The analysis of indexed astronomical time series – VI. Covariances of amplitude ratios and phase differences estimated from multicolour photometry of a pulsating star

One of the tools used to identify the pulsation modes of stars is a comparison of the amplitudes and phases as observed photometrically at different wavelengths. Proper application of the method requires that the errors on the measured quantities, and the correlations between them, be known (or at least estimated). It is assumed that contemporaneous measurements of the light intensity of a pulsating star are obtained in several wavebands. It is also assumed that the measurements are regularly spaced in time, although there may be missing observations. The amplitude and phase of the pulsation are estimated separately for each of the wavebands, and amplitude ratios and phase differences are calculated. A general scheme for estimating the covariance matrix of the amplitude ratios and phase differences is described. The first step is to fit a time series to the residuals after pre-whitening the observations by the best-fitting sinusoid. The residuals are then cross-correlated to study the interdependence between the errors in the different wavebands. Once the multivariate time-series structure can be modelled, the covariance matrix can be found by bootstrapping. An illustrative application is described in detail.     

The analysis of indexed astronomical time series – X. Significance testing of O−C data

It is assumed that   O − C   ('observed minus calculated') values of periodic variable stars are determined by three processes, namely measurement errors, random cycle-to-cycle jitter in the period, and possibly long-term changes in the mean period. By modelling the latter as a random walk, the covariances of all   O − C   values can be calculated. The covariances can then be used to estimate unknown model parameters, and to choose between alternative models. Pseudo-residuals which could be used in model fit assessment are also defined. The theory is illustrated by four applications to spotted stars in eclipsing binaries.     

The analysis of indexed astronomical time series –VII. Simultaneous use of times of maxima and minima to test for period changes in long-period variables

A statistical model is formulated that enables one to analyse jointly the times between maxima and minima in the light curves of monoperiodic pulsating stars. It is shown that the combination of both sets of data into one leads to analyses that are more sensitive. Illustrative applications to the American Association of Variable Star Observers data for a number of long-period variables demonstrate the usefulness of the approach.     

Detrending time series for astronomical variability surveys

We present a detrending algorithm for the removal of trends in time series. Trends in time series could be caused by various systematic and random noise sources such as cloud passages, changes of airmass, telescope vibration, CCD noise or defects of photometry. Those trends undermine the intrinsic signals of stars and should be removed. We determine the trends from subsets of stars that are highly correlated among themselves. These subsets are selected based on a hierarchical tree clustering algorithm. A bottom-up merging algorithm based on the departure from normal distribution in the correlation is developed to identify subsets, which we call clusters. After identification of clusters, we determine a trend per cluster by weighted sum of normalized light curves. We then use quadratic programming to detrend all individual light curves based on these determined trends. Experimental results with synthetic light curves containing artificial trends and events are presented. Results from other detrending methods are also compared. The developed algorithm can be applied to time series for trend removal in both narrow and wide field astronomy.     

The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations

The theory of low-order linear stochastic differential equations is reviewed. Solutions to these equations give the continuous time analogues of discrete time autoregressive time-series. Explicit forms for the power spectra and covariance functions of first- and second-order forms are given. A conceptually simple method is described for fitting continuous time autoregressive models to data. Formulae giving the standard errors of the parameter estimates are derived. Simulated data are used to verify the performance of the methods. Irregularly spaced observations of the two hydrogen-deficient stars FQ Aqr and NO Ser are analysed. In the case of FQ Aqr the best-fitting model is of second order, and describes a quasi-periodicity of about 20 d with an e-folding time of 3.7 d. The NO Ser data are best fitted by a first-order model with an e-folding time of 7.2 d.     

Background–source separation in astronomical images with Bayesian probability theory – I. The method

A probabilistic technique for the joint estimation of background and sources with the aim of detecting faint and extended celestial objects is described. Bayesian probability theory is applied to gain insight into the co-existence of background and sources through a probabilistic two-component mixture model, which provides consistent uncertainties of background and sources. A multiresolution analysis is used for revealing faint and extended objects in the frame of the Bayesian mixture model. All the revealed sources are parametrized automatically providing source position, net counts, morphological parameters and their errors.
We demonstrate the capability of our method by applying it to three simulated data sets characterized by different background and source intensities. The results of employing two different prior knowledge on the source signal distribution are shown. The probabilistic method allows for the detection of bright and faint sources independently of their morphology and the kind of background. The results from our analysis of the three simulated data sets are compared with other source detection methods. Additionally, the technique is applied to ROSAT All-Sky Survey data.     

The VOISE algorithm: a versatile tool for automatic segmentation of astronomical images

The auroras on Jupiter and Saturn can be studied with a high sensitivity and resolution by the Hubble Space Telescope ( HST ) ultraviolet (UV) and far-ultraviolet Space Telescope Imaging Spectrograph (STIS) and Advanced Camera for Surveys (ACS) instruments. We present results of automatic detection and segmentation of Jupiter's auroral emissions as observed by the HST ACS instrument with the VOronoi Image SEgmentation (VOISE). VOISE is a dynamic algorithm for partitioning the underlying pixel grid of an image into regions according to a prescribed homogeneity criterion. The algorithm consists of an iterative procedure that dynamically constructs a tessellation of the image plane based on a Voronoi diagram, until the intensity of the underlying image within each region is classified as homogeneous. The computed tessellations allow the extraction of quantitative information about the auroral features, such as mean intensity, latitudinal and longitudinal extents and length-scales. These outputs thus represent a more automated and objective method of characterizing auroral emissions than manual inspection.     

New periodic variables from the Hipparcos epoch photometry

Two selection statistics are used to extract new candidate periodic variables from the epoch photometry of the Hipparcos catalogue. The primary selection criterion is a signal-to-noise ratio. The dependence of this statistic on the number of observations is calibrated using about 30 000 randomly permuted Hipparcos data sets. A significance level of 0.1 per cent is used to extract a first batch of candidate variables. The second criterion requires that the optimal frequency be unaffected if the data are de-trended by low-order polynomials. We find 2675 new candidate periodic variables, of which the majority (2082) are from the Hipparcos 'unsolved' variables. Potential problems with the interpretation of the data (e.g. aliasing) are discussed.     

修正的极大似然法拟合幂律频数分布

针对包含饱和样本数据的频数幂律分布拟合,提出一个新的幂律分布指数的极大似然估计方法的修正公式.对比研究显示,修正公式适用于剔除异常饱和值的幂律频数拟合.如果不剔除饱和值,幂律指数的估计只能使用修正前的公式,其误差随幂律指数变化,指数较小时误差较大.由此建议,对于包含饱和样本的频数分布拟合,首先剔除异常的饱和值,然后对剩余不含饱和值的子集使用修正公式进行参数估计.     

Multiperiodicities from the Hipparcos epoch photometry and possible pulsation in early A-type stars

A selection criterion based on the relative strength of the largest peaks in the amplitude spectra, and an information criterion are used in combination to search for multiperiodicities in Hipparcos epoch photometry. The method is applied to all stars which have been classified as variable in the Hipparcos catalogue: periodic, unsolved and microvariables. Results are assessed critically: although there are many problems arising from aliasing, there are also a number of interesting frequency combinations which deserve further investigation. One such result is the possible occurrence of multiple periods of the order of a day in a few early A-type stars. The Hipparcos catalogue also contains a number of these stars with single periodicities: such stars with no obvious variability classifications are listed, and information about their properties (e.g., radial velocity variations) discussed. These stars may constitute a new class of pulsators.     

Significance of periodogram peaks and a pulsation mode analysis of the Beta Cephei star V403 Car

We discuss some commonly used methods for determining the significance of peaks in the periodograms of time series. We review methods for constructing the classical significance tests, their corresponding false alarm probability functions and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We discuss the concepts of independent frequencies and oversampling in periodogram analysis. We then compare the results of new Monte Carlo simulations for evenly spaced time series with results obtained previously by other authors, and present the results of Monte Carlo simulations for a specific unevenly spaced time series obtained for V403 Car.     

Towards a real‐time transient classification engine

Temporal sampling does more than add another axis to the vector of observables. Instead, under the recognition that how objects change (and move) in time speaks directly to the physics underlying astronomical phenomena, next‐generation wide‐field synoptic surveys are poised to revolutionize our understanding of just about anything that goes bump in the night (which is just about everything at some level). Still, even the most ambitious surveys will require targeted spectroscopic follow‐up to fill in the physical details of newly discovered transients. We are now building a new system intended to ingest and classify transient phenomena in near real‐time from high‐throughput imaging data streams. Described herein, the Transient Classification Project at Berkeley will be making use of classification techniques operating on “features” extracted from time series and contextual (static) information. We also highlight the need for a community adoption of a standard representation of astronomical time series data (ie. “VOTimeseries”). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)