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X-ray polarimetry has the potential to make key-contributions to ourunderstanding of galactic compact objects like binary black hole systems andneutron stars, and extragalactic objects like active galactic nuclei, blazars,and Gamma Ray Bursts. Furthermore, several particle astrophysics topics can beaddressed including uniquely sensitive tests of Lorentz invariance. In theenergy range from 10 keV to several MeV, Compton polarimeters achieve the bestperformance. In this paper we evaluate the benefit that comes from using theazimuthal and polar angles of the Compton scattered photons in the analysis,rather than using the azimuthal scattering angles alone. We study the case ofan ideal Compton polarimeter and show that a Maximum Likelihood analysis whichuses the two scattering angles lowers the Minimum Detectable Polarization (MDP)by ~20% compared to a standard analysis based on the azimuthal scatteringangles alone. The accuracies with which the polarization fraction and thepolarization direction can be measured improve by a similar amount. We concludeby discussing potential applications of Maximum Likelihood analysis methods forvarious polarimeter experiments.

Analysis of the Data from Compton X-ray Polarimeters which Measure the Azimuthal and Polar Scattering Angles