty according to Figure 3 to match the Bo¨otes I data (and if we had ob-tained similar SDSS-data instead of just the catalog magnitudes). We areable to detect the slight metallicity range contraction from the black points, − . < [ F e/H ] < − . , to the green points − . < [ F e/H ] < − . at the SGB in Figure 17e, but not in the Str¨omgren filters in Figure 17d,as expected from Figure 16 and Tables 7 & 8. The vertical section of theMSTO is likewise able to detect the age contraction from a spread of 1 Gyrto 0.4 Gyr. We confirm that the SGB is sensitive to metallicity and not age,and the MSTO is more sensitive to age, except if we had very metal-poorwith better than 1%-photometry in ( u − g ) at the MSTO. We note that asthe age spread contracts from the green to the yellow points for a few thou-sand stars in our models, and the RGB depopulates. The model-fits in Table9 have a smaller value of χ when we use ( b − y ) in addition to ( C − T ) ,rather than T − T . We conclude that only combining CT by can coverthis range in [ F e/H ] and age smoothly, with no break between the RGBand the MSTO stars, unless it is caused by photometric uncertainties. Theuncertainties in Table 9 metallicities are ± . dex in [ F e/H ] and ± . Gyr in age using 4 filters and with 1% photometry.Figure 18 shows the final CMD with the [ α/F e ] ∼ +0 . Dartmouthisochrones. The Class A–C objects in Bo¨otes I have an age slightly lessthan 12 Gyr, but a wide [Fe/H]-range, likely exceeding 2 dex (Norris et al.2008). It is possible to use the ( C − T ) -colours alone, if the upper-RGB iswell-populated and [ F e/H ] > − . , to get age and metallicity (Ross et al. 2014). For most dSphs, with few stars on the upper-RGB, the rRGB andMSTO stars are sufficient to break the age-metallicity degeneracy, if youhave 2 colours, ( C − T ) ) & ( b − y ) . Figure 17a shows that Str¨omgrencolours are not sufficient alone to extract age information from the RGBwith normal ∼ per cent photometry, and that high S/N is necessary at theMSTO to recover age information. We also note that Figure 18b shows ( C − T ) isochrones for − . > [ F e/H ] > − . maintain good separation forages 10–12 Gyr, only having a pinch-point at the base of the RGB. We have shown that the most efficient way to evaluate the metallicity, [ α/F e ] , and age of old, metal-poor systems is to observe individual starswith the CT by filters combined with the Dartmouth isochrones. Appli-cation to the real Bo¨otes I stars from Table 9 is as follows. If the dis-tance and reddening are known, use the T -magnitude and the ( C − T ) -colour to obtain [ F e/H ] , [ α/F e ] , age, log T eff and log g from a χ -fitto the Dartmouth α -enhanced course model-grid, with ages of (10, 12, &14 Gyr). Primarily, this fixes [ α/F e ] to ± . dex for the star (or to see if α -enhancement appears constant for the system). Then we use another χ -fit model stars’ T -magnitudes, ( C − T ) and ( b − y ) colours, to find thebest-fit [ F e/H ] , age, log T eff and log g for each star. A recovery-test ofthis method returns over 90 per cent of the model stars if we add in 1–5%photometric errors. Noting that spectroscopic surveys do not always agreewith each other (Gilmore et al. 2013a), our final estimates of [ F e/H ] fromphotometry agree with the spectroscopy measurements within ∼ . dex.If the model stars have [ F e/H ] = − . to − . , then T -magnitudes and ( C − T ) -colours are sufficient, and the metallicity of the whole system canbe defined by the m ∗ -index. If [ F e/H ] < − . , the ( b − y ) -colours needto be added and the metallicity alone can be found from m ∗∗ .Our Bo¨otes I data in Figure 18 is thus consistent with the models giventhe photometric scatter and that we can resolve the [ F e/H ] -spread fromat least -3.5 to -1.6, matching the ranges claimed by all the spectroscopicsurveys. The large range in [ F e/H ] , coupled with a small age range, whichcan be seen from combining the Str¨omgren and Washington data, indicatesa short SF history. The best-fit isochrones and Figure 18 give an age forBo¨otes I of . ± . Gyr, confirming that the ISM was lost at very earlytimes. The spectroscopic surveys are not spatially uniform, but we agreec (cid:13) , 000–000 J. Hughes et al.
Figure 16.
Proportional bar chart for the colour ranges for the models ofRGB stars (red), with log g of 1.0-2.0; log g of 2.0-3.0 for the rising-RGB(rRGB; gold), below the level of the HB, and log g ∼ . for the MSTO(violet). The colours are shown for the Str¨omgren, Washington and SDSSsystems, at: (a) fixed age of 11.5 Gyr and − . < [ F e/H ] < − . . Datafrom Table 7. (b) Constant [ F e/H ] = − . (which would be equivalentto α -enhanced more metal poor stars) and ages 10-14 Gyr. ( C − T ) ismost effective for all evolutionary stages in both age and metallicity, andrRGB colours are insensitive to age. Data from Table 8. (c) Colour-rangefor models with a fixed age of 11.5 Gyr and − . < [ F e/H ] < − . .Note that ( u − g ) > . becomes extremely sensitive for extremely metal-poor MSTO stars.with Gilmore et al. (2013a,b) and Koposov et al. (2011) that Bo¨otes I seemsto be comprised of more than one population distribution. A change in the α -element abundances is not seen in their data or our isochrone fits, sothat star formation is predicted to last at least 0.5 Gyr before any SN Iacontribute. The CEMP-no object (Boo-119) was likely to have formed fromthe ejecta of Pop III stars (Gilmore et al. 2013a,b), maybe only one (alsosee Kirby et al. 2012).We recommend that Washington filters are used for the study of dSphsystems beyond ∼ kpc (Bo¨otes I is at about 65 kpc), except whereconsiderable reddening present; although they would still be better than ugriz . For future surveys using the Sloan filters, we recommend addingthe Washington C-filter, as using ( C − r ) is the best (and cheapest) com-promise for comprehensive stellar population studies, but that ( u − g ) isvery effective at the MSTO. If a star is not carbon-enhanced, the [ F e/H ] -sensitivity of the Washington and Str¨omgren combination ( CT by ) is atleast twice as great as that of the SDSS filters. Below the horizontal branch,Str¨omgren and Washington filter sets lose metallicity sensitivity, but CT by succeeds where other calibrations fail. For upper-red-giant branch stars,the Str¨omgren m -index gives a more-accurate metallicity estimate thanthe Washington filters compared to recent spectroscopic studies (around ∼ . dex). Washington filters give better [ F e/H ] -resolution for the range Figure 17.
We show colour-magnitude diagrams for the Str¨omgren, Wash-ington and SDSS data models. The Dartmouth isochrones for several val-ues of [ F e/H ] and ages 10-12 Gyr are displayed. From left to right, theblue isochrones are [ F e/H ] = − . , -3.5, and -3.0, [ α/F e ] = +0 . ,all with an age of 12 Gyr, decreasing in thickness. The cyan line is [ F e/H ] = − . , [ α/F e ] = +0 . at 12 Gyr, the magenta dashed lineis [ F e/H ] = − . , [ α/F e ] = +0 . at 12 Gyr, the black long-dashed lineis [ F e/H ] = − . , [ α/F e ] = +0 . , at 11 Gyr, and the red dot-dashedline is [ F e/H ] = − . , [ α/F e ] = +0 . at 10 Gyr. Here, the black circlesare the 9133 stars from Case II with with − . < [ F e/H ] < − . . Themetallicity distribution terminated after star formation lasting at least 4 Gyr.Green circles are 3187 stars with ages 11-12Gyr and − . < [ F e/H ] < − . . The yellow circles further restrict the age to 11.3-11.7 Gyr whichshows the limits of age resolution for 1251 models stars. isochrones for sev-eral values of [ F e/H ] are displayed (a) Str¨omgren data for model stars withno added photometric scatter, but showing the broadened MS from the 0.5binary fraction. (b)
Washington CMD for the same sample. (c)
Str¨omgrendata with photometric scatter introduced according to Figure 3. (d)
Wash-ington CMD for the same sample, with the photometric scatter according toFigure 3. − . > [ F e/H ] > − . , but for lower values, [ F e/H ] < − . , CT by is the most effective combination for these populations. ACKNOWLEDGMENTS
This paper used observations obtained with the Apache Point Observatory3.5-meter telescope, which is owned and operated by the Astrophysical Re-search Consortium. Hughes wishes to thank the APO observing staff fortheir support and late-night instant-messaging and Myra Stone for helpwith data analysis. We also acknowledge financial support from the NSF,and the Kennilworth Fund of the New York Community Trust. We thankFrank Grundahl (for sharing his M92 data), and Myra Stone for help withDAOPHOT III. We are grateful to: Ata Sarajedini, Inese Ivans, Peter Stet-son, Jeff Brown, Beth Willman, John Norris, Anna Frebel, Marla Geha,Ricardo Munoz, Kim Venn, and Ryan Leaman for useful discussions. Wec (cid:13) , 000–000 hotometric Metallicities Figure 18.
We show colour-magnitude diagrams for the Str¨omgren, Wash-ington and SDSS data on Bo¨otes I objects. The Dartmouth isochronesfor several values of [ F e/H ] and ages 10-12 Gyr are displayed. Fromleft to right, the blue isochrones are [ F e/H ] = − . , -3.5, and -3.0, [ α/F e ] = +0 . , all with an age of 12 Gyr, decreasing in thickness. Thecyan line is [ F e/H ] = − . , [ α/F e ] = +0 . at 12 Gyr, the magentadashed line is [ F e/H ] = − . , [ α/F e ] = +0 . at 12 Gyr, the black long-dashed line is [ F e/H ] = − . , [ α/F e ] = +0 . , at 11 Gyr, and the reddot-dashed line is [ F e/H ] = − . , [ α/F e ] = +0 . at 10 Gyr. In all plots,open circles are sources from Table 3 and the large red filled triangles rep-resent the 8 proper motion-confirmed members. We use E ( B − V ) = 0 . and DM = 19 . for Bo¨otes I. (a) The Str¨omgren CMD with stars fromTable 3. (b)
The Washington CMD with stars from Table 3. (c)
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