Analysis of the data from Compton X-ray polarimeters which measure the azimuthal and polar scattering angles

Abstract

a b s t r a c t X-ray polarimetry has the potential to make key-contributions to our understanding of galactic compact objects like binary black hole systems and neutron stars, and extragalactic objects like active galactic nuclei, blazars, and Gamma-Ray Bursts. Furthermore, several particle astrophysics topics can be addressed including uniquely sensitive tests of Lorentz invariance. In the energy range from 10 keV to several MeV, Compton polarimeters achieve the best performance. In this paper we evaluate the benefit that comes from using the azimuthal and polar angles of the Compton scattered photons in the analysis, rather than using the azimuthal scattering angles alone. We study the case of an ideal Compton polarimeter and show that a Maximum Likelihood analysis which uses the two scattering angles lowers the Minimum Detectable Polarization (MDP) by %20% compared to a standard analysis based on the azimuthal scattering angles alone. The accuracies with which the polarization fraction and the polarization direction can be measured improve by a similar amount. We conclude by discussing potential applications of Maximum Likelihood analysis methods for various polarimeter experiments.

Compton polarimetry revisited

“…3). These results are in qualitative agreement with those obtained at 100 keV by a likelihood analysis of the doubly differential cross section [17].…”

“…1 of Ref. [17]). In this expression, φ is the azimuthal angle, that is the angle between the scattering plane and the direction of polarisation of the incident photon.…”

Maximum Likelihood Compton Polarimetry with the Compton Spectrometer and Imager

“…This is a consequence of the fact that the modulation of azimuthal scattering angles depends on energy (Equation 3, Figure 1). Nonetheless, given the ∼ 21% MDP improvement from Krawczynski (2011), as well as our MDP improvement of 20%, we conclude that roughly 20% is a good rule of thumb for the maximum improvement one can expect when using the MLM.…”

“…At the outset of this work, our expectation was that the MDP would improve by up to ∼ 21%, as Krawczynski (2011) showed that the MLM improved the MDP by ∼ 21% over the SM with an idealized Compton polarimeter at 100 keV, and under the assumption that the same number of counts was used in both the SM and MLM. However, as outlined in Section 2.2, the SM event selections must be optimized to give as low an MDP as possible.…”

“…While this approach is simple and effective, it disregards information that can be used to further constrain the polarization properties of the beam, such as the Compton (polar) scattering angle, and the initial photon energy. Krawczynski (2011) has shown that by combining the Compton scattering angle and photon energy measurements with the azimuthal scattering angle measurement in an unbinned, maximum likelihood analysis, the sensitivity of an ideal polarimeter is improved by ∼ 21% over the standard approach. In this paper, we describe our efforts to implement this maximum likelihood technique for a real, non-ideal polarimeter, namely the Compton Spectrometer and Imager (COSI) (Chiu et al 2015;Kierans et al 2017).…”