A fast Bayesian approach to discrete object detection in astronomical data sets – PowellSnakes I

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by (i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; (ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior and (iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of '100' as compared to existing Bayesian source extraction methods that use Monte Carlo Markov chain to explore the parameter space, such as that presented by Hobson & McLachlan. The method can be implemented in either real or Fourier space. In the case of objects embedded in a homogeneous random field, working in Fourier space provides a further speed up that takes advantage of the fact that the correlation matrix of the background is circulant. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore, PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (version I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.     

Primordial non-Gaussianity: local curvature method and statistical significance of constraints on fNL from WMAP data

We test the consistency of estimates of the non-linear coupling constant f _NL using non-Gaussian cosmic microwave background (CMB) maps generated by the method described in the work of Liguori, Matarrese & Moscardini. This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on the estimation of f _NL. Nevertheless, using spherical wavelets, we find results in very good agreement with Mukherjee & Wang, showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f _NL, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate   f _NL=−10⁺²⁷⁰₋₂₆₀  at the 2σ level (Bayesian) and   f _NL=−10⁺³¹⁰₋₂₇₀  (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of f _NL and therefore, as advocated in the work of Cabella et al., the estimates may be combined to reduce the error bars. In this way, we obtain   f _NL=−5 ± 85  and   f _NL=−5 ± 175  at the 1σ and 2σ level respectively using the frequentist approach.     

Feedback through multiple outbursts in the cluster 2A 0335+096

We examine the core of the X-ray bright galaxy cluster 2A 0335+096 using deep Chandra X-ray imaging and spatially resolved spectroscopy, and include new radio observations. The set of around eight X-ray bright blobs in the core of the cluster, appearing like eggs in a bird's nest, contains multiphase gas from ∼0.5 to 2 keV. The morphology of the coolest X-ray emitting gas at 0.5 keV temperature is similar to the Hα emitting nebula known in this cluster, which surrounds the central galaxy. XMM–Newton grating spectra confirm the presence of material at these temperatures, showing reasonable agreement with Chandra emission measures. On scales of 80 to 250 kpc, there is a low temperature, high metallicity, swirl of intracluster medium as seen in other clusters. In the core, we find evidence for a further three X-ray cavities, in addition to the two previously discovered. Enhancements in 1.5 GHz radio emission are correlated with the X-ray cavities. The total  4 PV   enthalpy associated with the cavities is around  5 × 10⁵⁹ erg  . This energy would be enough to heat the cooling region for  ∼5 × 10⁷ yr  . We find a maximum pressure discontinuity of 26 per cent (2σ) across the surface brightness edge to the south-west of the cluster core. This corresponds to an upper limit on the Mach number of the cool core with respect to its surroundings of 0.55.     

基于γ暴等观测限制宇宙学参数与暗能量模型

利用Union2 557个Ia型超新星数据限制宇宙学参数qo、jo和so,在红移z≤1.4范围内校准5个γ暴(gamma-ray burst,GRB)光度关系.假设γ暴光度关系不随红移演化,得到66个高红移γ暴的距离模数.最后综合利用宇宙微波背景(Cosmic Microwave Background,CMB)辐射观测数据、重子声波震荡(Baryon AcousticOscillations,BAO)观测数据与116个具有红移的γ暴数据限制几个常见的暗能量模型.根据贝叶斯判据(Bayesian Information Criterion,BIC),发现ACDM模型是最好的模型;根据Akaike判据(Akaike Information Criterion,AIC),发现JBP模型是最好的模型.     

Gamma-Ray Bursts and Other Observations: Constraints on Cosmographic Parameters and Dark Energy Models

We use the newly released Union2 SNe Ia dataset to constrain cosmographic parameters, namely the deceleration, jerk and snap parameters (q0, j0 and s0), then calibrate the five luminosity relations of Gamma-ray Bursts (GRBs) at redshift z ≤ 1.4. Assuming that the GRB luminosity relations do not evolve with the redshift, we obtain the distance moduli of 66 high-redshift GRBs. At last, we combine the observational datasets including the observations of the Cosmic Microwave Background (CMB), Baryon Acoustic Oscillation (BAO) and the 116 GRBs with known redshifts to constrain some widely-discussed dark energy models. We find that the ΛCDM model is the best according to the Bayesian Information Criterion (BIC), and the JBP model is the best according to the Akaike Information Criterion (AIC).     

Constraints on σ8 from galaxy clustering in N-body simulations and semi-analytic models

We generate mock galaxy catalogues for a grid of different cosmologies, using rescaled N -body simulations in tandem with a semi-analytic model run using consistent parameters. Because we predict the galaxy bias, rather than fitting it as a nuisance parameter, we obtain an almost pure constraint on σ₈ by comparing the projected two-point correlation function we obtain to that from the Sloan Digital Sky Survey (SDSS). A systematic error arises because different semi-analytic modelling assumptions allow us to fit the r -band luminosity function equally well. Combining our estimate of the error from this source with the statistical error, we find  σ₈= 0.97 ± 0.06  . We obtain consistent results if we use galaxy samples with a different magnitude threshold, or if we select galaxies by b _J-band rather than r -band luminosity and compare to data from the 2dF Galaxy Redshift Survey (2dFGRS). Our estimate for σ₈ is higher than that obtained for other analyses of galaxy data alone, and we attempt to find the source of this difference. We note that in any case, galaxy clustering data provide a very stringent constraint on galaxy formation models.     

Beyond maximum entropy: Fractal pixon-based image reconstruction

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodnessof-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.     

Dark matter in dwarf spheroidals – II. Observations and modelling of Draco

We present stellar radial velocity data for the Draco dwarf spheroidal (dSph) galaxy obtained using the AF2/WYFFOS instrument combination on the William Herschel Telescope. Our data set consists of 186 member stars, 159 of which have good quality velocities, extending to a magnitude   V ≈19.5  with a mean velocity precision of ≈2 km s⁻¹. As this survey is based on a high-precision photometric target list, it contains many more Draco members at large radii. For the first time, this allows a robust determination of the radial behaviour of the velocity dispersion in a dSph.
We find statistically strong evidence of a rising velocity dispersion consistent with a dark matter halo that has a gently rising rotation curve. There is a <2 σ signature of rotation about the long axis, inconsistent with tidal disruption as the source of the rising dispersion. By comparing our data set with earlier velocities, we find that Draco probably has a binary distribution and fraction comparable to those in the solar neighbourhood.
We apply a novel maximum likelihood algorithm and fit the velocity data to a two parameter spherical model with an adjustable dark matter content and velocity anisotropy. Draco is best fit by a weakly tangentially anisotropic distribution of stellar orbits in a dark matter halo with a very slowly rising rotation law  ( v _circ∝ r ^0.17)  . We are able to rule out both a mass-follows-light distribution and an extended halo with a harmonic core at the 2.5 to 3 σ significance level, depending on the details of our assumptions about Draco's stellar binary population. Our modelling lends support to the idea that the dark matter in dwarf spheroidals is distributed in the form of massive, nearly isothermal haloes.     

Likelihood analysis of repeating in the BATSE catalogue

I describe a new likelihood technique, based on counts-in-cells statistics, that I use to analyze repeating in the BATSE 1B and 2B catalogues. Using the 1B data, I find that repeating is preferred over non-repeating by 4.3:1 odds, with a peak at 5–6 repetitions per source. I find that the post-1B data are consistent with the repeating model inferred from the 1B data, after taking into account the lower fraction of bursts with well-determined positions. Combining the two data sets, I find that the odds favoring repeating over non-repeating are almost unaffected at 4:1, with a narrower peak at 5 repetitions per source. I conclude that the data sets are consistent both with each other and with repeating, and that for these data sets the odds favor repeating. Compton GRO Fellow - NASA grant GRO/PDP 93-08.     

Setting new constraints on the age of the Universe

There are three independent techniques for determining the age of the Universe: via cosmochronology of long-lived radioactive nuclei, via stellar modelling and population synthesis of the oldest stellar populations, and, most recently, via the precision cosmology that has become feasible with the mapping of the acoustic peaks in the cosmic microwave background. We demonstrate that all three methods give completely consistent results, and enable us to set rigorous bounds on the maximum and minimum ages that are allowed for the Universe. We present new constraints on the age of the Universe by performing a multiband colour analysis of bright cluster ellipticals over a large redshift range     , which allows us to infer the ages of their stellar populations over a wide range of possible formation redshifts and metallicities. Applying a prior to Hubble's constant of     we find the age of the Universe to be     (1 σ ), in agreement with the estimates from Type Ia supernovae, as well as with the latest uranium decay estimates, which yield an age for the Milky Way of     . If we combine the results from cluster ellipticals with the analysis of the angular power spectrum of the cosmic microwave background and with the observations of Type Ia supernovae at high redshift, we find a similar age:     . Without the assumption of any priors, universes older than 18 Gyr are ruled out by the data at the 90 per cent confidence level.     

The Two-Component Virial Theorem and the Physical Properties of Stellar Systems

Using eigenmode expansion of the Mark III and SFI surveys of cosmological radial velocities, a goodness-of-fit analysis is applied on a mode-by-mode basis. This differential analysis complements the Bayesian maximum likelihood analysis that finds the most probable model given the data. Analyzing the surveys with their corresponding most likely models from the CMB-like family of models, as well as with the currently popular LambdaCDM model, reveals a systematic inconsistency of the data with these "best" models. There is a systematic trend of the cumulative chi(2) to increase with the mode number (where the modes are sorted by decreasing order of the eigenvalues). This corresponds to a decrease of the chi(2) with the variance associated with a mode and hence with its effective scale. It follows that the differential analysis finds that on small (large) scales the global analysis of all the modes "puts" less (more) power than actually required by the data. This observed trend might indicate one of the following: (1) the theoretical model (i.e., power spectrum) or the error model (or both) have an excess of power on large scales, (2) velocity bias, or (3) the velocity data suffers from systematic errors that have not yet been corrected.     

High-precision VLBI astrometric observations of radio-emitting stars for detection of extra-solar planets

The displacement of a radio-emitting star around the barycenter of a possible planetary system can be measured by astrometric very long baseline interferometry (VLBI) observations. We have observed the radio-emitting star ² CrB at 8 epochs over 5 years by VLBI and fitted its 5 astrometric parameters to the observed coordinates. The post-fit coordinate residuals have an rms scatter of 0.22 milliarcseconds and show no systematic behavior. We use this result to set a limit on the presence of planets around ² CrB and conclude that our present VLBI astrometric precision corresponds to the threshold to detect a Jupiter-like planet around this star. We also discuss the astrometric monitoring program of 11 radio-emitting stars that we are conducting for the Hipparcos space mission and its possible contribution to a long-term planet search program.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

The warm absorber of the type 1 Seyfert galaxy H1419+480

The bright type 1 Seyfert galaxy H1419+480  ( z ∼ 0.072)  , whose X-ray colours from earlier HEAO-1 and ROSAT missions suggested a complex X-ray spectrum, has been observed with XMM–Newton . The EPIC spectrum above 2 keV is well fitted by a power law with photon index  Γ= 1.84 ± 0.01  and an Fe Kα line of equivalent width ∼250 eV. At softer energies, a decrement with respect to this model extending from 0.5 to 1 keV is clearly detected. After trying a number of models, we find that the best fit corresponds to O vii absorption at the emission redshift, plus a 2σ detection of O viii absorption. A photoionized gas model fit yields  log ξ∼ 1.15–1.30  (ξ in erg cm s⁻¹) with   N _H∼ 5 × 10²¹ cm⁻²  for solar abundances. We find that the ionized absorber was weaker or absent in an earlier ROSAT observation. An International Ultraviolet Explorer spectrum of this source obtained two decades before shows a variable (within a year) C iv absorber outflowing with a velocity ∼1800 km s⁻¹. We show that both X-ray and ultraviolet absorptions are consistent with arising in the same gas, with varying ionization.     

Adaptive stellar spectral subclass classification based on Bayesian SVMs

Stellar spectral classification is one of the most fundamental tasks in survey astronomy. Many automated classification methods have been applied to spectral data. However, their main limitation is that the model parameters must be tuned repeatedly to deal with different data sets. In this paper, we utilize the Bayesian support vector machines (BSVM) to classify the spectral subclass data. Based on Gibbs sampling, BSVM can infer all model parameters adaptively according to different data sets, which allows us to circumvent the time-consuming cross validation for penalty parameter. We explored different normalization methods for stellar spectral data, and the best one has been suggested in this study. Finally, experimental results on several stellar spectral subclass classification problems show that the BSVM model not only possesses good adaptability but also provides better prediction performance than traditional methods.     

Planck and re-ionization history: a model selection view

We use Bayesian model selection tools to forecast the Planck satellite's ability to distinguish between different models for the re-ionization history of the Universe, using the large angular scale signal in the cosmic microwave background polarization spectrum. We find that Planck is not expected to be able to distinguish between an instantaneous re-ionization model and a two-parameter smooth re-ionization model, except for extreme values of the additional re-ionization parameter. If it cannot, then it will be unable to distinguish between different two-parameter models either. However, Bayesian model averaging will be needed to obtain unbiased estimates of the optical depth to re-ionization. We also generalize our results to a hypothetical future cosmic variance limited microwave anisotropy survey, where the outlook is more optimistic.     

Statistical Feature Recognition for Multidimensional Solar Imagery

A maximum a posteriori (MAP) technique is developed to identify solar features in cotemporal and cospatial images of line-of-sight magnetic flux, continuum intensity, and equivalent width observed with the NASA/National Solar Observatory (NSO) Spectromagnetograph (SPM). The technique facilitates human understanding of patterns in large data sets and enables systematic studies of feature characteristics for comparison with models and observations of long-term solar activity and variability. The method uses Bayes’ rule to compute the posterior probability of any feature segmentation of a trio of observed images from per-pixel, class-conditional probabilities derived from independently-segmented training images. Simulated annealing is used to find the most likely segmentation. New algorithms for computing class-conditional probabilities from three-dimensional Gaussian mixture models and interpolated histogram densities are described and compared. A new extension to the spatial smoothing in the Bayesian prior model is introduced, which can incorporate a spatial dependence such as center-to-limb variation. How the spatial scale of training segmentations affects the results is discussed, and a new method for statistical separation of quiet Sun and quiet network is presented.     

The real- and redshift-space density distribution functions for large-scale structure in the spherical collapse approximation

We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the p -order hierarchical amplitudes S _p , in both real and redshift space. We compare our results with numerical simulations, focusing on the     standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for     , where σ _L is the linearly evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for     . Numerical simulations also yield a simple empirical relation between the real-space PDF and the redshift-space PDF: we find that for     , the redshift-space PDF, [ P δ _{( z )}], is, to a good approximation, a simple rescaling of the real-space PDF, P [ δ ], i.e.,     where σ and σ _{( z )} are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the ΛCDM model. It breaks down for SCDM at     , but provides a good fit to the ΛCDM models for σ _L as large as 0.8.     

Near ultraviolet–infrared colours of red-sequence galaxies in local clusters

We present GALEX near-ultraviolet ( NUV ) and Two-Micron All-Sky Survey J -band photometry for red-sequence galaxies in local clusters. We define quiescent samples according to a strict emission threshold, removing galaxies with very recent star formation. We analyse the NUV – J colour–magnitude relation (CMR) and find that the intrinsic scatter is an order of magnitude larger than for the analogous optical CMR (∼0.35 rather than 0.05 mag), in agreement with previous studies. Comparing the NUV – J colours with spectroscopically derived stellar population parameters, we find a strong  (>5.5σ)  correlation with metallicity, only a marginal trend with age, and no correlation with the α/Fe ratio. We explore the origin of the large scatter and conclude that neither aperture effects nor the UV upturn phenomenon contribute significantly. We show that the scatter could be attributed to simple 'frosting' by either a young or a low-metallicity subpopulation.     

Gaseous electron multiplier gain characteristics using low-pressure Ar/CO<Subscript>2</Subscript>

Gaseous Electron Multiplier detectors, or GEMs, show promise for use on space-based X-ray missions. Operating pressure strongly affects the gain of the detector and must be optimized for best performance. We have measured the gain characteristics of a GEM detector at various pressures below atmosphere using a mixture of Ar:CO₂ with the goal of maximizing gain to push GEM capabilities to the lowest energies possible. This paper discusses our tests, results, and their implications for choosing a detector pressure. We found that at any operating pressure the detector voltage can be adjusted to achieve roughly the same maximum gain prior to the onset of electrical discharges. We also find that the gain varies substantially by spatial location across the detector, but this variation is insensitive to changes in pressure allowing it to be calibrated and corrected if necessary. The detector pressure can therefore be optimized in the interest of other performance parameters such as leak rate, window stress, power requirements, or quantum efficiency without concern for negatively affecting the gain. These results can inform the choice of operating pressure and voltage for GEMs used onboard future space missions.