Kavli Affiliate: Herman L. Marshall
| First 5 Authors: Herman L. Marshall, , , ,
| Summary:
An event-based maximum likelihood method for handling X-ray polarimetry data
is extended to include the effects of background and nonuniform sampling of the
possible position angle space. While nonuniform sampling in position angle
space generally introduces cross terms in the uncertainties of polarization
parameters that could create degeneracies, there are interesting cases that
engender no bias or parameter covariance. When including background in
Poisson-based likelihood formulation, the formula for the minimum detectable
polarization (MDP) has nearly the same form as for the case of Gaussian
statistics derived by Elsner et al. (2012) in the limiting case of an
unpolarized signal. A polarized background is also considered, which
demonstrably increases uncertainties in source polarization measurements. In
addition, a Kolmogorov-style test of the event position angle distribution is
proposed that can provide an unbinned test of models where the polarization
angle in Stokes space depends on event characteristics such as time or energy.
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