Unbinned likelihood analysis for X-ray polarization

ABSTRACT We present a systematic study of the unbinned, photon-by-photon likelihood technique which can be used as an alternative method to analyse phase-dependent, X-ray spectro-polarimetric observations obtained with IXPE and other photoelectric polarimeters. apply unbinned models luminous pulsar Hercules X-1, for we produce simulated using ixpeobssim package. consider minimal knowledge about actual physical process responsible polarized emission from accreting assume that observed phase-dependent polarization angle described by rotating vector model. Using technique, detector’s modulation factor, information alone, found both model underlying spectro-polarimetry reconstruct equally well geometric configuration angles pulsar. However, measured fraction becomes biased respect unless energy dispersion effective area detector are also taken into account. To this end, energy-dispersed estimator is proved unbiased. For different analyses, obtain posterior distributions multiple realizations show yields $\sim 10{{\ \rm per\ cent}}$ smaller error bars than binned technique. discuss sources, such magnetars, in might applied.