The Distribution of Alpha Elements in Ultra-Faint Dwarf Galaxies
aa r X i v : . [ a s t r o - ph . C O ] F e b D RAFT VERSION S EPTEMBER
27, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE DISTRIBUTION OF ALPHA ELEMENTS IN ULTRA-FAINT DWARF GALAXIES L UIS
C. V
ARGAS , M ARLA G EHA , E VAN
N. K
IRBY , AND J OSHUA
D. S
IMON Department of Astronomy, Yale University, 260 Whitney Ave., New Haven, CT 06511, USA; [email protected] Department of Physics and Astronomy, University of California, Irvine, 4129 Reines Hall, Irvine, CA 92697, USA and Observatories of the Carnegie Institution of Washington, 813 Santa Barbara St., Pasadena, CA 91101, USA
Draft version September 27, 2018
ABSTRACTThe Milky Way ultra - faint dwarf galaxies (UFDs) contain some of the oldest, most metal - poor stars in theUniverse. We present [Mg/Fe], [Si/Fe], [Ca/Fe], [Ti/Fe], and mean [ α/ Fe] abundance ratios for 61 individualred giant branch stars across 8 UFDs. This is the largest sample of alpha abundances published to date in galax-ies with absolute magnitudes M V > -
8, including the first measurements for Segue 1, Canes Venatici II, UrsaMajor I, and Leo T. Abundances were determined via medium - resolution Keck/DEIMOS spectroscopy andspectral synthesis. The sample spans the metallicity range - < [Fe / H] < - on average lower [ α/ Fe] at higher metallicities,consistent with enrichment from Type Ia supernovae. Thus even the faintest galaxies have undergone at leasta limited level of chemical self - enrichment. Together with recent photometric studies, this suggests that starformation in the UFDs was not a single burst, but instead lasted at least as much as the minimum time delayof the onset of Type Ia supernovae ( ∼
100 Myr) and less than ∼ α/ Fe] abundance pattern that is inconsistent with a flat, Galactic halo - like alphaabundance trend, and is also qualitatively different from that of the more luminous CVn I dSph, which doesshow a hint of a plateau at very low [Fe/H]. Subject headings: galaxies: abundances — galaxies: dwarf galaxies — galaxies: evolution — Local Group INTRODUCTION
Ultra-faint dwarf (UFD) galaxies are the least luminous(M V > -
8) known galaxies in the Universe (Willman et al.2005b,a; Belokurov et al. 2006, 2007; Zucker et al. 2006a,b;Sakamoto & Hasegawa 2006, Walsh et al. 2007; Irwin et al.2007). Spectroscopic observations of individual starsdemonstrate that UFD galaxies are dark matter dominated(Simon & Geha 2007). They obey the metallicity - luminosityrelation found in the brighter, classical spheroidals (dSphs),and have large internal metallicity spreads greater than 0.5 dex(Kirby et al. 2008b).Recent HST photometry extending below the main se-quence turn - off demonstrates that at least three UFDs (Her-cules, Ursa Major I and Leo IV) are composed exclusively ofancient stars ∼
13 Gyr old (Brown et al. 2012). These datafurther suggest that the star formation lasted for less than ∼ on average increasing its metallicity over time(e.g., Lanfranchi & Matteucci 2004; Revaz et al. 2009). Inho-mogeneous gas mixing can also lead to a wide range of stellarmetallicities within a single satellite (e.g., Argast et al. 2000;Oey 2000). Finally, the merger of multiple progenitors withdifferent mean metallicities may also produce a wide metal-licity spread, as seen in recent simulations of more massivesatellites (Wise et al. 2012). Determining more detailed abun-dances of stars in the UFDs will provide insight into the his-tory of star formation at these very early epochs.The [ α/ Fe] abundance ratios, including [Mg/Fe], [Si/Fe], Center for Galaxy Evolution Fellow We reserve the use of unsubscripted [ α / Fe] to refer to alpha abun-dance ratios in general ; individual alpha elements are introduced where [Ca/Fe], and [Ti/Fe], provide important constraints on thechemical evolution history of a stellar population. In themost metal - poor stars, the ISM is polluted by the prod-ucts of massive stellar evolution and core-collapse Type IIsupernovae (SNe). The chemical yields from these explo-sions (Woosley & Weaver 1995; Nomoto et al. 2006) resultin super - solar [ α/ Fe] values. These yields may depend onthe mass, metallicity, and explosion energy of the supernova.Hence, individual Type II SNe may leave a unique signaturein the observed abundance patterns, provided that (a) the gasdid not have sufficient time to mix prior to the formation ofthe next generation of stars, or (b) the number of SNe wassmall, leading to stochastic sampling of the IMF. This wouldlead to intrinsic scatter in the [ α /Fe] ratios and/or abnormalabundance ratios. Given their low average metallicities, theUFDs are one of the best places to search for the signatureof chemical enrichment from metal - free Population III stars(Frebel & Bromm 2012).Type Ia SNe output negligible amounts of alpha - elementsin contrast to iron - peak elements resulting in lower [ α/ Fe]with rising [Fe/H]. Due to the time delay in the onset ofType Ia SNe, the low [ α/ Fe] signature is indicative ofstar formation lasting longer than the minimum time de-lay, t min , Ia ∼
100 Myr (Totani et al. 2008; Maoz et al. 2012).The [Fe/H] at which [ α/ Fe] starts to decrease helps con-strain the efficiency of star formation (Pagel 2009 andreferences therein). It thus provides a means to distin-guish stellar populations with different origins. Spectro-scopic studies of classical dSphs (e.g., Shetrone et al. 2001;Venn et al. 2004; Kirby et al. 2011) reported significantlylower [ α/ Fe] in comparison to the observable Milky Wayhalo at [Fe/H] & - .
5. This result has been used to show that appropriate. For any elements A and B, we use the standard notation[A/B] ≡ log (cid:0) N A / N A , ⊙ (cid:1) -log (cid:0) N B / N B , ⊙ (cid:1) . Vargas et al.the classical dSphs had a different chemical evolution than theprogenitor(s) of the bulk of the inner Milky Way halo, whichwere likely more massive dwarf systems (Robertson et al.2005). In contrast to the inner halo pattern, Nissen & Schuster(2010) have reported a population of nearby, low [ α/ Fe] starsconsistent with outer halo membership based on their kine-matics, thus providing some indication that accreted systemswith low [ α/ Fe] abundance ratios were important contribu-tors to the outer halo.Our knowledge of the distribution of chemical abun-dances in UFDs, their chemical evolution, and their simi-larity/difference with the halo stars, is still limited. High-resolution (R & < - < - .
0. In contrast, Frebel et al. (2010) foundsimilar [ α/ Fe] abundance patterns at [Fe / H] < - . α/ Fe] - [Fe/H] pattern in the inner Milky Way halo. Thus,the role of the UFDs in building even the most metal - poorend of the inner halo is still unclear.High - resolution abundance studies of UFDs are currentlylimited to relatively bright stars with apparent magnitude V .
19. Coupled with the sparseness of the RGBs in UFDsystems, high - resolution abundance studies using 8 -
10 me-ter class telescopes remain impractical for large samples.For example, the faintest star in a UFD studied to date athigh - resolution is the brightest known RGB star in Leo IVwith an apparent magnitude of V ∼ . - resolution studies (R ∼ - - resolutionspectroscopy has been used to successfully measure bothiron (Allende Prieto et al. 2006; Lee et al. 2008; Kirby et al.2008a) and alpha - element abundances (Kirby et al. 2009;Lee et al. 2011). Kirby et al. (2010) presented homoge-neous Keck/DEIMOS medium - resolution abundances forthousands of stars in eight of the classical dSphs, showingthat these systems may share a common trend of rising [ α /Fe]with decreasing [Fe/H] down to [Fe/H] ∼ - .
5. Lai et al.(2011) reported halo - like [ α /Fe] ratios in Böotes I spanning - . . [Fe / H] . - .
5, and Norris et al. (2010b) presented[C/Fe] for 16 stars in Böotes I and 3 stars in Segue 1, showinga wide range of carbon enhancements.In this paper, we present the first homogeneous abundancesfor [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe] for 61 stars in 8 ofthe UFDs: Segue 1 (Seg 1), Coma Berenices (Com Ber), UrsaMajor II (UMa II), Ursa Major I (UMa I), Canes Venatici II(CVn II), Leo IV, and Hercules (Herc). Our observations andabundance measurement technique are summarized in § 2 - - OBSERVATIONS AND SAMPLE SELECTION
We determine spectroscopic abundances for the sample ofUFD stars first presented by Simon & Geha (2007), here-after SG07, Geha et al. (2009), and Simon et al. (2011), here-after S11. The sample was observed with the Keck/DEIMOSspectrograph (Faber et al. 2003) using the 1200 line mm - grating, which provided wavelength coverage between 6300and 9100 Å with a resolution of ∼ . spec2d soft-ware pipeline (version 1.1.4) developed by the DEEP2 team(Newman et al. 2012; Cooper et al. 2012) optimized for stel-lar spectra (SG07). The final one-dimensional spectra in-clude the random uncertainties per pixel. Radial velocities aremeasured by cross - correlating the science spectra with stel-lar templates, and are used in this work to shift the sciencespectra to the rest frame.We analyze only stars identified as UFD members bySG07 and S11. These authors selected members on the ba-sis of: (i) position in color - magnitude space relative to anM92 isochrone shifted to the UFD distance; (ii) radial ve-locity within ∼ σ of the systemic UFD velocity; (iii) Na I λλ . II infrared triplet (CaT) estimate of the stellarmetallicity. The Na I criterion prevents contamination by diskdwarfs that share similar radial velocities and magnitudes asthe UFD RGB stars. We refer the reader to SG07 for a detailedexplanation of the data reduction and membership selectionfor each UFD. ABUNDANCE ANALYSIS
The metallicities of stars in our sample have been pre-viously presented in Kirby et al. (2008b) and Simon et al.(2011). Here, we measure for the first time [Mg/Fe], [Si/Fe],[Ca/Fe], [Ti/Fe], and an overall [ α/ Fe] abundance ratio us-ing the spectral matching technique described in Kirby et al.(2010) with an expanded error analysis accounting for asym-metric uncertainties in the abundance ratios.
Spectral Grid & Element Masks
Our technique consists of a pixel - by - pixel matching be-tween each stellar spectrum and a finely - spaced grid of syn-thetic spectra optimized for our spectral wavelength range. Tomeasure stellar parameters, we rely on the synthetic spec-tral grid synthesized by Kirby (2011) from plane - parallelATLAS9 stellar atmospheres using the LTE abundance codeMOOG (Sneden 1973). In addition, we make use of an un-published extension to the grid to measure individual alphaabundance ratios, as described in § 3.4.The primary synthetic spectral grid has four dimensions: T eff , log g , [Fe/H], and [ α/ Fe] atm . The quantity [ α/ Fe] atm isdefined as the [ α/ Fe] abundance ratio of O, Ne, Mg, Si, S, Ar,Ca, and Ti used to synthesize each spectrum. The grid spans3500 ≤ T eff ≤ ≤ log g ≤ - ≤ [Fe/H] ≤ - ≤ [ α /Fe] atm ≤ +1.2. Our sample is comprisedof RGB stars (log g < ξ , used for eachsynthesis was determined using an empirical ξ - log g relationvalid for RGB stars, derived from high - resolution spectro-scopic measurements (Kirby et al. 2009, Equation 2). Throughout this paper, we use metallicity and [Fe/H] interchangeably. lpha Elements in UFDs 3
Figure 1.
Left:
We plot the uncertainty in [Fe/H] and [ α / Fe] atm as a function of [Fe/H] for stars with S/N >
20 Å - and 10 < S/N <
20 Å - . In the case of[ α / Fe] atm , we have averaged the σ + and σ - components for each measurement. The colors and plot symbols denote uncertainties in [Fe/H] or [ α / Fe] atm fordifferent ranges of S/N. At a fixed S/N (Å - ), [ α / Fe] atm uncertainties increase towards lower [Fe/H] due to progressively weaker features, whereas such a trendis not visible for [Fe/H], at least for those stars with σ [Fe / H] < .
4. The plot shows a minimum at σ ∼ . - dependent systematic uncertainty σ sys added in quadrature to each random uncertainty. Right:
We show the asymmetry between uncertainties σ + [ α / Fe] atm and σ - [ α / Fe] atm for the same data, definedas σ + - σ - , plotted as a function of the mean uncertainty (average of σ + and σ - ). The negative component σ - is generally equal or larger than σ + . A similar trendis present for the individual [ α j / Fe] measurements.
We perform our analysis using only spectral regions withFe, Mg, Si, Ca, or Ti features to maximize sensitivity toeach element. The mask of usable spectral regions for agiven element X is constructed by synthesizing three spectrawith [X / H] = [ - . , - . , - . / H] = - .
5. The mask is comprisedof those wavelength segments where a 0.3 dex difference in[X/H] changes the normalized flux by & . T eff , the procedure wasrepeated at 1,000 K intervals between 4,000 K and 8,000 K,and the resulting masks joined. The Mg, Si, Ca and Ti ele-ment masks do not share wavelength segments in common,allowing us to measure individual abundances in § 3.4. Thecombined alpha mask is defined as the union of the Mg, Si,Ca, and Ti masks. We remove from the element masks spec-tral lines that are not modeled accurately by the LTE synthesiscode, as determined by Kirby et al. (2008a) and listed in theirTable 2. These include the Ca II triplet and the Mg I λ ∼ . χ Pixel - by - Pixel Matching
To perform the pixel fitting, we degrade the synthetic mod-els to the DEIMOS spectral resolution. We account for a smallquadratic dependence of the spectral FWHM on wavelengthby fitting to unblended sky lines. We then convolve the syn-thetic spectra with this variable FWHM Gaussian kernel. Foreach star, we determine log g by fitting the SDSS photometryto a grid of Yale - Yonsei isochrones, as detailed in Kirby et al.(2010). The alternate spectroscopic approach, based on ob-taining ionization equilibrium between Fe I and Fe II abun- The number of segments will vary slightly from star to star due to slightlyvarying wavelength coverage and the presence of bad pixels and other imper-fections in each spectrum. dances , is not applicable to our data due to the dearth of ab-sorption lines from ionized species in our red spectra. We nor-malize the flux - calibrated spectrum using a low order splinefit to wavelength regions not sensitive to any of Fe, Mg, Si,Ca or Ti. The normalization is later refined during the fittingprocess.The best - fit parameters ( T eff , [Fe/H], and [ α/ Fe] atm ) andindividual abundance ratios ([ α j / Fe], where α j = Mg, Si, Caand Ti in this work) are determined by minimizing the χ statistic between the rest - frame science spectrum and theconvolved model grid in a multi - step process described byKirby et al. (2010). We briefly describe the fitting procedurefor the various stellar parameters and abundance ratios, high-lighting the modifications implemented for this paper. In par-ticular, we have updated our uncertainty analysis to providemore accurate asymmetric [ α/ Fe] atm and [ α j / Fe] uncertain-ties.
Throughout, we maintain the order of steps described indetail by Kirby et al. (2010). T eff and [Fe/H] We fit T eff and [Fe/H] simultaneously using the Fe mask.Due to the wavelength overlap between the Fe and combinedalpha masks, we do not fit [Fe/H] and [ α/ Fe] atm simultane-ously. In order to optimize the fitting process in the two di-mensional T eff - [Fe/H] parameter space, we perform the χ minimization using the code mpfit (Markwardt 2009), whichis an IDL implementation of the Levenberg - Marquardt χ al-gorithm.We determine the random uncertainty in [Fe/H], σ [Fe / H] , ran ,by using the covariant error matrix of T eff and [Fe/H] calcu-lated by mpfit . Due to the non - zero cross - terms, σ [Fe / H] , ran islarger than if the [Fe/H] uncertainty was calculated by vary-ing [Fe/H] alone. The total uncertainty in [Fe/H], σ [Fe / H] , isequal to the addition in quadrature of σ [Fe / H] , ran to a system-atic uncertainty component σ [Fe / H] , sys . Kirby et al. (2010) es-timated σ [Fe / H] , sys by calculating the residual difference be- More generally, any element with two measurable species, e.g. Ti I - Ti II ;however, Fe by far contains the most signal. Vargas et al.tween DEIMOS and high - resolution abundances of globularcluster stars, after accounting for the random uncertainty inboth sets of measurements added in quadrature. In order tocheck the reliability of the mpfit - derived uncertainties, wecalculate χ around the best - fit T eff and [Fe/H]. We find that χ contours for T eff and [Fe/H] are symmetric about the mini-mum χ value for σ [Fe / H] . .
4, justifying our use of the sym-metric mpfit random uncertainties. Henceforth, we only in-clude stars with σ [Fe / H] ≤ . [ α/ Fe] atm and [ α j / Fe]
Abundance Ratios
We calculate [ α/ Fe] atm while fixing T eff and [Fe/H] to thebest - fit values, using the combined alpha mask defined in§ 3.1. We compute χ contours for [ α/ Fe] atm by measur-ing the sum of the pixel - to - pixel variation between the stel-lar spectrum and the primary spectral grid. We measure thebest - fit [ α/ Fe] atm value by finding the value corresponding tothe minimum in the χ contour. The measurement of best - fit[ α/ Fe] atm is analogous to that of Kirby et al., who performedthis optimization using mpfit . After all stellar parameters ( T eff ,[Fe/H], and [ α/ Fe] atm ) have converged to their best - fit values,we fit for the individual alpha abundances while keeping allstellar parameters fixed.To measure individual [ α j / Fe] abundance ratios, we com-pare each spectrum to a supplementary spectral grid that sam-ples values of [ α j / Fe] from - . + . α j / Fe] mask. We compute χ contours for each [ α j / Fe]by measuring the pixel - to - pixel variation between each spec-trum and the supplementary spectral grid, instead of the pri-mary grid.In contrast to [Fe/H], we find that a significant number of[ α/ Fe] atm and [ α j / Fe] contours are asymmetric about χ .We therefore estimate the random uncertainties by finding thetwo abundance values corresponding to χ + 1 without as-suming symmetry. We refer to the positive and negative dif-ference between these values and the best - fit abundance ra-tio, [ α/ Fe] as σ + [ α / Fe] and σ - [ α / Fe] , respectively, where [ α/ Fe]stands for any of [ α/ Fe] atm or [ α j / Fe].We also account for non - random errors due to, e.g., un-certainties in the other stellar parameters, by introducinga systematic error floor different for each abundance ratio, σ [ α / Fe]sys , measured by Kirby et al. (2010) in the same way as σ [Fe / H] , sys (§ 3.3). The systematic uncertainties for [ α/ Fe] atm [Mg/Fe], [Si/Fe], [Ca/Fe] and [Ti/Fe] are 0.08, 0.11, 0.18,0.09, and 0.10 dex, respectively. We calculate the total uncer-tainty by adding σ [ α / Fe]sys to the σ + [ α / Fe]ran and σ + [ α / Fe]ran ran-dom components in quadrature. We note that σ [ α / Fe]sys onlycontributes significantly to the error budget when the randomuncertainty is . . + . - . + . + . + .
02 dex for [Fe/H],[Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe], respectively, in thesense of this work minus Kirby et al. There is no differencein the mean [ α/ Fe] atm between the old and new abundancescales.We show the uncertainty in [Fe/H] and [ α/ Fe] atm for allUFD stars in the left panel of Figure 1. At a fixed S/N, the un-certainty increases towards lower [Fe/H] due to progressively
Figure 2.
We plot [ α /Fe] atm against [ α / Fe] avg the mean of [Mg/Fe], [Si/Fe],[Ca/Fe], [Ti/Fe] for the nine stars with measurements available for all ele-ments. The dashed (red) line is the y = x line. The small offset betweenthe data and the red line suggests a small difference between [ α / Fe] atm [ α / Fe] avg . The mean vertical offset is +0.063 dex. The dot - dash (blue) lineshows the improved agreement obtained after adding the offset to [ α / Fe] atm .We thus define [ α / Fe] avg as [ α / Fe] atm + .
63, and apply this correction to allstars in our sample. weaker spectral features. The right panel shows the associ-ated asymmetry in the [ α/ Fe] atm uncertainty as a functionof its average value. We find that σ - [ α / Fe] atm is preferentiallylarger than σ + [ α / Fe] atm , with a similar effect present for each[ α j / Fe] (not shown in the figure). In our analysis, we includeonly abundances with σ [Fe / H] ≤ . σ + [ α / Fe] atm ≤ σ + [ α j / Fe] ≤ α/ Fe] atm , [Mg/Fe], [Si/Fe],[Ca/Fe], and [Ti/Fe], respectively.In addition to the individual [ α j / Fe] , we report an overall alpha abundance ratio, which we denote as [ α/ Fe] avg . Thereis no homogeneous definition of [ α/ Fe] avg in the literature.Different authors use different combinations of [ α j / Fe] to es-timate [ α/ Fe] avg . We choose [ α /Fe] atm as our initial estimateof [ α/ Fe] avg because it was measured using the combined al-pha mask, thus being sensitive to Mg, Si, Ca and Ti. [ α/ Fe] atm has the added advantage of being measurable even when indi-vidual [ α j / Fe] are not, because it is measured from the com-bined signal of four elements.In Figure 2, we compare [ α /Fe] atm against the weightedmean of [ α j / Fe] for the nine stars with measurements forall elements. The comparison shows that [ α /Fe] atm is offsetrelative to the weighted mean by - . ± .
010 dex. Weattribute this offset to the influence of the [Mg/Fe] measure-ments, which are systematically higher than [ α /Fe] atm for allstars in this subsample. While the mean assigns equal weightto each element when the uncertainties are comparable, themeasurement of [ α /Fe] atm is less affected by the Mg abun-dance due to the relatively small number of Mg lines in theDEIMOS spectrum. We adjust the definition of [ α/ Fe] avg as[ α /Fe] atm + 0.063 dex in order to account for the systematicdiscrepancy described above.We note that although use of an [ α/ Fe] avg blurs nuanceddifferences that may be present between the different ele-ments, it is a useful quantity because of the closely relatednucleosynthetic origin of these elements. We report [ α/ Fe] avg measurements for 61 stars (equal to the number of [ α/ Fe] atm measurements) including seven stars for which no individuallpha Elements in UFDs 5
Figure 3.
Left:
We compare our DEIMOS [Fe/H] measurements against published high - resolution (HRS) measurements in Com Ber, UMa II (Frebel et al.2010), Leo IV (Simon et al. 2010), and Herc (Adén et al. 2011). We add to the comparison halo and classical dSphs stars presented in Kirby et al. (2010). Right:
Comparison of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe] abundance ratios for the same sample. The [ α j / Fe] abundance uncertainties for the UFD stars weremeasured as described in § 3.4. All measurements have been transformed to the Asplund et al. (2009) abundance scale. The dotted lines indicate a difference of + . - . [ α j / Fe] were detect due to a lack of signal. Table 1 sum-marizes basic properties for each UFD, the number of starswith available [ α/ Fe] measurements, and the weighed aver-age metallicity for each UFD using only these stars.
Comparison with High - Resolution Studies
To validate our technique, we compare our results againsthigh - resolution (HRS) abundances for overlapping stars inCom Ber, UMa II (Frebel et al. 2010), Leo IV (Simon et al.2010), and Herc (Adén et al. 2011). Figure 3 shows the re-sults of this comparison for [Fe/H] (left panel) and the indi-vidual [ α j / Fe] abundance ratios (right panel), where all abun-dances have been placed in the Asplund et al. (2009) abun-dance scale. Due to the small number of matching stars,we add to the comparison a set of halo stars with DEIMOSand high - resolution measurements analyzed by Kirby et al.(2010) using the same technique. We note that our modifi-cation to Kirby et al. (2010)’s approach lies in the determina-tion of abundance uncertainties , and hence does not affect thecomparison in Figure 3.We find good agreement between [Fe/H] in both sam-ples, with a mean difference of - . ± .
022 dex in thesense HRS - DEIMOS, where the uncertainty is the stan-dard error of the mean. The individual abundance ratiosdo not show any systematic offsets. The mean differencesfor [Mg/Fe], [Si/Fe], [Ca/Fe] and [Ti/Fe] are + . ± . - . ± . - . ± . . ± .
033 dex, re-spectively, demonstrating that we obtain accurate abundancesover our entire range of values. ABUNDANCE RESULTS I: INDIVIDUAL UFDS
The alpha abundances reflect the enrichment from SNe, andthus help constrain the underlying star formation history of agalaxy. In this section, we highlight the most salient quali-tative trends for each UFD. We present the abundance mea-surements for all eight UFDs in Table 2. Figure 4 shows the[ α/ Fe] avg - [Fe/H] trends for each UFD in our sample, in or-der of increasing luminosity. The stars in each of our UFDsspans a range in metallicity greater than 1 dex. We discuss theimplications of these trends in § 6.1. Segue 1. - Seg 1 is the faintest and nearest UFD known to date. We measure [ α/ Fe] abundances for the 5 stars for whichS11 reports metallicities (excluding the star with only an up-per metallicity limit, [Fe/H] < - . & α/ Fe] avg abundanceratios do not show any noticeable decrease with [Fe/H] andare roughly constant at ∼ + . / H] ∼ - . / H] ∼ - . ∼ . ∼ - .
6, sugges-tive of a lack of pollution by Type Ia SNe. The only published[ α/ Fe] abundance ratios in Seg 1 are those of Norris et al.(2010b). Using high - resolution, they report [Mg/Fe] = +0.94,[Si/Fe] = +0.80, [Ca/Fe] = + 0.84, and [Ti II/Fe] = +0.65 fora [Fe/H] = - star (not in our sample). Theirmeasurement agrees with the abundances measured in ourmost metal - poor star, which has a comparable metallicity . Coma Berenices. - Although there is no published con-straint on its age spread, Com Ber’s CMD appears consistentwith a very old age, with no intermediate age stars (Figure 3 ofMuñoz et al. 2010). Com Ber shows high [ α/ Fe] avg , greaterthan + .
4, at lower [Fe/H] and lower [ α/ Fe] avg by ∼ . - resolution spectroscopy, Frebel et al. (2010) also re-ported enhanced alpha abundances at [Fe/H] < - .
5, whereastheir most metal - rich star shows systematic lower [ α/ Fe]abundance ratios by ∼ . Ursa Major II. - As for Com Ber, the CMD of UMa II issuggestive of a very old stellar population with no interme-diate age stars (Muñoz et al. 2010). In contrast to Com Ber, CEMP-no: Carbon - enhanced, metal - poor star without heavy neutronelement enhancements, see summary of CEMP nomenclature in Norris et al.(2013) We cannot comment on the CEMP classification of our star, but note thata significant fraction of metal - poor stars are carbon - enhanced (Norris et al.2013). Thus, we caution the reader that this abundance comparison may onlybe fully warranted if our star is also a CEMP - no object. Vargas et al.
Table 1
UFD Basic DataUFD R a helio (kpc) V b rad (km/s) σ b V (km/s) M V c N Mg N Si N Ca N Ti N [ α / Fe] avg h [Fe / H] i d Segue 1 23 208 ± ± - - . ± . ± ± - - . ± . - ± ± - - . ± . - ± ± - - . ± . ± ± - - . ± . - ± ± - - . ± . ± ± - - . ± . ± ± - - . ± . a R helio from Martin et al. (2008b); see references therein for each UFD. b V rad and σ V taken from Simon & Geha (2007) except for Segue1, taken from Simon et al. (2011). c M V from Martin et al. (2008b) except for Leo T, taken from Irwin et al. (2007). d h [Fe / H] i is the mean metallicity for each UFD using only the stars with good [ α / Fe] avg measurements (see § 3.4.)
UMa II shows signs of tidal stripping, suggesting it may haveoriginally been a more luminous satellite. All of our [ α/ Fe] avg measurements cluster at [ α/ Fe] avg ∼ + .
4, spanning a largerange of metallicities up to [Fe / H] ∼ - .
1. The three mostmetal - poor stars are overabundant in [Si/Fe] by ∼ . < - .
3. We measure [Si / Ca] = + . ± .
37 for a sin-gle star, which was also studied by Frebel et al. (2010) (theirUMa - S2). They only measure an upper limit on [Si/Fe],[Si / Fe] < + .
46. In combination with their [Ca/Fe] measure-ment, their upper limit for [Si/Ca] is + .
08, in agreementwith our measurement. We defer the discussion of anomalousabundance ratios to § 5.3.
Canes Venatici II. - The next five UFDs are at consider-ably larger distances than the previous three (see Table 1).Ground - based photometry suggests that CVn II is composedexclusively of an old ( >
10 Gy) stellar population (Sand et al.2012; Okamoto et al. 2012). We present for the first time[ α/ Fe] abundance ratios for this galaxy. At [Fe / H] < - α/ Fe] avg abundance ratios, hint-ing at some intrinsic scatter. On average, [ α/ Fe] avg is higherat lower [Fe/H]. The distribution of [Ca/Fe] and [Ti/Fe] abun-dance ratios tentatively supports the presence of significantscatter at low [Fe/H].
Leo IV. - Brown et al. (2012) have recently constrained thespread of ages of the stellar population to less than ∼ α/ Fe] avg for four stars, which are consis-tent with either a shallow increase in [ α/ Fe] avg with decreas-ing [Fe/H], or a constant enhancement of ∼ . > . α/ Fe] avg . We note that the largeruncertainties in all abundance ratios (relative to other UFDs)are due to the low S/N of the DEIMOS spectra for this satel-lite. In agreement with our result, Simon et al. (2010) reportenhanced [ α/ Fe] abundance ratios for the brightest RGB, LeoIV S1. This star is also included in our sample; a comparisonof the abundance ratios can be seen in Figure 3.
Ursa Major I. - Brown et al. (2012) have shown that thestellar population is ancient, and constrained the spread inages to less than ∼ α/ Fe] abun-dance ratios measured in UMa I. The [ α/ Fe] avg abundancepattern for UMa I shows on average increasing [ α/ Fe] avg abundance ratios towards lower [Fe/H], with the possible ex-ception of [Ca/Fe]. There is a hint of increased intrinsic scat-ter in [ α/ Fe] avg and [Ca/Fe] at low [Fe/H], indicating that thisgalaxy might have experienced inhomogeneous chemical en-richment.
Hercules. - Brown et al. (2012) have constrained the ageand age spread in star formation to be similar to that in Leo IVand UMa I. We present measurements of [ α/ Fe] avg for 13stars, currently the largest published sample of [ α/ Fe] forthis UFD. One of our stars has [Mg / Ca] = + . ± .
21. Wediscuss its abundance pattern further in § 5.3. Herc shows aclear trend for rising [ α/ Fe] avg , [Si/Fe], and [Ca/Fe] towardslower [Fe/H], with little scatter, reaching [ α/ Fe] avg ∼ + . α/ Fe] avg enhancement seems system-atically lower at fixed [Fe/H] than in Seg 1 and Com Ber.The data is insufficient to suggest any pattern in the case of[Mg/Fe] and [Ti/Fe]. Recently, Adén et al. (2011) reportedhigh - resolution [Ca/Fe] abundance ratios for 10 RGB starsin Hercules (eight overlap with our sample) with [Ca/Fe]varying from ∼ + . ∼ - . ∼ - . ∼ -
2, concluding that Herc experienced very ineffi-cient star formation. Our measurements confirm the trend ofdecreasing [Ca/Fe] with rising [Fe/H].
Leo T . - Leo T (Irwin et al. 2007) is the only UFD withevidence for recent star formation (e.g., Weisz et al. 2012;Clementini et al. 2012). It also has a large amount of HI gas(Ryan-Weber et al. 2008). These two properties distinguishit from all the other UFDs in this study. We have measured[ α/ Fe] avg for 5 stars, 4 of which cluster around [Fe/H] ∼ - α/ Fe] avg from ∼ - . ∼ + .
7. Theonly element with > ∼ -
2. All [Ti/Fe] measure-ments cluster between - . + . α/ Fe] stars is expected for systems with extended starformation.
In summary , we observe the following trends for the indi-vidual UFDs: • All UFDs have on average high [ α/ Fe] abundance ra-tios ( & + .
3) at [Fe/H] < - .
5. High [ α/ Fe] abun-dance ratios are consistent with chemical enrichmentby Type II SNe. • Most stars with [Fe/H] > - . α/ Fe] avg abun-dance ratios, [ α/ Fe] avg < + .
4, suggesting that chem-ical evolution lasted at least as long as the minimumtime delay for Type Ia SNe. • Seg 1 and UMa II are alpha - enhanced across their en-lpha Elements in UFDs 7 Table 2
Abundance ResultsUFD RA (J2000) DEC (J2000) [Fe/H] [ α / Fe] avg [Mg/Fe] [Si/Fe] [Ca/Fe] [Ti/Fe]Seg 1 10 : 06 : 52 . +
16 : 02 : 35 . - ± + . - . +0.76 + . - . Seg 1 10 : 07 : 10 . +
16 : 06 : 23 . - ± + . - . +0.70 + . - . +0.68 + . - . +0.58 + . - . +0.39 + . - . Seg 1 10 : 07 : 14 . +
16 : 01 : 54 . - ± + . - . +0.43 + . - . +0.52 + . - . +0.33 + . - . +0.25 + . - . Seg 1 10 : 07 : 42 . +
16 : 01 : 06 . - ± + . - . +0.87 + . - . +0.99 + . - . +0.59 + . - . +0.71 + . - . Seg 1 10 : 07 : 02 . +
15 : 50 : 55 . - ± + . - . +0.74 + . - . +0.66 + . - . +0.58 + . - . Com Ber 12 : 26 : 29 . +
24 : 04 : 03 . - ± + . - . Com Ber 12 : 26 : 45 . +
23 : 50 : 44 . - ± + . - . +1.07 + . - . +0.26 + . - . +0.76 + . - . Com Ber 12 : 26 : 55 . +
23 : 56 : 09 . - ± + . - . +0.97 + . - . +1.20 + . - . +0.68 + . - . +0.57 + . - . ... ... ... ... ... ... ... Note . — Table 2 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here forguidance regarding its form and content.
Figure 4. [ α / Fe] avg as a function of [Fe/H] for each UFD in our sample, ordered by increasing galaxy luminosity. The bottom - right panel shows the combinedUFD sample, also seen in Figure 5. Each UFD is assigned a different color. We use the same color scheme throughout the paper. Five of the UFDs have ancientstellar populations and show an overall decrease in [ α / Fe] avg with increasing [Fe/H]. We discuss their evolution in § 6.1.1. We use filled squares for stars inthese galaxies and empty squares for the others. The presence of low [ α / Fe] avg stars at higher [Fe/H] strongly suggests that Type Ia SNe chemically enrichedthe ISM of these UFDs. Due to the time delay for Type Ia SNe after the onset of star formation, t min , Ia , our data suggests that most UFDs underwent at least alimited time period of extended chemical evolution, no shorter than t min , Ia ∼
100 Myr. tire metallicity range. They do not show a statisticallysignificant decrease in [ α/ Fe] abundance ratios as afunction of [Fe/H], in contrast to the other UFDs. • The degree of alpha enhancement shows some hint ofbeing different between UFDs, with Com Ber and Seg 1having higher [ α/ Fe] abundance ratios than Herc orUMa II at [Fe / H] ∼ -
3. This could be a reflection of adifferent mix of SNe across the various UFDs, stochas-tic sampling of the same IMF, and/or inhomogeneousmixing. ABUNDANCE RESULTS II: THE ENSEMBLE OF UFDS
A comparison of chemical abundances can shed light on therelationship between different stellar populations. It has beenpreviously shown that the [ α/ Fe] - [Fe/H] pattern in the clas-sical dSphs disagrees with the Milky Way inner halo patternfor [Fe/H] & -
2. Building on this difference, simulations byRobertson et al. (2005) have suggested that the major build-ing blocks of the inner halo had different star formation his-tory than the extant classical dwarf galaxies.Here, we compare the abundance patterns in our UFD sam- Vargas et al.ple against the inner halo, and also against one classical dSph,CVn I. With M V = - . ∼ &
10 Gy)population (Martin et al. 2008a; Okamoto et al. 2012). Weuse the CVn I sample from Kirby et al. (2010), reanalyzedto reflect our updated uncertainty analysis, which does notassume symmetric uncertainties (§ 3.4). We include the rean-alyzed abundance measurements for CVn I (referenced to theAsplund et al. 2009 solar abundance scale) at the bottom ofTable 2. The CVn I sample actually extends to [Fe / H] < - α/ Fe] abun-dance ratios for our combined UFD sample against the innerhalo population. For the halo sample, we calculated [ α/ Fe] avg as the mean of the available [Mg/Fe], [Si/Fe], [Ca/Fe], and[Ti/Fe] abundance ratios. The right panels show a compar-ison of the [ α/ Fe] abundance patterns of the more massivedSph CVn I against Milky Way inner halo stars. We explainour statistical comparison method in § 5.1, and describe theresults in § 5.2. We comment on the presence of two starswith anomalous abundance ratios in § 5.3.
MCMC Modeling of Empirical [ α j / Fe] - [Fe / H] Trends
In order to identify the best - fitting trend in [ α/ Fe] - [Fe/H]space in a statistically robust way, we define simple param-eterizations of the various trends predicted by chemical evo-lution models. In these models, the ISM is quickly enrichedby ejecta from Type II SNe, resulting in high [ α/ Fe] at low[Fe/H]. The onset of Type Ia SNe ejects more Fe - peak richmaterial and acts to lower [ α/ Fe]. Due to the delayed onsetof Type Ia relative to Type II SNe, the change in [ α/ Fe] canbe seen as a turnover or knee at a particular [Fe/H]. After-wards, the decrease in [ α/ Fe] is modulated by the number ofType II and Type Ia SNe that explode. It is possible to increase[ α/ Fe] with a late - time starburst (Gilmore & Wyse 1991). Empirical [ α j / Fe] - [Fe / H] Models
We consider three simple models describing a path in[ α j / Fe] - [Fe / H] space, where [Fe/H] and [ α j / Fe] are de-fined as the x and y coordinates. The "Constant [ α/ Fe]Model" (Model A) is a single - parameter model with a con-stant value of [ α j / Fe] at all [Fe/H], i.e. a flat line with y = y .It is representative of Type II SNe enrichment. The "SingleSlope Model" (Model B) is a two parameter linear modelwith freely - adjustable slope, m = dy / dx and y - intercept, b , y ( x ) = m x + b . This model is representative of Type Ia SNeenrichment.Equations 1 - α j / Fe] seg-ments. It represents early Type II SNe enrichment followedby a phase where Type Ia SNe contributed to the chemicalevolution. y ( x ) = m [Fe / H] + b ; x ≤ [Fe / H] (1) y ( x ) = m x + b ; x > [Fe / H] (2) Here, [Fe / H] defines the boundary between the two seg-ments, and is typically referred to as the knee. Parameters m and b are defined as in Model B. Probability Distribution Functions for each Model
We seek to calculate the best - fit parameters and associ-ated confidence intervals for each model given a dataset D ,where D is a set of [Fe/H] and [ α j / Fe] abundances.
Due toour asymmetric uncertainties, we cannot rely on a simple re-gression analysis . For this purpose, we use a Markov - chainMonte Carlo method to calculate P ( θ | D ), the joint probabilitydensity functions for each model as a function of its parame-ters θ given D . Specifically, we measure the probability den-sity functions P A ( y ), P B ( m , k icpt ), and P C ( m , k icpt , [Fe / H] )for models A, B, and C. The primary input to the Markovchain are likelihoods for the full dataset D given a realizationof θ , L ( D| θ ). This in turn requires calculating L i , the likeli-hood of star i being drawn from the model.Due to the non - Gaussian [ α/ Fe] atm and [ α j / Fe] uncertain-ties discussed in §3.4, we make use of the probability distribu-tion for each abundance to calculate L i . We denote these prob-ability distributions as F, to avoid confusion with P ( θ | D ). Wecompute the random component of F ([ α j / Fe]) from the χ contours described in § 3.4. The probability of a star havingabundance y is given by Equation 3, and peaks at χ .F ran ( y ) ∝ exp (cid:20) - (cid:0) χ ( y ) - χ (cid:1)(cid:21) (3)We incorporate the systematic uncertainty in each measure-ment by convolving F ran with a Gaussian with zero mean andstandard deviation equal to σ sys . The full probability functionfor [ α j / Fe] is given in Equation 4.F ( y ) = Z F ran ( y ′ ) 1 q πσ exp " - (cid:18) y - y ′ σ sys (cid:19) dy ′ (4)In contrast to [ α j / Fe] , the [Fe/H] χ contours are symmet-ric for total uncertainties up to σ [Fe / H] ∼ . x ), as a Gaus-sian with σ [Fe / H] , centered on the best - fit [Fe/H] value. Wenow calculate L i using Equation 5. L i ∝ Z F ( x ) F ( y ( x )) dx (5)The full likelihood L ( D| θ ) is the product of the individ-ual likelihoods for stars 1 ≤ i ≤ N, L = Q Ni =1 L i . We run theMarkov chain using the Metropolis-Hastings algorithm with aGaussian - distributed kernel. We constrain [Fe/H] to lie morethan 0.3 dex away from the minimum in the sample, and be-low [Fe / H] = -
2. We chose this prior by noting that no kneehas been observed in brighter dSphs at higher metallicities.We constrain the slope in Models B and C to m <
0. We runeach chain for 100,000 steps for models A and B, and 250,000steps for Model C. The larger number of steps is needed tobetter sample the larger parameter space in this model. Inall cases, the first 1,000 steps are discarded as a burn - in pe-riod. For each step k , we compute the ratio of likelihoods r ≡ L k / L k - between the k and k - The ratio r is actually defined using the ratio of posterior probabilities lpha Elements in UFDs 9 Figure 5.
We compare [ α / Fe] avg abundance ratios in the UFDs ( left panels : filled/empty colored squares, same color and point scheme as in Figure 4), theMilky Way inner halo (small gray crosses in both panels ), and the CVn I classical dSph ( right panels : filled black squares). In the left panels, we ask whetherthe UFD population shares a similar abundance pattern as the inner halo. In the right panels, we compare CVn I and the inner halo. From top to bottom, weplot the [ α / Fe] avg , [Mg/Fe], [Si/Fe], [Ca/Fe] & [Ti/Fe] abundance ratios. For the inner halo, we rely on the metal - poor star abundance compilation by Frebel(2010), with all abundances referenced to the Asplund et al. (2009) solar abundance scale. For CVn I, we use Kirby et al. 2010’s CVn I sample, reanalyzed usingour updated analysis technique (§ 3). We qualitatively summarize the results of the statistical comparison described in § 5. Both the UFDs and CVn I showlower [ α / Fe] abundances than the inner halo at higher [Fe/H]. In addition, CVn I shows a hint of a turnover in [ α / Fe] at a metallicity between - - - detection of a turnover at [Fe / H] > -
3. Our data highlightsthat both UFDs and classical dSphs have a different chemical evolution than the inner halo.
We accept the new set of parameters if r > < U (0 , < r <
1, where U (0 ,
1) is a uniform deviate be-tween 0 and 1. Otherwise, we reject the trial step and save theparameters from step k - k .The density of points in the chain defines P( θ |D ). Wedetermine the best - fit parameters from the peak of theone - dimensional probability distribution of each parameter.We determine the associated 68% Bayesian confidence inter-vals by constructing the cumulative probability function foreach parameter and finding the parameters associated withvalues of 0.16 and 0.84 in the cumulative function. We thenobtain an optimal set of parameters for each model, as well asan associated likelihood. for parameters θ k and θ k - given data D , P( θ k |D ) / P( θ k - |D ). P and L arerelated by Bayes’ Theorem as P k ( θ |D ) , ∝ L k ( D| θ ) π ( θ k ), where π ( θ k ) isthe prior probability of the set of parameters θ k . Under our assumption ofuniform priors, the two ratios are identical. Abundances in the UFD vs the Inner Halo and theClassical dSphs
High - resolution studies have shown that local Milky Wayhalo stars (mostly belonging to the inner halo) have ap-proximately constant [ α j / Fe] abundance ratios in the [Fe/H]range sampled by our data, - < [Fe/H] < - α j / Fe] is indeed flat in all fourelements in our [Fe/H] range. In contrast, the classical dSphsare known to have lower [ α/ Fe] at [Fe / H] & -
2, while their[ α/ Fe] abundance patters may broadly resemble the halo at[Fe / H] . - α/ Fe] with decreasing [Fe/H] (denoted by filled squaresin Figure 4); (b) the full UFD sample; and (c) the CVn I sam-0 Vargas et al.ple. For each dataset, we obtain best - fitting Models A, B, andC, and the associated maximum likelihoods, L A , L B , L C . Wethen assess the goodness of fit between each of the best - fittingmodels. We note that these are nested models, such thatModel A is a subset of Model B, itself a subset of Model C.We can thus use the likelihood ratio test in order to comparewhether the more complex model is statistically a better fitthat the simpler one. We compare two models at a time. Giventhe best - fit set of parameters for each of two models, e.g., Aand B, the simpler model can be rejected at the (1 - α ) × R B , A ≡ ln L B L A > F χ ( α ; n B - n A ) = F χ ( α ; k = 1) (6)Here, F χ ( α ; n B - n A ), is the cumulative χ function with n B - n A free parameters. In our case, n B - n A = 1.We report the likelihood ratio ( R values) in Table 3. Thebest - fit models for the restricted UFD sample and the CVn Isample in the [ α/ Fe] avg - [Fe/H] plane are presented in Figure6. In both the CVn I and UFD panels, the blue band representsthe range of slopes consistent within the joint σ uncertaintycontour of m and y .We first ask whether the UFD population has an abundancepattern consistent with the flat inner halo, using both the re-stricted and the full UFD sample. The Flat model can beruled out at the 90% (99.5%) level if R B , A ≥ + . R B , A = 6 .
02 for [Ca/Fe] in the UFD restricted sam-ple (+2.50 for the full sample), and R B , A >
10 for [Si/Fe],[Ti/Fe], and [ α/ Fe] avg for both samples, thus strongly rul-ing out the Flat model. This is also evident from a visual in-spection of Figure 6 in the case of [ α/ Fe] avg . We have notedthat only 10 stars have [Mg/Fe] measurements, and these arenot evenly distributed among all UFDs. Hence we do notregard this fit as significant. We also perform a comparisonof the Flat and Linear models for CVn I, and similarly con-clude that the Linear model is a better fit than the Flat Modelfor all abundance ratios ( R B , A ranges from +5.78 to +48.66). Hence, both UFDs and brighter dSphs have alpha abundancepatterns different than the Milky Way inner halo.
Next, we test the UFD sample and CVn I for the influenceof Type Ia SNe enrichment by comparing the Linear Modelagainst the Knee Model, which has one more free parameter.Again, we perform this test for the five UFDs with a clear[ α/ Fe] trend, and for the full UFD sample. In both cases, thelikelihood ratio test indicates that the UFD data is consistentwith the Linear model (within the range of [Fe/H] of our data),so that adding a knee does not improve the fit. In contrast, wefind that that the CVn I [ α/ Fe] avg data is best - fit by a Kneemodel with a knee at [Fe/H] = - . + . - . dex. The [Fe/H]value of the knee in the [ α/ Fe], and [Si/Fe] plots agree withintheir 1 σ uncertainties. While the R C , B value for [ α/ Fe] avg suggests that a knee is present at this low [Fe/H], our datacannot rule out a model without a knee in the case of the in-dividual alpha elements, for which R C , B < .
2. The hint of aknee in CVn I at [Fe/H] > - . & - flat abundance trend at lower[Fe/H] should be better interpreted broadly as evidence for achange in behavior in the [ α/ Fe] - [Fe/H] plane indicative of Figure 6.
Top panel:
Fits to models for [ α / Fe] avg - [Fe / H] trends for thefive UFDs with ancient stellar populations and increasing [ α / Fe] with de-creasing [Fe/H] (shown with filled squares). The empty squares indicate starsin the three excluded UFDs (see Figure 4).
Bottom panel : Fits to models forthe CVn I dSph. The green (dashed), blue (solid), and red (dot - dashed) linesindicate the best - fitting "Flat Model" (A), "Linear Model" (B), and "KneeModel" (C), respectively. The shaded blue band denotes the range of slopeswithin the joint 68% confidence region of the two parameters in the Lin-ear Model. In the CVn I panel the best - fitting trend for the Knee Model isclearly distinct from the 68% band of the Linear Model. Using a likelihoodratio test applied to both models, we show that the Knee Model is signifi-cantly preferred over the Linear Model in the case of [ α / Fe] avg for CVn IThe same test cannot distinguish between the Linear and Knee Models whenapplied to the combined UFD sample, even for [ α / Fe] avg . The results areunchanged if using all eight UFDs. Thus, the UFD sample is consistent withrising [ α / Fe] avg towards lower [Fe/H], but its abundance pattern may differfrom that of CVn I at [Fe / H] . - . the onset of Type Ia SNe, and not as strictly "flat" [ α /Fe] ra-tios at low metallicities. Even in the absence of Type Ia SNe,chemical enrichment likely depends on the mass of the pro-genitor Type II SNe (Woosley & Weaver 1995; Nomoto et al.2006). If the number of Type II SNe is small, then thefirst (most massive) SNe enrich the ISM with higher alphaabundance ratios, which then decrease as less massive SNeexplode. This can result in a non - zero negative slope in[ α/ Fe] - [Fe/H], if the UFDs metallicity increases with time. Anomalous Abundance Ratios
Anomalous abundance ratios may be associated withenrichment from individual Type II SNe, given themass - dependence of Type II SNe ejecta (e..g, Nomoto et al.2006). Recent papers (e.g., Koch et al. 2008; Feltzing et al.2009) have reported a few stars with anomalous abundanceratios, but the presence of such stars remains controversial(e.g., Gilmore et al. 2013 do not confirm the measurementby Feltzing et al. 2009). In the context of the UFDs studiedhere, Koch et al. (2008) reported a [Mg/Ca] = +0.94 star (theirHer - ∼ ⊙ Type II SN. We search oursample for anomalous [Mg/Ca] and [Si/Ca] abundance ratios.We conservatively define an abundance ratio between two al-lpha Elements in UFDs 11
Table 3
Relative Statistical Likelihood for Halo, Linear, and Knee ModelsElement R B , A (UFDs a ) R C , B (UFDs a ) R B , A (UFDs b ) R C , B (UFDs b ) R B , A (CVn I) R C , B (CVn I)[ α /Fe] +29.82 - - - - - - - - - - - Note . — Comparison of likelihood of best - fit parameters for the models discussed in § 5.2. Equation 6 defines R x , y for any two models x and y . The letters A, B, and C stand for "Flat Model", "Linear Model", and "Knee Model". Thebest model fits for the UFDs a and CVn I are presented in Figure 6. a Restricted UFD sample: Systems with ancient stellar populations and qualitative trends of increasing [ α / Fe] withdecreasing [Fe/H]: Com Ber, CVn II, Leo IV, UMa I, and Herc b All UFDs pha elements ([X/Y]) as anomalous if (a) the abundance ratiois more than 1 - σ greater than + . - σ less than - . and (b) the abundance ratio is discrepant by more than 1 - σ fromthe mean computed for the entire UFD sample, h [X / Y] i .We tentatively identify anomalous abundance ratios in twostars, one of which is the object reported in Koch et al.(2008). Our measurement for that star is [Mg/Ca] = + . ± .
21 at [Fe / H] = - . ± .
12. The mean [Mg/Ca] for thesubsample with both [Mg/Fe] and [Ca/Fe] measurementsis h [Mg / Ca] i = + . ± .
07 (error on the mean). We cau-tion that only 10 stars have a [Mg/Fe] measurement, dueto the weakness of Mg spectral features, making this sub-sample small. We also identify in UMa II a single star([Fe/H]= - . ± .
16) with an anomalous [Si/Ca] abundanceratio ([Si / Ca] = 1 . ± . h [Si / Ca] i = + . ± .
05. This star is alsostudied by Frebel et al. (2010) as UMa II - S2, but they only re-port an upper limit on [Si/Fe]. Using their [Si/Fe] upper limitand their [Ca/Fe] measurement, we obtain [Si / Ca] < + . DISCUSSION
Chemical Evolution in Individual UFDs
The distribution of alpha abundances allows to us to build ageneral picture of chemical evolution in the UFDs. The firstexplosions from Population III (Pop III) and/or massive PopII stars provide the initial chemical enrichment of the UFD’sISM, depositing large quantities of alpha elements into thegas from which later stars form. The low [Fe/H], high [ α/ Fe]stars in our sample are formed from metal - enriched gas fromthese early SNe. This is a general feature in all of our UFDs.In contrast, our sample includes UFDs with and without low[ α/ Fe] abundance ratios at high [Fe/H]. We note that the twodwarfs without low [ α/ Fe] avg both have M V > - .
2. Hence,this distinction may still hint at a threshold for significantchemical evolution at M V ∼ -
4. However, Com Ber also hasM V > - . α/ Fe] avg stars. In additionto the general trend with [Fe/H], we note that there is a hintfor an increase in scatter (beyond the observational uncertain-ties) in [ α/ Fe] avg at lower [Fe/H]. This may hint towards in-homogeneous chemical enrichment (e.g., Argast et al. 2000;Oey 2000), where the products of individual SNe contami-nate different regions of the ISM without complete mixing. We discuss the two different abundance patterns in turn, butstrongly caution that this distinction may only be the result ofsmall samples for individual UFDs. M V < - . UFDs and Com Ber
Every bright UFD in our sample with M V < - . α/ Fe] abundance ratios, the majority of whichcluster at high [Fe/H]. The presence of low [ α/ Fe] ratios isa strong indicator that star formation proceeded at least aslong as needed for Type Ia SNe to explode. The minimumtime delay between the onset of star formation and the firstType Ia SNe, t min , Ia , is not yet constrained precisely, but maybe as short as ∼
100 Myr (see review by Maoz & Mannucci2012). In our discussion, we adopt t min , Ia = 100 Myr. Thus,the low [ α/ Fe] stars suggest that star formation in theseUFDs lasted longer than t min , Ia , and that the first generation ofType II SNe does not succeed in quenching star formation inthese systems. Additionally, the decrease in [ α/ Fe] ratios at[Fe/H] ∼ - . - enrichmentprior to the onset of Type Ia SNe. This is consistent with asystem with a very low star formation rate. Seg 1 and UMa II (M V > - . ) The Seg 1 and UMa II UFDs are the only systems whichdo not show any low [ α/ Fe] stars. This suggests that starformation lasted less than ∼
100 Myr. In contrast to all otherUFDs, the high [ α/ Fe] stars extend to much higher [Fe/H].Such high [Fe/H] stars are difficult to explain using the trendsfound for the other UFDs, i.e. systems with low star forma-tion efficiencies. Frebel & Bromm (2012) have recently de-scribed a scenario for such one - shot chemical enrichment .In this picture, after the first Pop III stars, there is a singleepoch of star formation, after which all gas is blown out ofthe system by SNe feedback or reionization. In this picture,the large spread in [Fe/H] arises from highly inhomogeneousgas mixing, as also pointed out by Argast et al. (2000) andOey (2000). Large [Fe/H] spreads can perhaps instead be theresult of accretion of multiple progenitor systems, each with adifferent metallicity (Ricotti & Gnedin 2005). An alternativeexplanation for the early loss of gas before t min , Ia is gas strip-ping due to accretion onto the Milky Way. We thus considerin more detail the different possibilities for the quenching ofstar formation, taking into account our [ α/ Fe] results for eachUFD.
Quenching of Star Formation - day galactocentricposition and line - of sight velocities of subhalos in the ViaLactea 2 simulation, calculating the probability distributionof the infall time for UFDs and classical dSphs (their Figure4). Interestingly, only Seg 1 and UMa II, the two UFDs withflat [ α/ Fe] - [Fe/H] patterns, show a significant probability ofinfall onto the Milky Way halo more than 12 ago (Com Bermay have an infall time as old as ∼
11 Gyr ago). The early in-fall suggests that gas stripping and/or heating due to accretionplayed a role in terminating star formation before low [ α/ Fe]stars could form. However, the presence of high [Fe/H] starsposes a problem to this interpretation, since the presence ofhigh [ α/ Fe], high [Fe/H] stars is attributed to systems withhigh star formation efficiencies. Thus, it is also possible thatinternal effects, e.g., winds from SNe, managed to get rid ofor heat all of the remaining cold gas reservoir.In contrast to Seg 1 and UMa II, the other UFDs have in-ferred infall times younger than 10 Gyr (Rocha et al. 2012).Brown et al. (2012) have reported upper limits on the dura-tion of star formation of less than ∼ α/ Fe] abundance ratios suggests thatstar formation lasted for at least ∼
100 Myr in most UFDs.Assuming that the first Pop III stars form ∼
180 Myr ( z ∼ after z ∼ .
5. This approximate upperlimit on the redshift at which quenching occurred changes de-pending on the actual minimum time delay for Type Ia SNe.If the minimum time delay for Type Ia SNe is on the orderof 500 Myr instead (five times the value adopted above), thenquenching happened no earlier than z ∼ .
7. The process ofreionization likely extends for an extended range in redshift:14 . z . - drivenquenching (Bullock et al. 2000; Ricotti & Gnedin 2005). Inboth scenarios, the effect of the first SNe explosions (fromPop III and/or massive Pop II stars) must still allow for starformation to proceed long enough for Type Ia SNe to explodeand enrich the ISM. The UFDs and the Halo
In § 5.2, we characterized the distribution of [ α/ Fe] abun-dances as a function of [Fe/H]. We showed that the probabil-ity that this distribution is drawn from a flat, inner - halo-likeabundance pattern is less than a few percent. This fully agreeswith a picture where the bulk of the inner halo forms from theaccretion of a few massive satellites undergoing efficient starformation (Robertson et al. 2005), rather than the UFDs.The fractional contribution of stars to the halo from UFDsmay rise towards lower metallicities. The Milky Way halois known to host extremely metal - poor stars (EMPs) with[Fe / H] ≤ -
3. In contrast to the classical dSphs, the UFDs host a significant fraction of EMPs. Our sample, which isnot metallicity - biased, has 10 EMP stars out of 61. Atthese low [Fe/H], the similarity in alpha enhancement be-tween the halo and the combined UFD sample alone doessuggest a larger contribution of the UFDs or UFD - like sys-tems to the low metallicity tail of the inner halo. Since starformation likely ceased in the UFDs significantly prior to be-ing accreted into the Milky Way potential, it suggests that thepresent - day UFD abundance patterns may be similar to thoseof UFDs accreted in the past, so that a large population ofUFDs with similar abundance patterns may have contributedto the build - up of the EMP inner halo. This picture will needto be refined and tested by comparing other species with dif-ferent nucleosynthetic origins, such as neutron - capture ele-ments. For example, high - resolution studies of small num-bers of stars in the UFDs suggest that the mean [Ba/Fe] ratioin Com Ber (Frebel et al. 2010) is lower than in UMa II orBoötes I (Gilmore et al. 2013). In contrast to Com Ber, thesetwo UFDs have [Ba/Fe] ratios more similar to those of theMilky Way inner halo at [Fe / H] ∼ - . α/ Fe] stars in the range - . < [Fe / H] < - .
4. These are likely outer halo stars withhigh eccentricities, which thus take them as close as the So-lar radius. However, orbits calculated to date for a few dSphs(e.g., Piatek et al. 2005) show that their orbits are not likelyto pass as close as the Solar Galactocentric radius. All UFDsare at present at least as far as R GC ∼
28 kpc. Thus, a full un-derstanding of the UFD/dSph - outer halo connection awaits adetailed mapping of chemical abundances in the in - situ outerhalo. CONCLUSIONS
We analyze Keck/DEIMOS spectroscopy of RGB stars ineight UFDs using a spectral matching technique to measureand characterize the distribution of [ α/ Fe] abundance ratios.In this paper, we report [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe],as well as a combined alpha to Fe abundance ratio, [ α/ Fe] avg ,for 61 stars in these systems. We summarize our main con-clusions as follows: • Out of seven UFDs with ancient stellar populations,five (Coma Berenices, Canes Venatici II, Ursa MajorI, Leo IV and Hercules) show an increase of [ α/ Fe]towards lower [Fe/H], and low [ α/ Fe] ratios for theirhighest [Fe/H] stars, implying that Type Ia SNe hadenough time to pollute the ISM. This suggests thatstar formation was an extended process, lasting at least ∼
100 Myr, corresponding to the minimum time delaybetween the onset of star formation and the first Type IaSNe. Leo T, which has a much more extended star for-mation history, shows the same abundance pattern. • The remaining two UFDs with old populations, Segue 1and Ursa Major II, show enhanced [ α/ Fe] ratios at all metallicities, ranging from - . . [Fe / H] . - . - enhancement inlpha Elements in UFDs 13Segue I is higher than in UMa II by ∼ . α/ Fe] stars suggests that the star for-mation period was very short, less than ∼
100 Myr. • The combined population of UFDs shows a clear in-creasing trend in [ α/ Fe] with decreasing [Fe/H], withno evidence for a plateau within our entire metallicityrange. Although this rise in [ α/ Fe] disagrees with theflat inner halo abundance pattern, a significant numberof [Fe / H] < - . - poor star (EMP) halo abundance patternmay be more significant at the lowest metallicities. • The abundance pattern in the UFDs shows some differ-ence with respect to the brighter CVn I dSph. We showthat, in contrast to the UFD population, there is a hintfor a plateau at [Fe/H] ∼ - . α/ Fe] abundance ratios thatmost of the UFDs were able to retain gas and form stars longenough for the first Type Ia SNe to explode, and that this evo-lution proceeded inefficiently. The use of medium - resolutionspectroscopy has been instrumental in providing us with largeenough samples to begin to address the evolution of these sys-tems. Future studies will aim to study the details of this evo-lution by comparing the shape of the metallicity distributionfunction of each UFD to chemical evolution models. For in-stance, evidence for a rapid shutdown in star formation dueto reionization may appear as an abrupt cutoff in the metal-licity distribution function at the higher [Fe/H] end. Due tothe sparseness of the RGBs of the UFDs, it will become nec-essary to extend the power of multiplex spectroscopic obser-vations to the main sequence of the UFDs in order to obtainstatistically significant samples to achieve this goal. ACKNOWLEDGEMENTS
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