arXiv subjects

William H. Jefferys

Publications and source records attributed to William H. Jefferys.

9 recordsLinked to original sources

arXiv2016

The Power of Principled Bayesian Methods in the Study of Stellar Evolution

It takes years of effort employing the best telescopes and instruments to obtain high-quality stellar photometry, astrometry, and spectroscopy. Stellar evolution models contain the experience of lifetimes of theoretical calculations and testing. Yet most astronomers fit these valuable models to these precious datasets by eye. We show that a principled Bayesian approach to fitting models to stellar data yields substantially more information over a range of stellar astrophysics. We highlight advances in determining the ages of star clusters, mass ratios of binary stars, limitations in the accuracy of stellar models, post-main-sequence mass loss, and the ages of individual white dwarfs. We also outline a number of unsolved problems that would benefit from principled Bayesian analyses.

astro-ph.SR↗

arXiv2014

Bayesian Analysis for Stellar Evolution with Nine Parameters (BASE-9): User's Manual

BASE-9 is a Bayesian software suite that recovers star cluster and stellar parameters from photometry. BASE-9 is useful for analyzing single-age, single-metallicity star clusters, binaries, or single stars, and for simulating such systems. BASE-9 uses Markov chain Monte Carlo and brute-force numerical integration techniques to estimate the posterior probability distributions for the age, metallicity, helium abundance, distance modulus, and line-of-sight absorption for a cluster, and the mass, binary mass ratio, and cluster membership probability for every stellar object. BASE-9 is provided as open source code on a version-controlled web server. The executables are also available as Amazon Elastic Compute Cloud images. This manual provides potential users with an overview of BASE-9, including instructions for installation and use.

astro-ph.SR↗

arXiv2012

Bayesian Nonparametric Shrinkage Applied to Cepheid Star Oscillations

Bayesian nonparametric regression with dependent wavelets has dual shrinkage properties: there is shrinkage through a dependent prior put on functional differences, and shrinkage through the setting of most of the wavelet coefficients to zero through Bayesian variable selection methods. The methodology can deal with unequally spaced data and is efficient because of the existence of fast moves in model space for the MCMC computation. The methodology is illustrated on the problem of modeling the oscillations of Cepheid variable stars; these are a class of pulsating variable stars with the useful property that their periods of variability are strongly correlated with their absolute luminosity. Once this relationship has been calibrated, knowledge of the period gives knowledge of the luminosity. This makes these stars useful as "standard candles" for estimating distances in the universe.

stat.ME↗

arXiv2011

The White Dwarf Age of NGC 2477

We present deep photometric observations of the open cluster NGC 2477 using HST/WFPC2. By identifying seven cluster white dwarf candidates, we present an analysis of the white dwarf age of this cluster, using both the traditional method of fitting isochrones to the white dwarf cooling sequence, and by employing a new Bayesian statistical technique that has been developed by our group. This new method performs an objective, simultaneous model fit of the cluster and stellar parameters (namely age, metallicity, distance, reddening, as well as individual stellar masses, mass ratios, and cluster membership) to the photometry. Based on this analysis, we measure a white dwarf age of 1.035 +/- 0.054 +/- 0.087 Gyr (uncertainties represent the goodness of model fits and discrepancy among models, respectively), in good agreement with the cluster's main sequence turnoff age. This work is part of our ongoing work to calibrate main sequence turnoff and white dwarf ages using open clusters, and to improve the precision of cluster ages to the ~5% level.

astro-ph.SR↗

arXiv2009

Statistical analysis of stellar evolution

Color-Magnitude Diagrams (CMDs) are plots that compare the magnitudes (luminosities) of stars in different wavelengths of light (colors). High nonlinear correlations among the mass, color, and surface temperature of newly formed stars induce a long narrow curved point cloud in a CMD known as the main sequence. Aging stars form new CMD groups of red giants and white dwarfs. The physical processes that govern this evolution can be described with mathematical models and explored using complex computer models. These calculations are designed to predict the plotted magnitudes as a function of parameters of scientific interest, such as stellar age, mass, and metallicity. Here, we describe how we use the computer models as a component of a complex likelihood function in a Bayesian analysis that requires sophisticated computing, corrects for contamination of the data by field stars, accounts for complications caused by unresolved binary-star systems, and aims to compare competing physics-based computer models of stellar evolution.

stat.AP↗

arXiv2006

Inverting Color-Magnitude Diagrams to Access Precise Star Cluster Parameters: A Bayesian Approach

We demonstrate a new Bayesian technique to invert color-magnitude diagrams of main sequence and white dwarf stars to reveal the underlying cluster properties of age, distance, metallicity, and line-of-sight absorption, as well as individual stellar masses. The advantages our technique has over traditional analyses of color-magnitude diagrams are objectivity, precision, and explicit dependence on prior knowledge of cluster parameters. Within the confines of a given set of often-used models of stellar evolution, the initial-final mass relation, and white dwarf cooling, and assuming photometric errors that one could reasonably achieve with the Hubble Space Telescope, our technique yields exceptional precision for even modest numbers of cluster stars. For clusters with 50 to 400 members and one to a few dozen white dwarfs, we find typical internal errors of sigma([Fe/H]) <= 0.03 dex, sigma(m-M) <= 0.02 mag, and sigma(Av) <= 0.01 mag. We derive cluster white dwarf ages with internal errors of typically only 10% for clusters with only three white dwarfs and almost always <= 5% with ten white dwarfs. These exceptional precisions will allow us to test white dwarf cooling models and standard stellar evolution models through observations of white dwarfs in open and globular clusters.

astro-ph↗

arXiv2005

Infrared Surface Brightness Distances to Cepheids

Bayesian statistical calculations and linear-bisector calculations for obtaining Cepheid distances and radii by the infrared surface brightness method have been compared for a set of 38 Cepheids. The distances obtained by the two techniques agree to 1.5%+/-0.6% and the radii agree to 1.1%+/-0.7%. Thus the two methods yield the same distances and radii at the 2 sigma level. This implies that the short distance to the LMC found in recent linearbisector studies of Cepheids is not a result of simplifications in the mathematical approach. The computed uncertainties in distance and radius are larger in the Bayesian calculation typically by a factor of three.

astro-ph↗

arXiv2005

Infrared Surface Brightness Distances to Cepheids: a comparison of Bayesian and linear-bisector calculations

We have compared the results of Bayesian statistical calculations and linear-bisector calculations for obtaining Cepheid distances and radii by the infrared surface brightness method. We analyzed a set of 38 Cepheids using a Bayesian Markov Chain Monte Carlo method that had been recently studied with a linear-bisector method. The distances obtained by the two techniques agree to 1.5 \pm 0.6% with the Bayesian distances being larger. The radii agree to 1.1% \pm 0.7% with the Bayesian determinations again being larger. We interpret this result as demonstrating that the two methods yield the same distances and radii. This implies that the short distance to the LMC found in recent linear-bisector studies of Cepheids is not caused by deficiencies in the mathematical treatment. However, the computed uncertainties in distance and radius for our dataset are larger in the Bayesian calculation by factors of 1.4-6.7. We give reasons to favor the Bayesian computations of the uncertainties. The larger uncertainties can have a significant impact upon interpretation of Cepheid distances and radii obtained from the infrared surface brightness method.

astro-ph↗

arXiv2002

Central Mass Concentration and Bar Dissolution in Nearby Spiral Galaxies

We use data from the BIMA Survey of Nearby Galaxies (SONG) to investigate the relationship between ellipticity and central mass concentration in barred spirals. Existing simulations predict that bar ellipticity decreases as inflowing mass driven by the bar accumulates in the central regions, ultimately destroying the bar. Using the ratio of the bulge mass to the mass within the bar radius as an estimate of the central mass concentration, we obtain dynamical mass estimates from SONG CO 1-0 rotation curve data. We find an inverse correlation between bar ellipticity and central mass concentration, consistent with simulations of bar dissolution.

astro-ph↗