On understanding the figures of merit for detection and measurement of x-ray polarization

The prospects for accomplishing X-ray polarization measurements appear to have grown in recent years after a more than 35-year hiatus. Unfortunately, this long hiatus has brought with it some confusion over the statistical uncertainties associated with polarization measurements of astronomical sources. The heart of this confusion stems from a misunderstanding (or potential misunderstanding) of a standard figure of merit-the minimum detectable polarization (MDP)-that one of us introduced many years ago. We review the relevant statistics, and quantify the differences between the MDP and the uncertainty of an actual polarization measurement. We discuss the implications for future missions.Comment: 5 pages, 2 figures, to be presented at SPIE conference 7732 (paper 13), corrected typo

Measuring x-ray polarization in the presence of systematic effects: Known background

The prospects for accomplishing x-ray polarization measurements of astronomical sources have grown in recent years, after a hiatus of more than 37 years. Unfortunately, accompanying this long hiatus has been some confusion over the statistical uncertainties associated with x-ray polarization measurements of these sources. We have initiated a program to perform the detailed calculations that will offer insights into the uncertainties associated with x-ray polarization measurements. Here we describe a mathematical formalism for determining the 1- and 2-parameter errors in the magnitude and position angle of x-ray (linear) polarization in the presence of a (polarized or unpolarized) background. We further review relevant statistics-including clearly distinguishing between the Minimum Detectable Polarization (MDP) and the accuracy of a polarization measurement.Comment: 12 pages, 4 figures, for SPIE conference proceeding

Overcoming seed dormancy in Glaucium Spp. (Papaveraceae)

2007 Fall.Covers not scanned.Includes bibliographical references.The Horned Poppy, Glaucium sp., is a potential candidate for introduction as an herbaceous perennial to Colorado. However, its introduction has been hindered by poor germination, less than 10% in informal studies across the state. Nine seed lots of Glaucium sp., representing four different species and a hybrid harvested from four different year, were collected at Denver Botanic Gardens and used in research to develop a protocol for seed treatment to improve germination. Four different trials were conducted to evaluate germination. The first trial evaluated stratification temperatures and germination with and without light on two collection years of G. flavum. The greatest germination was 69.5% for the seeds collected in 2005 that were stratified for 45 days at 7°C and germinated with light. The seeds harvested in 2003 had 53 % germination with 7°C stratification for 45 days and germinated without light. The second trial evaluated scarification treatments, hot water, concentrated sulfuric acid (2 levels) and nicks in the seed coat, on two collection years of G. flavum and G. acutidentatum. 2005 G. flavum had the greatest germination at 57 % with a 30- minute sulfuric acid scarification. 2003 G. flavum had 20% germination with the 60- minute acid scarification. G. acutidentatum seeds from 2003 and 2005 germinated with acid treatments but not as well as G. flavum. 2003 G. acutidentatum had 6% germination with 60-minute acid scarification and 2005 G. acutidentatum had 1.5% germination with 30-minute acid scarification. Stratification and scarification were evaluated together in the third trial. Additional seed lots; 2003 G. grandiflorum, 2003 G. corniculatum and 1999 G. corniculatum x flavum were included. Although each seed lot had varying responses to the treatments, 30-minute acid scarification combined with 30- or 45-day stratification at 8°C were the optimal pretreatments. The germination percentages for these treatments ranged from 60 to 92%. The final trial compared gibberellic acid to stratification to determine if GA could substitute for cold stratification. Hydrogen peroxide was also evaluated for comparison purposes. For all the seed lots, 30-minute acid scarification with 400 ppm or 500 ppm GA3 generated the greatest germination. The percentages for these treatments ranged from 58 to 95%. Gibberellic acid proved to be a substitute for cold stratification; however, seeds germinated slower than cold stratification. Germination with GA took approximately 10 days while stratified seed germinated in five days. G. grandiflorum and G. acutidentatum can be considered to have intermediate complex morphophysiological dormancy with a hard seed coat, while G. corniculatum appears to have only a hard seed coat

Stabilized lanthanum sulphur compounds

Lanthanum sulfide is maintained in the stable cubic phase form over a temperature range of from 500 C to 1500 C by adding to it small amounts of calcium, barium, or strontium. This compound is an excellent thermoelectric material

Forecasting constraints from the cosmic microwave background on eternal inflation

We forecast the ability of cosmic microwave background (CMB) temperature and polarization datasets to constrain theories of eternal inflation using cosmic bubble collisions. Using the Fisher matrix formalism, we determine both the overall detectability of bubble collisions and the constraints achievable on the fundamental parameters describing the underlying theory. The CMB signatures considered are based on state-of-the-art numerical relativistic simulations of the bubble collision spacetime, evolved using the full temperature and polarization transfer functions. Comparing a theoretical cosmic-variance-limited experiment to the WMAP and Planck satellites, we find that there is no improvement to be gained from future temperature data, that adding polarization improves detectability by approximately 30%, and that cosmic-variance-limited polarization data offer only marginal improvements over Planck. The fundamental parameter constraints achievable depend on the precise values of the tensor-to-scalar ratio and energy density in (negative) spatial curvature. For a tensor-to-scalar ratio of $0.1$ and spatial curvature at the level of $10^{-4}$, using cosmic-variance-limited data it is possible to measure the width of the potential barrier separating the inflating false vacuum from the true vacuum down to $M_{\rm Pl}/500$, and the initial proper distance between colliding bubbles to a factor $\pi/2$ of the false vacuum horizon size (at three sigma). We conclude that very near-future data will have the final word on bubble collisions in the CMB.Comment: 14 pages, 6 figure

The Simplicial Characterisation of TS networks: Theory and applications

We use the visibility algorithm to construct the time series networks obtained from the time series of different dynamical regimes of the logistic map. We define the simplicial characterisers of networks which can analyse the simplicial structure at both the global and local levels. These characterisers are used to analyse the TS networks obtained in different dynamical regimes of the logisitic map. It is seen that the simplicial characterisers are able to distinguish between distinct dynamical regimes. We also apply the simplicial characterisers to time series networks constructed from fMRI data, where the preliminary results indicate that the characterisers are able to differentiate between distinct TS networks.Comment: 11 pages, 2 figures, 4 tables. Accepted for publication in Proceedings of the 4th International Conference on Applications in Nonlinear Dynamics (ICAND 2016

Methods of optimizing X-ray optical prescriptions for wide-field applications

We are working on the development of a method for optimizing wide-field X-ray telescope mirror prescriptions, including polynomial coefficients, mirror shell relative displacements, and (assuming 4 focal plane detectors) detector placement along the optical axis and detector tilt. With our methods, we hope to reduce number of Monte-Carlo ray traces required to search the multi-dimensional design parameter space, and to lessen the complexity of finding the optimum design parameters in that space. Regarding higher order polynomial terms as small perturbations of an underlying Wolter I optic design, we begin by using the results of Monte-Carlo ray traces to devise trial analytic functions, for an individual Wolter I mirror shell, that can be used to represent the spatial resolution on an arbitrary focal surface. We then introduce a notation and tools for Monte-Carlo ray tracing of a polynomial mirror shell prescription which permits the polynomial coefficients to remain symbolic. In principle, given a set of parameters defining the underlying Wolter I optics, a single set of Monte-Carlo ray traces are then sufficient to determine the polymonial coefficients through the solution of a large set of linear equations in the symbolic coefficients. We describe the present status of this development effort.Comment: 14 pages, to be presented at SPIE conference 7732 (paper 93

Study of HST counterparts to Chandra X-ray sources in the Globular Cluster M71

We report on archival Hubble Space Telescope (HST) observations of the globular cluster M71 (NGC 6838). These observations, covering the core of the globular cluster, were performed by the Advanced Camera for Surveys (ACS) and the Wide Field Planetary Camera 2 (WFPC2). Inside the half-mass radius (r_h = 1.65') of M71, we find 33 candidate optical counterparts to 25 out of 29 Chandra X-ray sources while outside the half-mass radius, 6 possible optical counterparts to 4 X-ray sources are found. Based on the X-ray and optical properties of the identifications, we find 1 certain and 7 candidate cataclysmic variables (CVs). We also classify 2 and 12 X-ray sources as certain and potential chromospherically active binaries (ABs), respectively. The only star in the error circle of the known millisecond pulsar (MSP) is inconsistent with being the optical counterpart. The number of X-ray faint sources with L_x>4x10^{30} ergs/s (0.5-6.0 keV) found in M71 is higher than extrapolations from other clusters on the basis of either collision frequency or mass. Since the core density of M71 is relatively low, we suggest that those CVs and ABs are primordial in origin.Comment: 12 pages, 6 figures. Accepted for publication in Astronomy and Astrophysic