| { | |
| "MEASURING DETAILED CHEMICAL ABUNDANCES FROM CO-ADDED MEDIUM RESOLUTION SPECTRA. I. TESTS USING MILKY WAY DWARF SPHEROIDAL GALAXIES AND GLOBULAR CLUSTERS ": [ | |
| "arXiv:1303.1222v1 [astro-ph.GA] 5 Mar 2013 " | |
| ], | |
| "ABSTRACT ": [ | |
| "The ability to measure metallicities and α-element abundances in individual red giant branch (RGB) stars using medium-resolution spectra (R ≈ 6000) is a valuable tool for deciphering the nature of Milky Way dwarf satellites and the history of the Galactic halo. Extending such studies to more distant systems like Andromeda is beyond the ability of the current generation of telescopes, but by co-adding the spectra of similar stars, we can attain the necessary signal-to-noise ratio to make detailed abundance measurements. In this paper, we present a method to determine metallicities and α-element abundances using the co-addition of medium resolution spectra. We test the method of spectral co-addition using high-S/N spectra of more than 1300 RGB stars from Milky Way globular clusters and dwarf spheroidal galaxies obtained with the Keck II telescope/DEIMOS spectrograph a (<>). We group similar stars using photometric criteria and compare the weighted ensemble average abundances ([Fe/H], [Mg/Fe], [Si/Fe], [Ca/Fe] and [Ti/Fe]) of individual stars in each group with the measurements made on the corresponding co-added spectrum. We find a high level of agreement between the two methods, which permits us to apply this co-added spectra technique to more distant RGB stars, like stars in the M31 satellite galaxies. This paper outlines our spectral co-addition and abundance measurement methodology and describes the potential biases in making these measurements. Subject headings: galaxies: abundances — galaxies: dwarf — galaxies: evolution — galaxies: Local Group— galaxies: stellar content " | |
| ], | |
| "1. INTRODUCTION ": [ | |
| "The Local Group is dominated by the Milky Way and Andromeda galaxies, with large families of dwarf satellite galaxies. The accessibility of these fantastic targets, particularly the dwarf spheroidals (dSphs) around the Milky Way, enables us to trace the dynamical and chemical properties of individual stars in order to investigate their formation. For decades, evidence has been growing that much of the material in the Universe condensed into small dark matter halos at an early stage, and over a Hubble time, many of these halos contribute to the growth of massive galaxies in a “chaotic accretion” (Searle & Zinn 1978; White & Rees 1978; Cole et al. 2000; Die-mand et al. 2007). From observations, Helmi et al. (2006) showed that there were metal-poor stars in the Milky Way halo with [Fe/H] < −3.0 dex, which did not seem to exist in dwarf spheroidal galaxies, and therefore ruled out present day dSphs as the building blocks of the Milky Way halo. Recently, however, Kirby et al. (2008a, hereafter KGS08, 2009, 2010) determined the iron abundance distribution of vast majority of red giant branch stars (RGBs) in globular clusters (GCs) and ultra-faint dSphs, and they found a significant metal-poor tail of stars does exist in the Milky Way satellites, supporting the hierarchical formation of the stellar halo. ", | |
| "To investigate the formation of big spiral galaxies, espe-", | |
| "cially their stellar halo accretion history, chemical abundance patterns obtained from individual stars are crucial indicators (Wheeler et al. 1989; Worthey 1994; Mannucci et al. 2010). Stars produce a diversity of elements through nucleosynthe-sis, which are dispersed into the interstellar medium, and are then mixed with material in subsequent star formation. Generally, iron-peak elements, such as vanadium and iron, are mainly generated by Type Ia supernovae (SNe Ia —Tins-ley 1980) which are important contributors to the total iron fraction in galaxies (Greggio & Renzini 1983). Correspondingly, the α-elements, like oxygen, magnesium, silicon, calcium, titanium, etc., are produced in core collapse supernovae (SNe II) whose progenitors are massive stars with typical stellar masses greater than 9M (Wheeler et al. 1989; Woosley & Weaver 1995; Gilmore 2004). Furthermore, compared to Type II supernovae, which have a timescale of around ∼ 10 million years (Pagel 1997; Woosley & Janka 2005), Type Ia supernovae have a longer timescale of at least ∼ 1 Gyr (Mat-teucci & Recchi 2001; Ishigaki et al. 2012). Hence, a plot of [α/Fe] versus [Fe/H] tells us about the relative contribution of SNe Ia and SNe II in star formation and evolution of a stellar system as a function of time, and can be used as a clock to measure the intensity of star formation at early stages. Additionally, comparing the distribution of metallicity and α-element abundances between the different stellar components of the Milky Way and its companions is a way of determining their evolutionary relationships. ", | |
| "Photometry is commonly used to determine the metallici-ties of old RGB stars. This technique uses the locations of ", | |
| "RGB stars in the color magnitude diagram and compares them to empirical relations (Armandroff et al. 1993), fitting functions (Saviane et al. 2000), or theoretical stellar tracks (e.g., Harris & Harris 2000; Mouhcine et al. 2005; Lianou et al. 2010) to derive photometric estimates of the metallicity. The metallicities of distant stars in the Andromeda system have also been estimated in this way. Da Costa et al. (1996, 2000, 2002) used HST/WFPC2 to measure photometric metallici-ties and obtained age estimates using the RGB and horizontal branch in three dwarf spheroidal galaxies, Andromeda I, Andromeda II, and Andromeda III, around M31. Kalirai et al. (2010) studied hundreds of RGB stars in six M31 dSphs, producing a luminosity-metallicity relation for dwarfs and compared it with that of their Milky Way counterparts. However, photometric metallicity estimates are often not as accurate as spectroscopic metallicity for two main reasons. First, the α abundance of star often has to be assumed. Second, the degeneracy of age and metallicity (Worthey 1994), even with resolved color-magnitude diagrams, is difficult to untangle. Lianou et al. (2011) compared photometric metallicity and spectroscopic metallicity based on the near-infrared Ca triplet analysis of RGBs in five Galactic dSphs, and they found that the agreement is good for metallicities between −2.0 dex to −1.5 dex but that a high fraction of intermediate-age stars would produce unreliable values. ", | |
| "Deriving chemical abundances using spectroscopy is much more reliable, but also expensive in terms of data collection. A stellar spectrum contains a wealth of information, allowing us to derive important stellar parameters like effective temperature, surface gravity, metallicity and other heavy elements abundances. Several empirical calibrations can be employed to measure metallicity. Popular methods include Ca II K λ3933 (Preston 1961; Zinn & West 1984; Beers et al. 1999) and the Ca near-infrared triplet calibration (Bica & Alloin 1987; Armandroff & Zinn 1988; Olszewski et al. 1991; Rutledge et al. 1997; Foster et al. 2010) with the prerequisite that [Ca/Fe] must be assumed. Unfortunately, these calibrations fail when [Fe/H] < −2.2 (Kirby et al. 2008b). ", | |
| "The most reliable way to measure abundances is to use high-resolution spectroscopy (R 20000). This technique has been used to analyze the detailed chemical abundance distribution of the Milky Way system and its satellites (Shetrone et al. 1998, 2001, 2003; Venn et al. 2004; Tolstoy et al. 2009; Letarte et al. 2010). High-resolution spectroscopic measurements of individual stars beyond the Milky Way and its satellites, however, is extremely challenging. Moreover, high resolution spectroscopy is difficult to multiplex and often requires observing one star at a time. For these reasons, medium-resolution spectroscopy (R ≈ 6000), for which abundances of some elements can still be well-measured, is an optimal choice for large sample stars in Milky Way satellites, and even for the M31 system (Guhathakurta et al. 2006; Koch et al. 2007). ", | |
| "Previous studies have targeted stars in the Milky Way satellites (e.g., Lanfranchi & Matteucci 2004; Shetrone et al. 2009; Strigari et al. 2010). The largest sample was given by KGS08 and Kirby et al. (2009, 2010) who observed more than 2500 RGB stars in Milky Way GCs and dSphs at medium-resolution using Keck/DEIMOS (Faber et al. 2003). They performed a multi-element abundance analysis using pixel-to-pixel matching based on a grid of synthetic stellar spectra. They verified their abundance measurement technique by comparing their results with the abundances derived from high-resolution spectra. In their study, in addition to finding a ", | |
| "long metal-poor tail in ultra-faint dSphs, matching that of the Galactic halo, they derived trends for individual α-elements (Mg, Si, Ca, Ti) versus metallicity, demonstrating that there was not much metal enrichment before the onset of SNe I (Kirby et al. 2011a, 2011b). ", | |
| "Observations of M31’s halo present a more complex accretion history (Ibata et al. 2001; Choi et al. 2002; Reitzel & Guhathakurta 2002; McConnachie et al. 2004; Guhathakurta et al. 2006, 2010; Kalirai et al. 2009, 2010; Collins et al. 2010; Tanaka et al. 2010), indicating that a study of abundance trends in its satellites could be more interesting and challenging. However, the larger distance and fainter apparent magnitudes hamper any detailed investigation of individual stellar abundances for dwarf satellites in M31, although there have been attempts to obtain detailed chemical abundance patterns in M31 globular clusters using high-resolution, integrated-light spectroscopy (Colucci et al. 2009). One way to address this problem is by co-adding many similar stars to produce spectra with higher signal-to-noise (S/N). This process, if done properly, would extend our ability to obtain elemental abundance analysis to larger distances, but there is also the potential for introducing biases. ", | |
| "The co-addition of spectra to measure the ensemble properties of similar objects has a long history in spectral processing. Adelman & Leckrone (1985) used co-addition for the ultraviolet and optical region of spectrum. Holberg et al. (2003) co-added multiple observations of individual white dwarf stars to enhance the signal-to-noise ratio and combined them into a single spectrum. Gallazzi et al. (2008) used co-added spectra of galaxies with similar velocity dispersions, absolute r-band magnitude and 4000Å-break values for those regions of parameter space where individual spectra had lower S/N. Most recently, Schlaufman et al. (2011, 2012) compared the average metallicities and α-element abundances between the elements of cold halo substructure (ECHOS) and the kine-matically smooth stellar inner halo along lines of sight in the Sloan Extension for Galactic Understanding and Exploration (SEGUE) by co-adding spectra of the metal-poor main sequence turnoff stars identified by the SEGUE Stellar Parameter Pipeline. Using noise-degraded spectra, they found that the mean square error (MSE) of abundances derived from co-added spectra is from 0.05 dex for metal-rich (iron-rich) stars to 0.2 dex for [Fe/H] and [α/Fe] for the most metal-poor stars. In a test using the globular clusters M13 and M15, the MSE roughly equals to 0.1 dex for most of the metal-rich stars and to 0.2 dex for metal-poor stars, in both [Fe/H] and [α/Fe]. However, the individual abundances of α-elements are inaccessible in their measurements. In this work, we use weighted spectral co-addition of RGB stars that share similar intrinsic properties to increase the S/N so that individual α-elements can be measured. ", | |
| "All data used in this paper are from the same data sets used in KGS08 and Kirby et al. (2009, 2010), which involves thousands RGB stars in Milky Way GCs and dSphs. We test our co-addition method by measuring metallicity ([Fe/H]) and four α-element abundances ([Mg/Fe], [Si/Fe], [Ca/Fe], [Ti/Fe]). We used the same definition of chemical abundances as defined in KGS08 1 (<>). ", | |
| "First, we present a short summary of the observations and ", | |
| "data reduction in §2. In §3 we describe the method of abundance determination using a synthetic spectral grid, as well as our method of co-addition: star selection and grouping, weighted co-adding, and abundance measurement. In §4, we present the comparison of weighted ensemble average of individual abundances to abundances measured from co-added spectra. We also discuss discrepancies and biases between the two results. We summarize our work in §5. " | |
| ], | |
| "2. OBSERVATION AND DATA REDUCTION ": [ | |
| "All the medium-resolution spectra of RGB stars used in this study are from KGS08 and Kirby et al. (2009, 2010), which include 2947 RGB stars in 8 Milky Way dSph galaxies and 654 RGB stars in 14 Galactic globular clusters. The observations were performed with DEIMOS on the Keck II telescope. The spectrograph configuration used the OG550 filter with the 1200 line mm−1 grating at a central wavelength of ∼7800Å with a slit width of 0. 7. The spectral resolution is ∼1.2Å to ∼1.3Å (corresponding to a resolving power 6500 < R < 7000 at 8500Å) with a spectral range of 6300–9100Å. Exposures of Kr, Ne, Ar, and Xe arc lamps were used for wavelength calibration and exposure of a quartz lamp provided the flat field. The DEIMOS data reduction pipeline developed by the DEEP galaxy redshift survey 2 (<>)was used to extract one dimensional spectra (Newman et al. 2012; Cooper et al. 2012). The pipeline traced the edges of slits in the flat field to determine the CCD location of each slit. A polynomial fit to the CCD pixel locations of arc lamp lines provided the wavelength solution. Each exposure of stellar targets was rectified and then sky subtracted based on a B-spline model of the night sky emission lines. Then, the exposures were combined with cosmic ray rejection into one two-dimensional spectrum for each slit. Finally, the one-dimensional stellar spectrum was extracted from a small spatial window encompassing the light of star in the two-dimensional spectrum. The product of the pipeline was a wavelength calibrated, sky-subtracted, cosmic-ray-cleaned, one dimensional spectrum for each target. A hot star template spectrum was employed to remove the terrestrial atmospheric absorption introduced into the stellar spectra. In continuum determination, a B-spline was used to fit the “continuum regions”3 (<>)of the spectra. Each pixel was weighted by its inverse variance in the fit, and the fit was performed iteratively such that pixels that deviated from the fit by more than 5σ were removed from the next iteration of the fit. For further details, please see KGS08. Table (<>)1 lists all the stellar systems used in this study. " | |
| ], | |
| "3. ABUNDANCE MEASUREMENTS ": [ | |
| "Kirby et al. presented a technique for multi-element abundance measurements of medium-resolution spectra, which enable them to determine individual α-element abundances of RGB stars in the Milky Way globular clusters and dwarf satellite galaxies. In this technique a large grid of synthetic spectra is used, so there is no restriction imposed on the metallicity range, overcoming the problems encountered by other methods. In brief, the photometric effective temperature (Teff ) and surface gravity (log g) are determined from isochrone-fitting on the color-magnitude diagram using three ", | |
| "Table 1 RGB spectral data sets ", | |
| "different model isochrones (Kirby et al. 2009)—Yonsei-Yale (Demarque et al. 2004), Victoria-Regina (VandenBerg et al. 2006), and Padova (Girardi et al. 2002)—and an empirical color-based Teff (Ram´ırez & Melendez´ 2005). Then, they adopted the Levernberg-Marquardt algorithm (mpfit, written by Markwardt 2009) to find the best-fitting synthetic spectrum to the observed spectrum in several iterative steps by minimizing the χ 2 calculated from the degraded synthetic spectrum and the observed spectrum. Lastly, the stellar parameters of the best-fitting synthetic spectrum is presented as the observed one’s. With different elemental masks, the abundances measured include iron abundance ([Fe/H]) and four α elements (Mg, Si, Ca and Ti). The four individual α elements were measured by considering only spectral regions most sensitive to the corresponding element. For example, the Mg wavelength mask covers about 20 neutral Mg lines in the DEIMOS spectral range. Even though all of the α elements vary together in the synthetic spectrum, only Mg lines are used to determine [Mg/Fe]. For those are interested in elemental masks, KGS084 (<>)and Kirby et al. (2009)5 (<>)depicted more details on the construction of the wavelength masks. They performed extensive comparisons of their medium resolution results with high-resolution spectroscopic elemental abundances from previous studies to validate their technique. In this study, we inherit the idea of Kirby’s technique and make proper modification to meet our demands to determine chemical abundances of more distant RGB stars beyond the ", | |
| "Table 2 ", | |
| "Atmospheric Parameter Grid. ", | |
| "Figure 1. The comparison of metallicity measured from medium-resolution spectra for individual stars between Kirby et al. and our codes, developed for co-added spectra. The left panel presents results for 8 GCs and the right panel for 8 dSphs. All these RGB stars meet the log g ≤ 1.4 threshold. The key difference between these two measurements for individual stars is in our codes we used a fixed Teff and log g derived from photometric estimates versus allowing Teff to float during the spectral fitting in Kirby et al.’s codes. The Levenberg-Marquardt algorithm is adopted to find the best-fitting spectrum with several iterative steps then give the abundance. The error bars shown include both the random errors in the fit and the systematic errors adopted from Kirby et al.. ", | |
| "Milky Way. But firstly, we aim to test our co-add spectra method with the medium-resolution spectra used by Kirby et al., and the membership of these RGB stars has been confirmed by Kirby et al.. " | |
| ], | |
| "3.1. Synthetic Spectral Library ": [ | |
| "We accomplished all chemical abundance analysis on the basis of a large grid of synthetic spectra generated by Kirby et al. (KGS08, 2009, 2010). Based on ATLAS9 model atmospheres (Kurucz 1993; Sbordone et al. 2004; Sbordone 2005) without convective overshooting (Castelli et al. 1997, 2004; Castelli 2005), and a line list of atomic and molecular transition data from the Vienna Atomic Line Database (Kupka et al. 1999), Kirby et al. synthesized spectra using the local equilibrium, plane-parallel spectrum synthesis code MOOG (Sneden 1973), which span the same wavelength range as the data (6300 to 9100Å) with a resolution of 0.02Å. The synthetic spectra fail in modeling of the Ca II triplet, Mg I ", | |
| "λ8807 and the absorption lines of TiO. To avoid an unexpected discontinuity they recomputed new ODFs for the new grid with DFSYNTHE code (Castelli 2005) and employed the solar composition of Anders & Grevesse (1989), but for Fe they used Sneden et al. (1992) (Kirby et al. 2009). To prevent unwittingly discarding the extremely metal-poor stars beyond the preliminary boundary of grid, they also expanded the synthetic spectral grid limit to [Fe/H]= −5.0 (Kirby et al. 2010). The value of [α/Fe] for the stellar model atmospheres would be different for each individual α-elements because elements have been measured only with the spectral regions where are the most sensitive to the corresponding element. Therefore, an additional subgrid with the extra dimension of α-element abundance ([α/Fe]abund) is also generated for more accurate measurement of [Mg/Fe], [Si/Fe], [Ca/Fe] and [Ti/Fe] at fixed [α/Fe]atm. This spectral library includes four dimensions: effective temperature (Teff ), surface gravity (log g), metallicity ([Fe/H] ), α abundance ([α/Fe]atm) of the ", | |
| "stellar atmosphere. Table (<>)2 gives the limited ranges and steps of these five parameters. This spectral grid is available on-line, and readers with interests in this grid are recommended to refer to more details in Kirby (2011c). " | |
| ], | |
| "3.2. Individual Stellar Abundances ": [ | |
| "To determine stellar abundances, we developed an independent code based on Kirby et al.’s technique with some refinements for the application to co-added spectra. For testing purposes, most of the medium-resolution spectra used have S/N > 20/pixel with mean S/N around 80/pixel. ", | |
| "In spectral co-addition, an essential step is to rebin the spectra in preparation for co-adding. Our approach rebins each science spectrum onto a common wavelength region (6300– 9100Å with step 0.25Å). The same has been done to the degraded synthetic spectrum which is going to be compared with the rebinned science one. Considering our co-added spectra approach aims to be applied on the RGB stars of M31 dwarf satellite galaxies whose spectroscopic temperatures are not available, we fixed the effective temperature, as well as the surface gravity, with the value derived from photometry. When we measured the effective temperature and surface gravity, the Yonsei-Yale isochrones fitting was carried out on the CMD at an assumed age of 14 Gyr and [α/Fe] = +0.3 for all RGB stars, however, in Kirby et al.’s work they only estimated log g by photometry. After setting the initial parameters, we performed the abundance determination on the re-binned spectra. In order to verify that our method works well on individual stars, we redetermined chemical abundances of all RGB stars with our code. Figure (<>)1 shows the comparison of [Fe/H] between Kirby’s and ours. The stars in the Figure 1 are also used for later co-addition test, but some stars whose spectra had insufficient S/N to measure a particular element have been removed. The selection detailed is discussed in next section §3.3. " | |
| ], | |
| "3.3. Surface Gravity Restriction ": [ | |
| "To start, we performed chemical abundance determination for more than 3600 RGB stars from 14 globular clusters and 8 dwarf spheroidal galaxies. The stellar ages of these RGB stars are difficult to estimate but fortunately have only a small impact on the measured chemical abundances (Harris et al. 1999; Frayn & Gilmore 2002; Lianou et al. 2010), so we assumed an age of 14 Gyr for all RGB stars (Grebel & Gallagher 2004) and set [α/Fe] = +0.3 empirically. Then, the effec-tive temperature (Teff ) and surface gravity (log g) of member stars were estimated by fitting Yonsei-Yale isochrones on the color-magnitude diagram. We then proceeded to measure the individual abundances as described in §3.2. We found some element abundances of some stars were unmeasurable, and we expected that low S/N is a possible reason. Thus, for the purposes of this test, stars for which we cannot measure a particular element abundance were not used in the co-addition. Additionally, previous observations of RGB stars in M31 showed that only stars with MI ≤ −2.5 are accessible for spectroscopy. So we further introduced a cut in log g. Given the roughly linear relationship between MI and Teff , this corresponds to a selection in log g. Figure 2 shows the linear relationship between photometric log g and absolute magnitude in the I-band (MI) for 7 dSphs (except Fornax, for which we do not have I-band data). From Figure (<>)2 MI = −2.5 roughly corresponds to a cut at log g = 1.40. Thus, we only selected stars having photometric log g ≤ 1.40 for the co-addition. The number of ", | |
| "Figure 2. We use a linear relationship between photometric surface gravity (log g) and I-band absolute magnitude (MI), which is converted from apparent magnitude with the extinction-corrected distance modulus, to select stars whose log g ≤ 1.40 ( (MI) ≥ −2.5 ). The plot contains all dSph RGB stars except for Fornax for which we have no I-band data. The line is the best fit linear relation. Stars with log g ≤ 1.4 are used to produce co-added spectra. stars left for each dSph and GC after this selection is listed in Table (<>)3. Only 8 globular clusters have enough stars for the following test. ", | |
| "Table 3 Star groups " | |
| ], | |
| "3.4. Grouping and co-addition ": [ | |
| "We consider photometric effective temperature (Teff ) and the photometric metallicity estimate ([Fe/H]phot), respectively, to organize the remaining stars into groups for co-adding. The photometric metallicities are also derived by ", | |
| "Yonsei-Yale theoretical isochrones fitting with an age of 14 Gyr (See §3.3). We used a cut at log g ≤ 1.40 to ensure that all stars lie in a range of about 1 dex in log g. Moreover, the synthetic spectral measurements use neutral metal lines only which are nearly insensitive to surface gravity. Therefore, log g barely changes the strength of spectral features, making it acceptable not to include log g in the binning. ", | |
| "The goal of this study is, for each grouping, to compare the weighted average abundances of the individual stars (the input) with the abundances measured on the co-added spectra (the output). For this purpose, it is important that each star used has a measurable abundance. Our pipeline is able to measure [Fe/H] in all sample stars, but for some of them, individual α elements (e.g., Mg) may not be measurable due to the quality of the spectra. Including these spectra in the grouping would bias the measurement on the co-added spectrum (but contribute nothing to the weighted average), so we are very careful to construct separate groupings for each element measured, i.e., a co-added spectrum for testing [Mg/Fe] consists only of stars that have reliable [Mg/Fe] measurements individually. This allows us to use the maximum number of available stars for testing each element. ", | |
| "After ranking member stars by their (Teff )phot and [Fe/H]phot separately, we make sure that each group contains at least 5 stars for which all five elemental abundances are measurable individually. We set 8 as the minimum number of stars for Fornax, Leo II and Sculptor, and 10 for Leo I for their large number of stars. Table 3 lists details for each GC and dSph. When we co-add spectra together for one bin, we produce five different co-adds, that is for each elemental abundance of [Fe/H], [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe], we only add the spectra whose elemental abundance is measurable individually, and use that co-added spectrum to determine the corresponding elemental abundance. The bad spectral regions therefore make no contribution to the co-added spectrum for the element of interest, which is equivalent to the elemental abundance derived from the weighted ensemble average. Figure (<>)3 shows two binning scenarios in detail for 8 GCs and 8 dSphs, by photometric effective temperature and metallicity. As the left panels show, stars having expanded distribution in Teff are binned more evenly, especially for Fornax, Leo I, and Sculptor, whose [Fe/H]phot are more concentrated. The impacts of this difference to the measured metallicities for these bins are clearly shown in the later figures. ", | |
| "For the observed spectrum, we use pixel masks to remove bad spectral regions, like telluric absorption and cosmic rays, before rebinning. Keck/DEIMOS has eight CCD and the whole spectrum spans two CCDs, so we exclude 5 pixels near the end of each CCD which may cause artifacts. We then re-bin the spectrum onto a common wavelength range (6300Å to 9100Å) and add fluxes of the normalized rebinned spectra together weighted by the rebinned inverse variance. The co-addition equation is: ", | |
| "(1) ", | |
| "where xpixel,i j represents the flux in the i-th pixel of j-th spectrum in a group of stars, σ2 is the variance of xpixel,i j,pixel,i j n represents the total number of spectra in the group, xpixel,i is the weighted average flux of i-th pixel of n spectra. ", | |
| "For consistency, we also create a grid of co-added synthetic spectra. First, for one group of stars, we pick the same number ", | |
| "Figure 3. Two scenarios have been used to bin stars. The open circles are individual stars used in this test. The vertical lines split the test stars into groups by two ways. Left panels show stars binned by photometric effec-tive temperature. Right panels show stars binned by photometric metallicity. There are five GCs (M2, M5, M13, NGC7006, and NGC7492) have one bin for the limited number of stars. From this comparison, the dSphs, which are most affected by the two scenarios, are Fornax, Leo I, and Sculptor. We detail the impact of different binning schemes in the discussion section. ", | |
| "of synthetic spectra with same chemical abundances but with different Teff and log g. The synthetic spectra are chosen to have the Teff and log g as determined by the photometric estimates of the observed stars. Second, we smoothed all the synthetic spectra with a Gaussian filter to match the spectral resolution science spectra. Then, we co-add the synthetic spectra in the same way as the science spectra (Equation (<>)1), with each pixel of the synthetic spectrum having the same weight as the corresponding pixel in the science spectrum. ", | |
| "Figure (<>)4 presents an example of a co-added observed spectrum (blue in the top panel and black in the bottom panel and its best fit co-added synthetic spectrum (red in the bottom panel). Stars with similar stellar properties should have the most similar spectra which are then used to determine chemical abundances and stellar parameters. When we carried out the co-addition, we also avoided the calcium triplet, which failed in spectra synthesis. When the comparison was exe-", | |
| "rameters determined in step 1 and 2, resulting in a quotient spectrum without absorption lines. Then we used a B-spline with a breakpoint spacing of 250 pixels to fit the quotient. Finally, we divided the co-added observed spectrum by the spline fit. This forces a better continuum match between the observed and synthetic spectra. " | |
| ], | |
| "4. COMPARISON OF CO-ADDED SPECTRAL ABUNDANCES AND WEIGHTED AVERAGE ABUNDANCES ": [ | |
| "The test we conduct in this study is to measure abundances on co-added spectra and see if the results we get are consistent with the measured abundances of the input RGB stars. In future applications, the individual star will be too faint to measure abundance, so any biases should be anticipated by using this nearby star sample. In this section, we compared the weighted-average abundances of each bin with the abundances measured from the co-added spectra in order to test the feasibility of the co-addition method. The spectra we used in this test have a relatively high S/N, and the final goal of our work is to apply this method to more distant and fainter RGB stars beyond the Milky Way system. " | |
| ], | |
| "4.1. Weighted-Average Abundances ": [ | |
| "In this and subsequent sections, we refer to “weighted-average” abundances, which are the weighted ensemble averages of the measured abundances for individual stars in a given bin. Correspondingly, the “co-added” abundances are those derived from a measurement on the co-added spectra. ", | |
| "We have tried different weights to combine the individual abundances in bins, then compared weighted-average abundances with the abundances measured from co-added spectra. ", | |
| "We found that the same weights that we used in the combining of individual spectrum in co-addition (described in Section (<>)3.4) were the best weights to use if we wanted the two procedures to be consistent and produce the most unbiased results. Taking [Fe/H] as an example, we used the elemental mask for Fe, which covers the wavelength regions used to determine [Fe/H], resulting in an inverse variance array. The average inverse variance across the entire spectrum, calculated as in Equation (<>)2 and Equation (<>)3, is then used as the weight for that star when combining the individual abundances together to create the weighted-average abundance for that bin. The weights ω j used for individual abundances in the weighted average are ", | |
| "(2) ", | |
| "(3) ", | |
| "In Equation (<>)2, σ2 is the variance of i-th pixel of j-th pixel,i j spectrum in the bin. mpixel is total number of pixels in a spectrum. Melemental,X is the elemental mask for measurement of X, where X could be abundances of [Fe/H], [Mg/Fe], [Si/Fe], [Ca/Fe], or [Ti/Fe]. Melemental,X is a binary array in which only the pixels that most sensitive to corresponding element X absorption lines are set to 1. σ2spec, j is the weighted variance for the whole j-th spectrum. In Equation (<>)3, ω j(X) denotes the weight of X for j-th star, and there are n stars in that group. Then, the weighted average abundance is ", | |
| "(4) ", | |
| "We calculated the weighted-average abundances of the four α-elements in the same way as [Fe/H] for each group. As mentioned before, some stars’ individual element abundances were unavailable and these stars were not included in the co-added spectra, so we ignored them when determined weighted-average abundances. " | |
| ], | |
| "4.2. Errors ": [ | |
| "We considered two kind of errors that contribute to the scatter in the abundance distribution: fitting error and systematic error. The fitting error was given by the Levenberg-Marquardt algorithm code. The MPFIT program determined the best-fit synthetic spectrum by minimizing χ2 and gave an estimate of the fitting error based on the depth of the χ2 minimum in parameter space. There are many other sources of error like the inaccuracy of atmospheric parameters, imperfect spectral modeling and imprecise continuum placement. We considered all other uncertainties as systematic error. For individual stars, we used abundance error floors derived by Kirby et al. (2010) as systematic error6 (<>). Therefore, the total error for individual stars, σtotal, j for j-th star, is calculated as: ", | |
| "(5) ", | |
| "where σ f it, j(X) is the fit error for abundance X of the j-th star, and σsys, j(X) is systematic error. The fit error and systematic error for individual stars should be uncorrelated, in which case the total error (σtotal, j(X)) is simply the fit error (σ f it, j(X)) and systematic error (σsys, j(X)) added in quadrature, where X is either [Fe/H] or [α/Fe], and α denotes Mg, Si, Ca, or Ti. ", | |
| "For the weighted average abundance Xbin,wa, we estimated the variance for each bin weighted by σ2 total, j(X) which are same weights used for weighted-average abundances (see Equation (<>)3 and Equation (<>)4): ", | |
| "(6) ", | |
| "the σbin,wa(X), then, is the weighted error of weighted mean abundance Xbin,wa. ", | |
| "For abundances derived from the co-added spectra, we tried to use the same method in Kirby et al. (2010) to estimate the systematic errors. The distribution of the difference between the measured co-added values and the weighted mean values for same bins, divided by the expected errors, should be well fit by a Gaussian with unit variance, as shown in Equation (<>)7: ", | |
| "(7) ", | |
| "where, σ f it,coadd(X) is the fitting error of the co-added results, σbin,wa(X) is weighted mean error calculated from Equation (<>)6, and σsys,coadd(X) represents the systematic error for the co-added results. These three types of errors are supposed to be independent to each other. In our case, however, the fitting errors (σ f it,coadd(X)) and weighted mean errors (σbin,wa(X)) are already large enough, such that it is impossible to estimate systematic errors for the co-added results from Equation (<>)7. Figure (<>)5 shows the distributions of the difference, divided by the expected errors, and not including σsys,coadd(X), for all GC and dSph bins. The best-fit Gaussian is narrower than the unit Gaussian in all distributions, indicating that either the differ-ences of the two quantities in the numerator are too small, or the errors in the denominator are too large. However, this does not mean we have overestimated our uncertainties. Since we use the exact same stars for uncertainty estimating, they should contribute both to the weighted average and to the co-added spectral measurements. It is possible that the random and systematic errors in the mean abundance of each bin cancel out to some degree. These could include errors such as those related to a spread of intrinsic abundances within a bin, a spread caused by spectral noise, and systematic errors resulting from Teff mismatch. Some of the errors are correlated between the two quantities in the numerator and cancel out when we take the differences. On the other hand, the co-addition enhances S/N of the spectra, then some flavors of systematic errors on the measured abundances, e.g., those resulting the photometric estimate of Teff being different from the true Teff , may indeed average down in the case of abundance determination from the co-added spectrum. So we expect the systematic errors for co-added abundances should be smaller than the systematic error floors of individual stars. If the errors are correlated at some level, then there must be a non-negligible negative covariance term in the denominator. Both effects could be going on in our case. Here, we make a simplification for the systematic errors of the co-added results, that we used the abundance error floors of individual ", | |
| "Figure 5. Distribution of the difference between the measurements from co-adds and weighted mean for 132 bins from 8 GCs and 8 dSphs divided by the errors of difference; systematic errors for co-adds are not included. Distributions in left panels are stars binned by (Teff )phot, right panels show stars binned by [Fe/H]phot. The solid blue curves are the best-fit Gaussian for distributions. The dashed red curved are unit Gaussian with σ = 1. The areas of the unit Gaussian are normalized to the number of bins. stars for the co-added uncertainties and calculated them as: ", | |
| "where σ f it,coadd(X) is the fit error of co-added abundance from Equation (<>)7. σsys(X) is the systematic error from Equation (<>)5. σtotal,coadd(X) is the total error used for co-added abundances. As Figure (<>)5 shows, our error estimates are conservative. The true errors, accounting for covariance, must be slightly smaller. For the RGB stars of M31 satellites, there will be non-negligible random errors that result from the analysis of low S/N spectra. Random errors often have a Gaussian normal distribution and contribute to the total errors in the measurements. We will discuss the effects of random errors to the error budget in future work of M31. " | |
| ], | |
| "4.3. Comparison ": [ | |
| "We expect that the abundances measured on the co-added spectra should match the weighted-average abundances of the stars that were used to produce the co-add. By using high S/N medium-resolution spectra of nearby RGB stars, we can know both the input and output abundances and make a robust comparison. The co-added abundances for 8 GCs and 8 dSphs are derived from co-added spectra as described in §(<>)3.4, and the weighted-average abundances are calculated based on individual abundances from §(<>)3.2 and combined as described in §(<>)4.1. ", | |
| "For 8 GCs, the test is cleaner because we can reasonably assume no age, metallicity, or α abundance spread. Figure (<>)6 ", | |
| "Figure 21. Comparison for α-element abundances between weighted-average abundances and co-added degraded spectral abundances for four α-elements, Mg, Si, Ca, and Ti (top to bottom). Stars used for these plots are from the 8 dSph galaxies. Points in the left panels are stars binned by Teff and right hand panels are binned by [Fe/H]phot. The symbols are same as in Figure (<>)20. Figure (<>)9 presents the same information based on non-degraded spectra with the observed S/N. ", | |
| "seen in the measurements of degraded spectra (Figure (<>)19). For dSphs, the number of bins makes the impacts of different parameters on the residual biases more clear. [Si/Fe], [Ca/Fe] and [Ti/Fe] show good agreement between co-addition and weighted average abundances in Figure (<>)9. We suspect that the large scatter for Leo I results from the low S/N and relatively high and extended coverage in Teff . For the outliers, CVnI, Sculptor, and Sextans, uncertainty in photometrically estimating Teff and [Fe/H], which we used to bin the stars, is another possible biasing source (Figure (<>)17). Comparing Figures (<>)12, (<>)14, and (<>)16, it seems that S/N, Teff , and log g are all possible reasons for the residual biases, especially for stars binned by (Teff )phot. Digging deeper, log g is a function of stellar mass and radius, but the mass and radius of star are also related to Teff . If [Fe/H] is fixed, increasing Teff will make absorption lines more shallow and narrow, but increasing log g will broaden these lines. If we consider variation in [Fe/H], then it becomes even more difficult to distinguish which matters most. These small features affect the abundance measure-", | |
| "ments for both individual and co-added spectrum. Although stars in each bin have similar properties, the exact values of these important stellar parameters are different. We used the same chemical abundances to select the synthetic spectra for each bin, but the photometric Teff and log g values used were those of individual observed stars. Considering the sensitivity of α elements to the metallicity, this assumption may play a role in the large scatter of [α/Fe]. Compared to other α elements, [Mg/Fe] is the most difficult one to measure accurately because of weak absorption lines. Magnesium is a product of Type II supernova, and it is the least visible of the α elements in the DEIMOS spectra (KGS08). The elemental mask for [Mg/Fe] contains a limited number of absorption lines compared with other elemental masks, therefore results in a larger uncertainty for [Mg/Fe]. ", | |
| "All 8 dSphs in this work have significant intrinsic spread in metallicity (Figure (<>)8). The intrinsic spread in the abundance distribution of dwarf satellite galaxies indicates their extended star formation history (Venn et al. 2004; Helmi et al. 2006; Cohen & Huang 2009; Kirby et al. 2009). The target selection of a stellar system which has radial metallicity gradient like Sculptor (Tolstoy et al. 2004; Walker et al. 2009; Kirby et al. 2009) may influence the measured abundance distribution for the co-added spectra method. Therefore, when we apply co-addition to dSphs, the effect of a metallicity spread on the α-elements abundance measurements with limited absorption lines need to be considered carefully. Particularly for the stars in M31 satellite galaxies with low S/N, Figures (<>)19 and (<>)21 show similar scatter amplitudes, demonstrating that we can estimate the mean values and trends for α elements from low S/N spectra with the coaddition technique. " | |
| ], | |
| "4.4.3. [α/Fe] versus [Fe/H] ": [ | |
| "Figure (<>)22 and Figure (<>)23 present the individual α-element distribution versus metallicity determined from co-added spectra for 8 GCs and 8 dSphs, respectively. The trends are clearly shown for the majority of bins, and only Leo I and Fornax display a very blurred trend in [Ca/Fe] distribution. We add individual stars’ abundances in the figures as Figure (<>)24 shows. The distributions of [Ti/Fe] from Leo I and Fornax seem to display an upward tendency with increasing metallicity compared with previous results shown by individual stars (Kirby et al. 2011b, their Figure 13). We speculate that it is mainly because our surface gravity restriction has removed fainter RGB stars, which are located in the metal-rich region in Figure (<>)23. Yet, we still consider the co-added spectra method as an efficient and feasible tool to proceed the detailed multi-element abundance measurement with medium-resolution spectra. Based on the detailed α-element abundance analysis (Shetrone et al. 2001, 2003; Venn et al. 2004; Kirby et al. 2011b), we expect to extend our understanding and insight into the star formation history and galaxy evolution to the Andromeda galaxy system and even farther systems with this technique. " | |
| ], | |
| "4.4.4. Binning Scenarios ": [ | |
| "By comparing two binning algorithms, we can assess which one better reflects the true values of groups of stars. The two parameters we used to bin, Teff and [Fe/H]phot, are primarily estimated from isochrone-fitting on CMD. Stellar parameters estimated from photometry are far less accurate than the ones derived by spectroscopy. On the other hand, some assumptions must be made to constrain the parameter space in the ", | |
| "binning scenario since our co-addition scenario for synthetic spectra can account for a spread in Tteff within a bin, but not for a spread in [Fe/H] or [α/Fe]. ", | |
| "Last, the precision of the abundances measured from co-added MRS does not appear to be a strong function of S/N over the range we have explored: co-added spectral S/N ∼ 200/pixel − 2000/pixel for GCs (see Figure (<>)11) and S/N ∼ 50/pixel − 300/pixel for dSphs (see Figure (<>)12). The S/N of the individual M31 RGB spectra to which we plan to apply this co-addition method is typically much lower than that of the individual spectra analyzed in this paper, but many more stars are co-added together in the M31 bins so that the S/N of the co-added M31 RGB spectra are expected to be comparable to that of the co-added spectra used here (Kirby et al. 2010). The comparisons of metallicity and α elements derived from the degraded spectra with S/N comparable to RGB stars of M31 satellite galaxies and weighted average results demonstrate the feasibility of this technique. ", | |
| "We conclude that we can safely apply this method of spectral coaddition to analyze chemical abundance patterns in M31 satellite galaxies using medium resolution spectra of RGB stars. This will be a provide a useful start for detailed chemical abundance exploration beyond the Milky Way system. ", | |
| "L. Y. and E. W. P. gratefully acknowledge partial support from the Peking University Hundred Talent Fund (985) and grants 10873001 and 11173003 from the National Natural Science Foundation of China (NSFC). L. Y. also acknowledges support from the LAMOST-PLUS collaboration, a partnership funded by NSF grant AST-09-37523, and NSFC grants 10973015 and 11061120454. ", | |
| "Support for this work was also provided by NASA through Hubble Fellowship grant 51256.01 awarded to E.N.K. by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. ", | |
| "P. G. acknowledges support from NSF grant AST-10-10039. He would like to thank the staff of the Kavli Institute for Astronomy and Astrophysics at Peking University for their generous hospitality during his collaborative visits. ", | |
| "L. C. was supported by UCSC’s Science Internship Program (SIP). ", | |
| "Facilities: Keck(DEIMOS). " | |
| ] | |
| } |