Bayesian Geometrical Modeling of IXPE Polarization Angle Curves of the Magnetars 1E 2259+586 and 1E 1547.0-5408

Abstract

X-ray polarimetry directly probes the radiation geometry and large-scale magnetic configuration of magnetars. We present a uniform Bayesian comparison between a dipole-dominated classical rotating vector model (CRVM) and a modified rotating vector model (MRVM) including a first-order magnetospheric twist correction. The models are applied to the phase-resolved IXPE polarization position angle (PA) curves of 1E~2259+586 and 1E~1547.0$-$5408. Parameters are inferred with a PA-level likelihood, and the models are compared using $\chi^2$, AIC, BIC, and Bayesian evidence. For 1E~1547.0$-$5408, we also test radio-derived geometrical constraints using radio-informed priors and radio-fixed fits. The current IXPE PA data for both sources are consistent with a dipole-dominated geometry and do not require a significant global twist. The MRVM gives only a marginal improvement for 1E~2259+586, with a Bayes factor of $\simeq3.3$, and no meaningful improvement for 1E~1547.0$-$5408, with a Bayes factor of $\simeq1.29$. We confirm that for 1E 1547, the nearly aligned radio geometry is not ruled out, but the radio RVM central geometry is not preferred by the X-ray PA data alone. The two sources show different impact angles, suggesting that magnetar X-ray polarization diversity reflects both viewing geometry and source-dependent emission physics. This work provides a framework for future Stokes-level and multi-epoch polarimetric studies with missions such as eXTP.