Fourier Analysis of Gapped Time Series: Improved Estimates of Solar and Stellar Oscillation Parameters

Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on the total length (T), quality, and completeness of the observations. Except in a few simple cases, the effect of gaps in the data on measurement precision is poorly understood, in particular in Fourier space where the convolution of the observable with the observation window introduces correlations between different frequencies. Here we describe and implement a rather general method to retrieve maximum likelihood estimates of the oscillation parameters, taking into account the proper statistics of the observations. Our fitting method applies in complex Fourier space and exploits the phase information. We consider both solar-like stochastic oscillations and long-lived harmonic oscillations, plus random noise. Using numerical simulations, we demonstrate the existence of cases for which our improved fitting method is less biased and has a greater precision than when the frequency correlations are ignored. This is especially true of low signal-to-noise solar-like oscillations. For example, we discuss a case where the precision on the mode frequency estimate is increased by a factor of five, for a duty cycle of 15%. In the case of long-lived sinusoidal oscillations, a proper treatment of the frequency correlations does not provide any significant improvement; nevertheless we confirm that the mode frequency can be measured from gapped data at a much better precision than the 1/T Rayleigh resolution.Comment: Accepted for publication in Solar Physics Topical Issue "Helioseismology, Asteroseismology, and MHD Connections

Spectral Energy Distribution Fitting: Application to Lyman Alpha-Emitting Galaxies

Spectral Energy Distribution (SED) fitting is a well-developed astrophysical tool that has recently been applied to high-redshift Lyman Alpha-emitting galaxies. If rest-frame ultraviolet through near-infrared photometry is available, it allows the simultaneous determination of the star formation history and dust extinction of a galaxy. Lyman Alpha-emitter SED fitting results from the literature find star formation rates ~3 M_sun/yr, stellar masses ~10^9 M_sun for the general population but ~10^10 M_sun for the subset detected by IRAC, and very low dust extinction, A_V < 0.3, although a couple of outlying analyses prefer significantly more dust and higher intrinsic star formation rates. A checklist of 14 critical choices that must be made when performing SED fitting is discussed.Comment: A review and discussion from the "Understanding Lyman-alpha Emitters" meeting in Heidelberg, Oct. 2008, 10 pages, to be published in New Astronomy Reviews. Full conference summary available as arXiv:0904.3335. Conference home-page, with presentations, is http://www.mpia.de/Public/Aktuelles/Tagungen/lae08/lae08.htm

A New Method for Protecting Interrelated Time Series with Bayesian Prior Distributions and Synthetic Data

Organizations disseminate statistical summaries of administrative data via the Web for unrestricted public use. They balance the trade-off between confidentiality protection and inference quality. Recent developments in disclosure avoidance techniques include the incorporation of synthetic data, which capture the essential features of underlying data by releasing altered data generated from a posterior predictive distribution. The United States Census Bureau collects millions of interrelated time series micro-data that are hierarchical and contain many zeros and suppressions. Rule-based disclosure avoidance techniques often require the suppression of count data for small magnitudes and the modification of data based on a small number of entities. Motivated by this problem, we use zero-inflated extensions of Bayesian Generalized Linear Mixed Models (BGLMM) with privacy-preserving prior distributions to develop methods for protecting and releasing synthetic data from time series about thousands of small groups of entities without suppression based on the of magnitudes or number of entities. We find that as the prior distributions of the variance components in the BGLMM become more precise toward zero, confidentiality protection increases and inference quality deteriorates. We evaluate our methodology using a strict privacy measure, empirical differential privacy, and a newly defined risk measure, Probability of Range Identification (PoRI), which directly measures attribute disclosure risk. We illustrate our results with the U.S. Census Bureau’s Quarterly Workforce Indicators

Questionnaire study to gain an insight into the manufacturing and fitting process of artificial eyes in children: an ocularist perspective

Purpose To gain an insight into the manufacturing and fitting of artificial eyes in children and potential improvements to the process. Method An online qualitative survey was distributed to 39 ocularists/prosthetists in Europe and Canada. Participants were recruited through purposive sampling, specifically maximum variation sampling from the researcher’s contacts and an online search. Results The findings highlighted the current impression technique as being the most difficult yet most important part of the current process for both the ocularist and child patient. Negatively affecting obtaining a good impression, the child patients distress can be reduced by their parents by providing encouragement, reassurance, practicing the insertion and removal of the artificial eye and being matter of fact. Whilst improvements to the current process provided mixed views, the incorporation of current technology was perceived as not being able to meet the requirements to produce aesthetically pleasing artificial eyes. Conclusion The current artificial eye process can be seen as an interaction with its success being dependent on the child patient’s acceptance and adjustment which is dependent on the factors associated to the process. Investigation into the needs of the patient and whether technology can improve the process are the next steps in its advancement

Magellanic Cloud Structure from Near-IR Surveys I: The Viewing Angles of the LMC

We present a detailed study of the viewing angles of the LMC disk plane. We find that our viewing direction differs considerably from the commonly accepted values, which has important implications for the structure of the LMC. The discussion is based on an analysis of spatial variations in the apparent magnitude of features in the near-IR color-magnitude diagrams extracted from the DENIS and 2MASS surveys. Sinusoidal brightness variations with a peak-to-peak amplitude of approximately 0.25 mag are detected as function of position angle, for both AGB and RGB stars. This is naturally interpreted as the result of distance variations, due to one side of the LMC plane being closer to us than the opposite side. The best fitting geometric model of an inclined plane yields an inclination angle i = 34.7 +/- 6.2 degrees and line-of-nodes position angle Theta = 122.5 +/- 8.3 degrees. There is tentative evidence that the LMC disk plane may be warped. Traditional methods to estimate the position angle of the line of nodes have used either the major axis position angle Theta_maj of the spatial distribution of tracers on the sky, or the position angle Theta_max of the line of maximum gradient in the velocity field, given that for a circular disk Theta_maj = Theta_max = Theta. The present study does not rely on the assumption of circular symmetry, and is considerably more accurate than previous studies of its kind. We find that the actual position angle of the line of nodes differs considerably from both Theta_maj and Theta_max, for which measurements have fallen in the range 140-190 degrees. This indicates that the intrinsic shape of the LMC disk is not circular, but elliptical, as discussed further in Paper II. [Abridged]Comment: Astronomical Journal, in press. 44 pages, LaTeX, with 8 PostScript figures. Contains minor revisions with respect to previously posted version. Check out http://www.stsci.edu/~marel/lmc.html for a large scale (23x21 degree) stellar number-density image of the LMC constructed from RGB and AGB stars in the 2MASS and DENIS surveys. The paper is available with higher resolution figures from http://www.stsci.edu/~marel/abstracts/abs_R31.htm

On Physical Scales of Dark Matter Halos

It is common practice to describe formal size and mass scales of dark matter halos as spherical overdensities with respect to an evolving density threshold. Here, we critically investigate the evolutionary effects of several such commonly used definitions and compare them to the halo evolution within fixed physical scales as well as to the evolution of other intrinsic physical properties of dark matter halos. It is shown that, in general, the traditional way of characterizing sizes and masses of halos dramatically overpredicts the degree of evolution in the last 10 Gyr, especially for low-mass halos. This pseudo-evolution leads to the illusion of growth even though there are no major changes within fixed physical scales. Such formal size definitions also serve as proxies for the virialized region of a halo in the literature. In general, those spherical overdensity scales do not coincide with the virialized region. A physically more precise nomenclature would be to simply characterize them by their very definition instead of calling such formal size and mass definitions 'virial'. In general, we find a discrepancy between the evolution of the underlying physical structure of dark matter halos seen in cosmological structure formation simulations and pseudo-evolving formal virial quantities. We question the importance of the role of formal virial quantities currently ubiquitously used in descriptions, models and relations that involve properties of dark matter structures. Concepts and relations based on pseudo-evolving formal virial quantities do not properly reflect the actual evolution of dark matter halos and lead to an inaccurate picture of the physical evolution of our universe.Comment: 17 pages, 14 figures, 1 table, ApJ accepte

The Megamaser Cosmology Project: IV. A Direct Measurement of the Hubble Constant from UGC 3789

In Papers I and II from the Megamaser Cosmology Project (MCP), we reported initial observations of water masers in an accretion disk of a supermassive black hole at the center of the galaxy UGC 3789, which gave an angular-diameter distance to the galaxy and an estimate of Ho with 16% uncertainty. We have since conducted more VLBI observations of the spatial-velocity structure of these water masers, as well as continued monitoring of its spectrum to better measure maser accelerations. These more extensive observations, combined with improved modeling of the masers in the accretion disk of the central supermassive black hole, confirm our previous results, but with signifcantly improved accuracy. We find Ho = 68.9 +/- 7.1 km/s/Mpc; this estimate of Ho is independent of other methods and is accurate to +/-10%, including sources of systematic error. This places UGC 3789 at a distance of 49.6 +/- 5.1 Mpc, with a central supermassive black hole of (1.16 +/- 0.12) x 10^7 Msun.Comment: to appear in Ap