Automated classification of stellar spectra — II. Two-dimensional classification with neural networks and principal components analysis

We investigate the application of neural networks to the automation of MK spectral classification. The data set for this project consists of a set of over 5000 optical (3800–5200 Å) spectra obtained from objective prism plates from the Michigan Spectral Survey. These spectra, along with their two-dimensional MK classifications listed in the Michigan Henry Draper Catalogue, were used to develop supervised neural network classifiers. We show that neural networks can give accurate spectral type classifications (σ₆₈= 0.82 subtypes, σ_rms= 1.09 subtypes) across the full range of spectral types present in the data set (B2–M7). We show also that the networks yield correct luminosity classes for over 95 per cent of both dwarfs and giants with a high degree of confidence.   Stellar spectra generally contain a large amount of redundant information. We investigate the application of principal components analysis (PCA) to the optimal compression of spectra. We show that PCA can compress the spectra by a factor of over 30 while retaining essentially all of the useful information in the data set. Furthermore, it is shown that this compression optimally removes noise and can be used to identify unusual spectra.   This paper is a continuation of the work carried out by von Hippel et al. (Paper I).     

Massive lossless data compression and multiple parameter estimation from galaxy spectra

We present a method for radical linear compression of data sets where the data are dependent on some number M of parameters. We show that, if the noise in the data is independent of the parameters, we can form M linear combinations of the data which contain as much information about all the parameters as the entire data set, in the sense that the Fisher information matrices are identical; i.e. the method is lossless. We explore how these compressed numbers fare when the noise is dependent on the parameters, and show that the method, though not precisely lossless, increases errors by a very modest factor. The method is general, but we illustrate it with a problem for which it is well-suited: galaxy spectra, the data for which typically consist of ∼10³ fluxes, and the properties of which are set by a handful of parameters such as age, and a parametrized star formation history. The spectra are reduced to a small number of data, which are connected to the physical processes entering the problem. This data compression offers the possibility of a large increase in the speed of determining physical parameters. This is an important consideration as data sets of galaxy spectra reach 10⁶ in size, and the complexity of model spectra increases. In addition to this practical advantage, the compressed data may offer a classification scheme for galaxy spectra which is based rather directly on physical processes.     

Recovering physical parameters from galaxy spectra using MOPED

We derive physical parameters of galaxies from their observed spectra using MOPED, the optimized data compression algorithm of Heavens, Jimenez & Lahav. Here we concentrate on parametrizing galaxy properties, and apply the method to the NGC galaxies in Kennicutt's spectral atlas. We focus on deriving the star formation history, metallicity and dust content of galaxies. The method is very fast, taking a few seconds of CPU time to estimate ∼17 parameters, and is therefore specially suited to studying large data sets, such as the Anglo-Australian two-degree-field (2dF) galaxy survey and the Sloan Digital Sky Survey (SDSS). Without the power of MOPED, the recovery of star formation histories in these surveys would be impractical. In Kennicutt's atlas, we find that for the spheroidals a small recent burst of star formation is required to provide the best fit to the spectrum. There is clearly a need for theoretical stellar atmospheric models with spectral resolution better than 1 Å if we are to extract all the rich information that large redshift surveys contain in their galaxy spectra.     

Objective classification of galaxy spectra using the information bottleneck method

A new method for classification of galaxy spectra is presented, based on a recently introduced information theoretical principle, the information bottleneck . For any desired number of classes, galaxies are classified such that the information content about the spectra is maximally preserved. The result is classes of galaxies with similar spectra, where the similarity is determined via a measure of information. We apply our method to ∼6000 galaxy spectra from the ongoing 2dF redshift survey, and a mock-2dF catalogue produced by a cold dark matter (CDM) based semi-analytic model of galaxy formation. We find a good match between the mean spectra of the classes found in the data and in the models. For the mock catalogue, we find that the classes produced by our algorithm form an intuitively sensible sequence in terms of physical properties such as colour, star formation activity, morphology, and internal velocity dispersion. We also show the correlation of the classes with the projections resulting from a principal component analysis.     

A new method for determining physical parameters of fundamental mode RR Lyrae stars from multicolour light curves

We present a new method for determining physical parameters of RRab variables exclusively from multicolour light curves. Our method is an inverse photometric Baade–Wesselink analysis which, using a non-linear least-squares algorithm, searches for the effective temperature ( T _eff) and pulsational velocity ( V _p) curves and other physical parameters that best fit the observed light curves, utilizing synthetic colours and bolometric corrections from static atmosphere models. The T _eff and V _p curves are initially derived from empirical relations then they are varied by the fitting algorithm. The method yields the variations and the absolute values of the radius, the effective temperature, the visual brightness and the luminosity of individual objects. Distance and mass are also determined. The method is tested on nine RRab stars subjected to Baade–Wesselink analyses earlier by several authors. The physical parameters derived by our method using only the light-curve data of these stars are well within their possible ranges defined by direct Baade–Wesselink and other techniques. A new empirical relation between the I _C magnitude and the pulsational velocity is also presented, which allows to construct the V _p curve of an RRab star purely from photometric observations to an accuracy of about 3.5 km s⁻¹.     

A robust statistical estimation of the basic parameters of single stellar populations – I. Method

The colour–magnitude diagrams of resolved single stellar populations, such as open and globular clusters, have provided the best natural laboratories to test stellar evolution theory. Whilst a variety of techniques have been used to infer the basic properties of these simple populations, systematic uncertainties arise from the purely geometrical degeneracy produced by the similar shape of isochrones of different ages and metallicities. Here we present an objective and robust statistical technique which lifts this degeneracy to a great extent through the use of a key observable: the number of stars along the isochrone. Through extensive Monte Carlo simulations we show that, for instance, we can infer the four main parameters (age, metallicity, distance and reddening) in an objective way, along with robust confidence intervals and their full covariance matrix. We show that systematic uncertainties due to field contamination, unresolved binaries, initial or present-day stellar mass function are either negligible or well under control. This technique provides, for the first time, a proper way to infer with unprecedented accuracy the fundamental properties of simple stellar populations, in an easy-to-implement algorithm.     

Merging of low-mass systems and the origin of the fundamental plane

We present the preliminary results of a study of how small stellar systems merge to form larger ones. As we display the families of galaxies in the μ_e - R_e plane (effective surface brightness versus effective radius) we realize that different morphological types occupy different loci, evidencing the different physical mechanisms operating in each family. As proposed by Capaccioli et al. (1992) this diagram is the logical equivalent of the HR diagram for stars. Here we take some initial steps in understanding of how we can establish the evolutionary tracks, solely due to dynamical processes, in the μ_e - R_e plane, ultimately making a dwarf elliptical to turn into a normal elliptical galaxy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Principal components in active galactic nuclei variability data and the estimation of the flux contributions from different components

It has been found that the near-infrared flux variations of Seyfert galaxies satisfy relations of the form   F_i ≈α _{i j} +β _{i j} F_j   , where F_i , F_j are the fluxes in filters i and j ; and  α _{i , j} , β _{i , j}   are constants. These relations have been used to estimate the constant contributions of the non-variable underlying galaxies. The paper attempts a formal treatment of the estimation procedure, allowing for the possible presence of a third component, namely non-variable hot dust. In an analysis of a sample of 38 Seyfert galaxies, inclusion of the hot dust component improves the model fit in approximately half the cases. All derived dust temperatures are below 300 K, in the range 540–860 K or above 1300 K. A noteworthy feature is the estimation of confidence intervals for the component contributions: this is achieved by bootstrapping. It is also pointed out that the model implies that such data could be fruitfully analysed in terms of principal components.     

A spectroscopic study of V603 Aquilae: stellar parameters and continuumline variations

A time-resolved spectroscopic study of V603 Aql (Nova Aquilae 1918) is presented. An orbital period of P _orb=01385±00002, consistent with previous results, and a radial velocity semi-amplitude of K =20±3 km s¹ are obtained from the radial velocity variations of the H emission line. Similar K values are also found in H , H , and He  i emission lines. Using the measured FWHM of the H line and assuming that the derived semi-amplitude is that of the white dwarf, we deduce a most likely mass ratio of q =0.24±0.05 and stellar masses of M ₂=0.29±0.04 M and M ₁=1.2±0.2 M for the secondary and primary (the white dwarf) star, respectively. The dynamical solution also indicates a very low orbital inclination, i =13°±2°. We find that the continuum and line variations are modulated with both the positive and the negative superhump periods, indicating that they arise from similar regions of the accretion disc. Moreover, we find, for the first time from spectroscopy, evidence of negative superhumps in addition to the positive superhumps. Positive superhumps are explained within the disc instability model as caused by an eccentric disc surrounding the white dwarf, which is precessing (apsidal advance) because of tidal instabilities, causing the observed positive superhumps. A nodal precession in the accretion disc is currently believed to be the cause of the observed negative superhumps. The low value of q is consistent with the expected value for systems that show superhumps, in accordance with the eccentric disc model. We find no evidence of periodicity associated with the spin period.     

Effect of the stellar inclination angle upon theoretical errors of l = 1 p‐mode parameters

The asteroseismic observations provided by current and future missions like CoRoT or Kepler will have a quality closer to those obtained for the Sun. In this context, tools and methods developed for helioseismology can be applied to other stars. In this paper, we focus on solar‐like oscillations of stars with an unknown rotation axis inclination and study, by means of maximum‐likelihood estimation, the errors on the determination of l = 1 p‐mode parameters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)