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

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

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

Image analysis of the AXAF VETA-I x ray mirror

Initial core scan data of the VETA-I x-ray mirror proved disappointing, showing considerable unpredicted image structure and poor measured FWHM. 2-D core scans were performed, providing important insight into the nature of the distortion. Image deconvolutions using a ray traced model PSF was performed successfully to reinforce our conclusion regarding the origin of the astigmatism. A mechanical correction was made to the optical structure, and the mirror was tested successfully (FWHM 0.22 arcsec) as a result

The Development and Scientific Impact of the Chandra X-Ray Observatory

I review the operational capabilities of the Chandra X-ray Observatory, including some of the spectacular results obtained by the general observer community. A natural theme of this talk is that Chandra is revealing outflows of great quantities of energy that were not previously observable. I highlight the Chandra studies of powerful X-ray jets. This subject is only possible due to the sub-arcsecond resolution of the X-ray telescope.Comment: 8 pages, 4 figures. Talk given at the International Workshop on Astronomy and Relativistic Astrophysics (IWARA2003), Olinda, Brasil, October 2003. To appear in the International Journal of Modern Physics

Calibration of the AXAF Observatory: Overview

The Advanced X-ray Astrophysics Facility (AXAF) will soon begin its exploration of the x-ray universe, providing unprecedented angular and spectral resolution. Also unprecedented is the ambitious goal of calibrating the AXAF observatory to an accuracy of a few percent. Toward this end, AXAF science and engineering teams undertook an extensive calibration program at component, subsystem, and system levels. This paper is an overview of the system-level calibration activities, conducted over the past year at the Marshall Space Flight Center (MSFC) X-Ray Calibration Facility (XRCF)

Influence of radiative damping on the optical-frequency susceptibility

Motivated by recent discussions concerning the manner in which damping appears in the electric polarizability, we show that (a) there is a dependence of the nonresonant contribution on the damping and that (b) the damping enters according to the "opposite sign prescription." We also discuss the related question of how the damping rates in the polarizability are related to energy-level decay rates

Calibration of the AXAF Observatory: Overview

The Advanced X-ray Astrophysics Facility (AXAF) will soon begin its exploration of the x-ray universe, providing unprecedented angular and spectral resolution. Also unprecedented is the ambitious goal of calibrating the AXAF observatory to an accuracy of a few percent. Toward this end, AXAF science and engineering teams undertook an extensive calibration program at component, subsystem, and system levels. This paper is an overview of the system-level calibration activities, conducted over the past year at the Marshall Space Flight Center (MSFC) X-Ray Calibration Facility (XRCF)

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