1 Introduction2 Principal Component Decomposition of SDSS Stellar Spectra 2.1 The properties of SDSS spectra 2.2 Sample selection 2.3 The g-r Color Binning 2.4 Principal Components Decomposition3 Analysis of PC Decomposition Results3.1 Correlations between eigencoefficients and SSPP parameters 3.2 Mean Stellar Spectra Determined by PCA3.3 Variation of Mean Stellar Spectra with Metallicity and Gravity 4 SummaryarXiv:1001.4340v2 [astro-ph.SR] 26 Jan 2010Principal Component Analysis of SDSS Stellar SpectraRosalie C. McGurk, Amy E. Kimball,ˇZeljko Ivezi´cDepartment of Astronomy, University of Washington, Box 351580, Seattle, WA 98195ABSTRACTWe apply Principal Component Analysis (PCA) to ∼100,000 stellar spec-tra obtained by the Sloan Digital Sky Survey (SDSS). In order to avoid strongnon-linear variation of spectra with effective temperature, the sample is binnedinto 0.02 mag wide intervals of the g − r color (−0.2 0 < g − r < 0.90, roughlycorresponding to MK spectral types A3 to K3), and PCA is applied indepen-dently fo r each bin. In each color bin, the first four eigenspectra are sufficientto describe the observed spectra within the measurement noise. We discuss cor-relations of eigencoefficients with metallicity and gravity estimated by the SloanExtension for Galactic Understanding and Exploration (SEGUE) Stellar Param-eters Pipeline. The resulting high signal-to-noise mean spectra a nd the otherthree eigenspectra are made publicly available. These data can be used to gen-erate high quality spectra for an arbitrary combination of effective temperature,metallicity, and gravity within the parameter space probed by the SDSS. TheSDSS stellar spectroscopic database and the PCA results presented here offera convenient method to classify new spectra, to search for unusual spectra, totrain various spectral classification methods, and to synthesize accurate colors inarbitrary optical bandpasses.Subject headings: stars: abundances – stars: statistics – methods: data analysis– stars: fundamental parameters1. IntroductionA large number of homogeneously-obtained stellar spectra have recently become avail-able. For example, the Sloan Digital Sky Survey (SDSS) (York et al. 2000) has made publiclyavailable1over 460,000 stellar spectra as a part o f its Data Release 7 (Abazajian & Sloan Digital Sky Survey1See http://www.sdss.org/dr7– 2 –2008), and Radial Velo city Experiments2(RAVE) may provide up to a million spectra overthe next few years. This rapid progress in the availability of stellar spectra re-opens theold question of optimal stellar parameter extraction. For example, the SDSS estimateseffective temperature, gravity, and metallicity using a variety of standard methods imple-mented in a n automated pipeline (SEGUE3Stellar Para meters Pipeline, hereafter SSPP;Beers et al. 2006). A detailed discussion of these methods and their performance can befound in Allende Prieto et al. (2006, 2007) and Lee et al. (2007a,b). The results of differ-ent metho ds implemented in the SSPP are averaged to o btain the final adopted values inthe SD SS Spectr al Parameter Pipeline table (sppParams). Although a detailed analysis byLee et al. (2007a,b) demonstrates that systematic metallicity differences between the meth-ods used in averaging do not exceed ∼0.1 dex (with random errors in the range 0.1–0.3 dex),it is fair to ask whether a single method could be used to obtain the same level of systematicand random errors, instead of combining different methods with varying error properties.Principal Component Analysis (PCA) has been demonstrated as a viable tool in solvingthis classification problem (Connolly et al. 1995; Connolly & Szalay 1998; Bailer-Jones et al.1998; and references therein). Yip et al. (2004) have developed a PCA-based analysis codespecialized to SDSS spectra. Here we use the same code to investigate whether the PCAeigencoefficients are corr elat ed with the metallicity and gravity obtained by the SSPP.Byproducts of this analysis are high signal-to- noise eigensp ectra that can be used to generatespectra for any combination of basic stellar parameters (effective temperature, metallicity,and gravity) within the parameter space probed by SDSS. Hence, given an arbitrary spec-trum, one can attempt a low- dimensional fit using our library of eigenspectra. Amongnumerous drivers for such a library, we single out a photometric calibrat ion scheme for theLarge Synoptic Survey Telescope (LSST)4. LSST plans to use an auxiliary spectroscopictelescope to obtain spectra of standard stars at the same time as the main imaging surveyis performed (see Ivezi´c et al. 2008b). The atmospheric transmission pro perties, required tophotometrically calibrate the imaging survey, will be obtained by simultaneously fitting thestellar spectrum and a sophisticated atmospheric model with six free par ameters for eachobservation. The ability to describe the expected stellar spectra in a low-dimensional con-tinuous space by using a small number of eigencomponents, with eigencoefficients that a renot defined on a fixed grid, might increase the fidelity of the fitted model.In Section 2 we describe our sample selection and t he applicat ion of PCA to SDSS stellar2See http://www.rave-survey.aip.de/rave3Sloan Extension for Galactic Understanding and Exploration4See http://www.lsst.org/– 3 –spectra. We discuss our results in Section 3, and end with a summary in Section 4.2. Principal Component Decomposition of SDSS Stellar Spectra2.1. The properties of SDSS spectraIn addition to massive amounts of optical photometry of unprecedented quality, theSDSS has also produced a large spectroscopic da t abase. A compendium of technical detailsabout SDSS can be found on the SDSS web site5, which also provides an interface for publicdata access. Targets for the spectroscopic survey ar e chosen from the SDSS imaging databased on their colors and morphological properties (Strauss et al. 2002; Eisenstein et al.2001; Richards et al. 2002). In the spectro scopic survey, stars are targeted either as cali-brators o r for scientific reasons in specific parts of the four-dimensional SDSS color space(Yanny et al. 2009).A pair of multi-object fiber-fed spectrographs mounted onto the SDSS 2.5m telescope(Gunn et al. 2006) are used to take 640 simultaneous spectra within a radius of 1.49 de-grees, each with wavelength coverage 3800–9200˚A and spectral resolution of ∼2000, andwith a signal-to-noise ratio o f >4
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