2,252 research outputs found
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
The Anderson model of localization: a challenge for modern eigenvalue methods
We present a comparative study of the application of modern eigenvalue
algorithms to an eigenvalue problem arising in quantum physics, namely, the
computation of a few interior eigenvalues and their associated eigenvectors for
the large, sparse, real, symmetric, and indefinite matrices of the Anderson
model of localization. We compare the Lanczos algorithm in the 1987
implementation of Cullum and Willoughby with the implicitly restarted Arnoldi
method coupled with polynomial and several shift-and-invert convergence
accelerators as well as with a sparse hybrid tridiagonalization method. We
demonstrate that for our problem the Lanczos implementation is faster and more
memory efficient than the other approaches. This seemingly innocuous problem
presents a major challenge for all modern eigenvalue algorithms.Comment: 16 LaTeX pages with 3 figures include
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
Measurements with the Chandra X-Ray Observatory's flight contamination monitor
NASA's Chandra X-ray Observatory includes a Flight Contamination Monitor
(FCM), a system of 16 radioactive calibration sources mounted to the inside of
the Observatory's forward contamination cover. The purpose of the FCM is to
verify the ground-to-orbit transfer of the Chandra flux scale, through
comparison of data acquired during the ground calibration with those obtained
in orbit, immediately prior to opening the Observatory's sun-shade door. Here
we report results of these measurements, which place limits on the change in
mirror--detector system response and, hence, on any accumulation of molecular
contamination on the mirrors' iridium-coated surfaces.Comment: 7pages,8figures,for SPIE 4012, paper 7
Unbiased methods for removing systematics from galaxy clustering measurements
Measuring the angular clustering of galaxies as a function of redshift is a powerful method for extracting information from the three-dimensional galaxy distribution. The precision of such measurements will dramatically increase with ongoing and future wide-field galaxy surveys. However, these are also increasingly sensitive to observational and astrophysical contaminants. Here, we study the statistical properties of three methods proposed for controlling such systematics – template subtraction, basic mode projection, and extended mode projection – all of which make use of externally supplied template maps, designed to characterize and capture the spatial variations of potential systematic effects. Based on a detailed mathematical analysis, and in agreement with simulations, we find that the template subtraction method in its original formulation returns biased estimates of the galaxy angular clustering. We derive closed-form expressions that should be used to correct results for this shortcoming. Turning to the basic mode projection algorithm, we prove it to be free of any bias, whereas we conclude that results computed with extended mode projection are biased. Within a simplified setup, we derive analytical expressions for the bias and discuss the options for correcting it in more realistic configurations. Common to all three methods is an increased estimator variance induced by the cleaning process, albeit at different levels. These results enable unbiased high-precision clustering measurements in the presence of spatially varying systematics, an essential step towards realizing the full potential of current and planned galaxy surveys
Algebraic results for the values and of the Jacobi theta-constant
Let denote the classical Jacobi theta-constant. We prove that the two values and are algebraically independent over for any in the upper half-plane such that is an algebraic number, where are distinct integers
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
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