Analyzing the Data from X-ray Polarimeters with Stokes Parameters

X-ray polarimetry promises to deliver unique information about the geometry of the inner accretion flow of astrophysical black holes and the nature of matter and electromagnetism in and around neutron stars. In this paper, we discuss the possibility to use Stokes parameters - a commonly used tool in radio, infrared, and optical polarimetry - to analyze the data from X-ray polarimeters such as scattering polarimeters and photoelectric effect polarimeters, which measure the linear polarization of the detected X-rays. Based on the azimuthal scattering angle (in the case of a scattering polarimeter) or the azimuthal component of the angle of the electron ejection (in the case of a photoelectric effect polarimeter), the Stokes parameters can be calculated for each event recorded in the detector. Owing to the additive nature of Stokes parameters, the analysis reduces to adding the Stokes parameters of the individual events and subtracting the Stokes parameters characterizing the background (if present). The main strength of this kind of analysis is that the errors on the Stokes parameters can be computed easily and are well behaved - in stark contrast of the errors on the polarization fraction and polarization direction. We demonstrate the power of the Stokes analysis by deriving several useful formulae, e.g. the expected error on the polarization fraction and polarization direction for a detection of $N_S$ signal and $N_{BG}$ background events, the optimal observation times of the signal and background regions in the presence of non-negligible background contamination of the signal, and the minimum detectable polarization (MDP) that can be achieved when following this prescription.Comment: 9 pages, 2 figures, accepted for publication in Astropart. Phy

Comparison of techniques to reconstruct VHE gamma-ray showers from multiple stereoscopic Cherenkov images

For air showers observed simultaneously by more than two imaging atmospheric Cherenkov telescopes, the shower geometry is overconstrained by the images and image information should be combined taking into account the quality of the images. Different algorithms are discussed and tested experimentally using data obtained from observations of Mkn 501 with the HEGRA IACT system. Most of these algorithms provide an estimate of the accuracy of the reconstruction of shower geometry on an event-by-event basis, allowing, e.g., to select higher-quality subsamples for precision measurements.Comment: 14 Pages, 6 figures, Late