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

Design and Tests of the Hard X-ray Polarimeter X-Calibur

X-ray polarimetry promises to give qualitatively new information bout high-energy astrophysical sources, such as binary black hole  systems, micro-quasars, active galactic nuclei, and gamma-ray bursts. We designed, built and tested ahard X-ray polarimeter, X-Calibur, to be used in the focal plane of the InFOCuS grazing incidence hard X-ray telescope.X-Calibur combines a low-Z Compton scatterer with a CZT detector assembly to measure the polarization of 20−60 keV X-rays making use of the fact that polarized photons Compton scatter preferentially perpendicular to the electric field orientation; in principal, a similar space-borne experiment could be operated in the 5−100 keV regime. X-Calibur achieves a high detection efficiency of order unity

Systematic effects on a Compton polarimeter at the focus of an X-ray mirror

XL-Calibur is a balloon-borne Compton polarimeter for X-rays in the $\sim$15-80 keV range. Using an X-ray mirror with a 12 m focal length for collecting photons onto a beryllium scattering rod surrounded by CZT detectors, a minimum-detectable polarization as low as $\sim$3% is expected during a 24-hour on-target observation of a 1 Crab source at 45$^{\circ}$ elevation. Systematic effects alter the reconstructed polarization as the mirror focal spot moves across the beryllium scatterer, due to pointing offsets, mechanical misalignment or deformation of the carbon-fiber truss supporting the mirror and the polarimeter. Unaddressed, this can give rise to a spurious polarization signal for an unpolarized flux, or a change in reconstructed polarization fraction and angle for a polarized flux. Using bench-marked Monte-Carlo simulations and an accurate mirror point-spread function characterized at synchrotron beam-lines, systematic effects are quantified, and mitigation strategies discussed. By recalculating the scattering site for a shifted beam, systematic errors can be reduced from several tens of percent to the few-percent level for any shift within the scattering element. The treatment of these systematic effects will be important for any polarimetric instrument where a focused X-ray beam is impinging on a scattering element surrounded by counting detectors.Comment: Submitted to Astroparticle Physic

High-Energy Polarimetry - a new window to probe extreme physics in AGN jets

The constantly improving sensitivity of ground-based and space-borne observatories has made possible the detection of high-energy emission (X-rays and gamma-rays) from several thousands of extragalactic sources. Enormous progress has been made in measuring the continuum flux enabling us to perform imaging, spectral and timing studies. An important remaining challenge for high-energy astronomy is measuring polarization. The capability to measure polarization is being realized currently at X-ray energies (e.g. with IXPE), and sensitive gamma-ray telescopes capable of measuring polarization, such as AMEGO, AdEPT, e-ASTROGAM, etc., are being developed. These future gamma-ray telescopes will probe the radiation mechanisms and magnetic fields of relativistic jets from active galactic nuclei at spatial scales much smaller than the angular resolution achieved with continuum observations of the instrument. In this white paper, we discuss the scientific potentials of high-energy polarimetry, especially gamma-ray polarimetry, including the theoretical implications, and observational technology advances being made. In particular, we will explore the primary scientific opportunities and wealth of information expected from synergy of multi-wavelength polarimetry that will be brought to multi-messenger astronomy.Comment: submitted to Astro2020 (Astronomy and Astrophysics Decadal Survey

Observations of a GX 301-2 Apastron Flare with the X-Calibur Hard X-Ray Polarimeter Supported by NICER, the Swift XRT and BAT, and Fermi GBM

The accretion-powered X-ray pulsar GX 301-2 was observed with the balloon-borne X-Calibur hard X-ray polarimeter during late December 2018, with contiguous observations by the NICER X-ray telescope, the Swift X-ray Telescope and Burst Alert Telescope, and the Fermi Gamma-ray Burst Monitor spanning several months. The observations detected the pulsar in a rare apastron flaring state coinciding with a significant spin-up of the pulsar discovered with the Fermi GBM. The X-Calibur, NICER, and Swift observations reveal a pulse profile strongly dominated by one main peak, and the NICER and Swift data show strong variation of the profile from pulse to pulse. The X-Calibur observations constrain for the first time the linear polarization of the 15-35 keV emission from a highly magnetized accreting neutron star, indicating a polarization degree of (27+38-27)% (90% confidence limit) averaged over all pulse phases. We discuss the spin-up and the X-ray spectral and polarimetric results in the context of theoretical predictions. We conclude with a discussion of the scientific potential of future observations of highly magnetized neutron stars with the more sensitive follow-up mission XL-Calibur