Unbinned likelihood analysis for Xray polarization
Abstract
We present a systematic study of the unbinned, photonbyphoton likelihood technique which can be used as an alternative method to analyse phasedependent, Xray spectropolarimetric observations obtained with IXPE and other photoelectric polarimeters. We apply the unbinned technique to models of the luminous Xray pulsar Hercules X1, for which we produce simulated observations using the IXPEOBSSIM package. We consider minimal knowledge about the actual physical process responsible for the polarized emission from the accreting pulsar and assume that the observed phasedependent polarization angle can be described by the rotating vector model. Using the unbinned technique, the detector's modulation factor, and the polarization information alone, we found that both the rotating vector model and the underlying spectropolarimetry model can reconstruct equally well the geometric configuration angles of the accreting pulsar. However, the measured polarization fraction becomes biased with respect to the underlying model unless the energy dispersion and effective area of the detector are also taken into account. To this end, we present an energydispersed likelihood estimator that is proved to be unbiased. For different analyses, we obtain posterior distributions from multiple IXPEOBSSIM realizations and show that the unbinned technique yields $\sim 10{{\ \rm per\ cent}}$ smaller error bars than the binned technique. We also discuss alternative sources, such as magnetars, in which the unbinned technique and the rotating vector model might be applied.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 2023
 DOI:
 10.1093/mnras/stad033
 arXiv:
 arXiv:2204.00140
 Bibcode:
 2023MNRAS.519.5902G
 Keywords:

 methods: data analysis;
 methods: statistical;
 techniques: polarimetric;
 Xrays: general;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 11 pages, 9 figures. Accepted for publication in MNRAS. Source code available at https://github.com/UBCAstrophysics/UnbinnedXraypolarimetry