The ILIUM forward modelling algorithm for multivariate parameter estimation and its application to derive stellar parameters from Gaia spectrophotometry

I introduce an algorithm for estimating parameters from multidimensional data based on forward modelling. In contrast to many machine learning approaches it avoids fitting an inverse model and the problems associated with this. The algorithm makes explicit use of the sensitivities of the data to the parameters, with the goal of better treating parameters which only have a weak impact on the data. The forward modelling approach provides uncertainty (full covariance) estimates in the predicted parameters as well as a goodness-of-fit for observations. I demonstrate the algorithm, ILIUM, with the estimation of stellar astrophysical parameters (APs) from simulations of the low resolution spectrophotometry to be obtained by Gaia. The AP accuracy is competitive with that obtained by a support vector machine. For example, for zero extinction stars covering a wide range of metallicity, surface gravity and temperature, ILIUM can estimate Teff to an accuracy of 0.3% at G=15 and to 4% for (lower signal-to-noise ratio) spectra at G=20. [Fe/H] and logg can be estimated to accuracies of 0.1-0.4dex for stars with G<=18.5. If extinction varies a priori over a wide range (Av=0-10mag), then Teff and Av can be estimated quite accurately (3-4% and 0.1-0.2mag respectively at G=15), but there is a strong and ubiquitous degeneracy in these parameters which limits our ability to estimate either accurately at faint magnitudes. Using the forward model we can map these degeneracies (in advance), and thus provide a complete probability distribution over solutions. (Abridged)Comment: MNRAS, in press. This revision corrects a few minor errors and typos. A better formatted version for A4 paper is available at http://www.mpia.de/home/calj/ilium.pd

The expected performance of stellar parametrization with Gaia spectrophotometry

Gaia will obtain astrometry and spectrophotometry for essentially all sources in the sky down to a broad band magnitude limit of G=20, an expected yield of 10^9 stars. Its main scientific objective is to reveal the formation and evolution of our Galaxy through chemo-dynamical analysis. In addition to inferring positions, parallaxes and proper motions from the astrometry, we must also infer the astrophysical parameters of the stars from the spectrophotometry, the BP/RP spectrum. Here we investigate the performance of three different algorithms (SVM, ILIUM, Aeneas) for estimating the effective temperature, line-of-sight interstellar extinction, metallicity and surface gravity of A-M stars over a wide range of these parameters and over the full magnitude range Gaia will observe (G=6-20mag). One of the algorithms, Aeneas, infers the posterior probability density function over all parameters, and can optionally take into account the parallax and the Hertzsprung-Russell diagram to improve the estimates. For all algorithms the accuracy of estimation depends on G and on the value of the parameters themselves, so a broad summary of performance is only approximate. For stars at G=15 with less than two magnitudes extinction, we expect to be able to estimate Teff to within 1%, logg to 0.1-0.2dex, and [Fe/H] (for FGKM stars) to 0.1-0.2dex, just using the BP/RP spectrum (mean absolute error statistics are quoted). Performance degrades at larger extinctions, but not always by a large amount. Extinction can be estimated to an accuracy of 0.05-0.2mag for stars across the full parameter range with a priori unknown extinction between 0 and 10mag. Performance degrades at fainter magnitudes, but even at G=19 we can estimate logg to better than 0.2dex for all spectral types, and [Fe/H] to within 0.35dex for FGKM stars, for extinctions below 1mag.Comment: MNRAS, in press. Minor corrections made in v

Estimation of stellar atmospheric parameters from SDSS/SEGUE spectra

We present techniques for the estimation of stellar atmospheric parameters (Teff,logg,[Fe/H]) for stars from the SDSS/SEGUE survey. The atmospheric parameters are derived from the observed medium-resolution (R=2000) stellar spectra using non-linear regression models trained either on (1) pre-classified observed data or (2) synthetic stellar spectra. In the first case we use our models to automate and generalize parametrization produced by a preliminary version of the SDSS/SEGUE Spectroscopic Parameter Pipeline (SSPP). In the second case we directly model the mapping between synthetic spectra (derived from Kurucz model atmospheres) and the atmospheric parameters, independently of any intermediate estimates. After training, we apply our models to various samples of SDSS spectra to derive atmospheric parameters, and compare our results with those obtained previously by the SSPP for the same samples. We obtain consistency between the two approaches, with RMS deviations of 150K in Teff, 0.35dex in logg, and 0.22dex in [Fe/H]. The models are applied to pre-processed spectra, either via Principal Components Analysis or a Wavelength Range Selection method, which employs a subset of the full 3850-9000A spectral range. This is both for computational reasons, and because it delivers higher accuracy. From an analysis of cluster candidates with available SDSS spectroscopy (M15, M13, M2, and NGC2420), we find evidence for small systematic offsets in Teff and/or logg for the atmospheric parameter estimates from the model trained on real data with the SSPP. Thus, this model turns out to derive more precise, but less accurate, atmospheric parameters than the model trained on synthetic data.Comment: 17 pages, 13 figures, accepted for publication in A&

The SEGUE Stellar Parameter Pipeline. II. Validation with Galactic Globular and Open Clusters

We validate the performance and accuracy of the current SEGUE (Sloan Extension for Galactic Understanding and Exploration) Stellar Parameter Pipeline (SSPP), which determines stellar atmospheric parameters (effective temperature, surface gravity, and metallicity) by comparing derived overall metallicities and radial velocities from selected likely members of three globular clusters (M 13, M 15, and M 2) and two open clusters (NGC 2420 and M 67) to the literature values. Spectroscopic and photometric data obtained during the course of the original Sloan Digital Sky Survey (SDSS-I) and its first extension (SDSS-II/SEGUE) are used to determine stellar radial velocities and atmospheric parameter estimates for stars in these clusters. Based on the scatter in the metallicities derived for the members of each cluster, we quantify the typical uncertainty of the SSPP values, sigma([Fe/H]) = 0.13 dex for stars in the range of 4500 K < Teff < 7500 K and 2.0 < log g < 5.0, at least over the metallicity interval spanned by the clusters studied (-2.3 < [Fe/H] < 0). The surface gravities and effective temperatures derived by the SSPP are also compared with those estimated from the comparison of the color-magnitude diagrams with stellar evolution models; we find satisfactory agreement. At present, the SSPP underestimates [Fe/H] for near-solar-metallicity stars, represented by members of M 67 in this study, by about 0.3 dex.Comment: 56 pages, 8 Tables, 15 figures, submitted to the Astronomical Journa

PCA Tomography: how to extract information from datacubes

Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies it is possible to obtain datacubes in which one combines both techniques simultaneously, producing images with spectral resolution. To extract information from them can be quite complex, and hence the development of new methods of data analysis is desirable. We present a method of analysis of datacube (data from single field observations, containing two spatial and one spectral dimension) that uses PCA (Principal Component Analysis) to express the data in the form of reduced dimensionality, facilitating efficient information extraction from very large data sets. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates ordered by principal components of decreasing variance. The new coordinates are referred to as eigenvectors, and the projections of the data onto these coordinates produce images we will call tomograms. The association of the tomograms (images) to eigenvectors (spectra) is important for the interpretation of both. The eigenvectors are mutually orthogonal and this information is fundamental for their handling and interpretation. When the datacube shows objects that present uncorrelated physical phenomena, the eigenvector's orthogonality may be instrumental in separating and identifying them. By handling eigenvectors and tomograms one can enhance features, extract noise, compress data, extract spectra, etc. We applied the method, for illustration purpose only, to the central region of the LINER galaxy NGC 4736, and demonstrate that it has a type 1 active nucleus, not known before. Furthermore we show that it is displaced from the centre of its stellar bulge.Comment: 13 pages, 16 figures, accepted for publication on MNRA

The SEGUE Stellar Parameter Pipeline. I. Description and Initial Validation Tests

We describe the development and implementation of the SEGUE (Sloan Extension for Galactic Exploration and Understanding) Stellar Parameter Pipeline (SSPP). The SSPP derives, using multiple techniques, radial velocities and the fundamental stellar atmospheric parameters (effective temperature, surface gravity, and metallicity) for AFGK-type stars, based on medium-resolution spectroscopy and $ugriz$ photometry obtained during the course of the original Sloan Digital Sky Survey (SDSS-I) and its Galactic extension (SDSS-II/SEGUE). The SSPP also provides spectral classification for a much wider range of stars, including stars with temperatures outside of the window where atmospheric parameters can be estimated with the current approaches. This is Paper I in a series of papers on the SSPP; it provides an overview of the SSPP, and initial tests of its performance using multiple data sets. Random and systematic errors are critically examined for the current version of the SSPP, which has been used for the sixth public data release of the SDSS (DR-6).Comment: 64 pages, 8 tables, 12 figures, submitted to the Astronomical Journa

The SEGUE Stellar Parameter Pipeline. III. Comparison with High-Resolution Spectroscopy of SDSS/SEGUE Field Stars

We report high-resolution spectroscopy of 125 field stars previously observed as part of the Sloan Digital Sky Survey and its program for Galactic studies, the Sloan Extension for Galactic Understanding and Exploration (SEGUE). These spectra are used to measure radial velocities and to derive atmospheric parameters, which we compare with those reported by the SEGUE Stellar Parameter Pipeline (SSPP). The SSPP obtains estimates of these quantities based on SDSS ugriz photometry and low-resolution (R = 2000) spectroscopy. For F- and G-type stars observed with high signal-to-noise ratios (S/N), we empirically determine the typical random uncertainties in the radial velocities, effective temperatures, surface gravities, and metallicities delivered by the SSPP to be 2.4 km/s, 130 K (2.2%), 0.21 dex, and 0.11 dex, respectively, with systematic uncertainties of a similar magnitude in the effective temperatures and metallicities. We estimate random errors for lower S/N spectra based on numerical simulations.Comment: 37 pages, 6 tables, 6 figures, submitted to the Astronomical Journa

Two Stellar Components in the Halo of the Milky Way

The halo of the Milky Way provides unique elemental abundance and kinematic information on the first objects to form in the Universe, which can be used to tightly constrain models of galaxy formation and evolution. Although the halo was once considered a single component, evidence for its dichotomy has slowly emerged in recent years from inspection of small samples of halo objects. Here we show that the halo is indeed clearly divisible into two broadly overlapping structural components -- an inner and an outer halo -- that exhibit different spatial density profiles, stellar orbits and stellar metallicities (abundances of elements heavier than helium). The inner halo has a modest net prograde rotation, whereas the outer halo exhibits a net retrograde rotation and a peak metallicity one-third that of the inner halo. These properties indicate that the individual halo components probably formed in fundamentally different ways, through successive dissipational (inner) and dissipationless (outer) mergers and tidal disruption of proto-Galactic clumps.Comment: Two stand-alone files in manuscript, concatenated together. The first is for the main paper, the second for supplementary information. The version is consistent with the version published in Natur

The Milky Way Tomography With SDSS. III. Stellar Kinematics

We study Milky Way kinematics using a sample of 18.8 million main-sequence stars with r 20 degrees). We find that in the region defined by 1 kpc < Z < 5 kpc and 3 kpc < R < 13 kpc, the rotational velocity for disk stars smoothly decreases, and all three components of the velocity dispersion increase, with distance from the Galactic plane. In contrast, the velocity ellipsoid for halo stars is aligned with a spherical coordinate system and appears to be spatially invariant within the probed volume. The velocity distribution of nearby (Z < 1 kpc) K/M stars is complex, and cannot be described by a standard Schwarzschild ellipsoid. For stars in a distance-limited subsample of stars (< 100 pc), we detect a multi-modal velocity distribution consistent with that seen by HIPPARCOS. This strong non-Gaussianity significantly affects the measurements of the velocity-ellipsoid tilt and vertex deviation when using the Schwarzschild approximation. We develop and test a simple descriptive model for the overall kinematic behavior that captures these features over most of the probed volume, and can be used to search for substructure in kinematic and metallicity space. We use this model to predict further improvements in kinematic mapping of the Galaxy expected from Gaia and the Large Synoptic Survey Telescope.NSF AST-615991, AST-0707901, AST-0551161, AST-02-38683, AST-06-07634, AST-0807444, PHY05-51164NASA NAG5-13057, NAG5-13147, NNXO-8AH83GPhysics Frontier Center/Joint Institute for Nuclear Astrophysics (JINA) PHY 08-22648U.S. National Science FoundationMarie Curie Research Training Network ELSA (European Leadership in Space Astrometry) MRTN-CT-2006-033481Fermi Research Alliance, LLC, United States Department of Energy DE-AC02-07CH11359Alfred P. Sloan FoundationParticipating InstitutionsJapanese MonbukagakushoMax Planck SocietyHigher Education Funding Council for EnglandMcDonald Observator

Coude-feed stellar spectral library - atmospheric parameters

Context: Empirical libraries of stellar spectra play an important role in different fields. For example, they are used as reference for the automatic determination of atmospheric parameters, or for building synthetic stellar populations to study galaxies. The CFLIB (Coude-feed library, Indo-US) database is at present one of the most complete libraries, in terms of its coverage of the atmospheric parameters space (Teff, log g and [Fe/H]) and wavelength coverage 3460 - 9464 A at a resolution of 1 A FWHM. Although the atmospheric parameters of most of the stars were determined from detailed analyses of high-resolution spectra, for nearly 300 of the 1273 stars of the library at least one of the three parameters is missing. For the others, the measurements, compiled from the literature, are inhomogeneous. Aims: In this paper, we re-determine the atmospheric parameters, directly using the CFLIB spectra, and compare them to the previous studies. Methods: We use the ULySS program to derive the atmospheric parameters, using the ELODIE library as a reference. Results: Based on comparisons with several previous studies we conclude that our determinations are unbiased. For the 958 F,G, and K type stars the precision on Teff, log g, and [Fe/H] is respectively 43 K, 0.13 dex and 0.05 dex. For the 53 M stars they are 82 K, 0.22 dex and 0.28 dex. And, for the 260 OBA type stars the relative precision on Teff is 5.1%, and on log g, and [Fe/H] the precision is respectively 0.19 dex and 0.16 dex. These parameters will be used to re-calibrate the CFLIB fluxes and to produce synthetic spectra of stellar populations.Comment: 51 pages, accepted for publication in Astronomy and Astrophysic