Analyzing the data from X-ray polarimeters with Stokes parameters

Abstract

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.

Searching for Axion-Like Particles with X-ray Polarimeters

“…Based on Chandra observations of NGC1275, we will conservatively assume a signal to background ratio of R S/B = 1/3. As derived in [33], the optimal fraction of the total observation time spent observing the background rather than the source is…”

Unveiling the magnetic structure of VHE SNRs/PWNe with XIPE, the x-ray imaging-polarimetry explorer

“…respectively 4 cos 2 (2φ k ), 4 sin 2 (2φ k )). These equations look very similar to the definition of Stokes parameters based on the electromagnetic vector angle ψ, but an additional factor 2 is included, to compensate for the fact that not the electric vector angle ψ is measured, but a realisation of a cos 2 modulation of it [27]. In principle, another, energy dependent, factor can be included f (E i ) in the kernel of Q and U and their variances, in order to compensate for the energy dependent measurement error of φ i .…”

“…From the resulting Monte Carlo event list Stokes I, Q, and U images can be made following the procedure explained in [27]. For N i, j events for a given image pixel, the estimated values for the stokes parameters are…”

Nonlinear QED effects in X-ray emission of pulsars

“…Therefore a polarimeter will collect a large number of seed photons to measure the polarization properties of a given source. Unlike radio or optical telescopes, which measure the intensity of the radiation from the source, most X-ray instruments detect individual photons [57,58]. In the previous section, we presented the main features of polarization evolution along a single radial ray in which the magnetic dipole vector during rotation around its spin axis, intersects the line of sight (LOS) at ωt = 0.…”