Optimal Summary Statistics for X-ray Polarization

We develop two new highly efficient estimators to measure the polarization (Stokes parameters) in experiments that constrain the position angle of individual photons such as scattering and gas-pixel-detector polarimeters, and analyse in detail a previously proposed estimator. All three of these estimators are at least fifty percent more efficient on typical datasets than the standard estimator used in the field. We present analytic estimates of the variance of these estimators and numerical experiments to verify these estimates. Two of the three estimators can be calculated quickly and directly through summations over the measurements of individual photons

X-ray polarimetry of the accreting pulsar GX 301-2

The phase- and energy-resolved polarization measurements of accreting X-ray pulsars (XRPs) allow us to test different theoretical models of their emission, as well as to provide an avenue to determine the emission region geometry. We present the results of the observations of the XRP GX 301-2 performed with the Imaging X-ray Polarimetry Explorer (IXPE). GX 301-2 is a persistent XRP with one of the longest known spin periods of ~680 s. A massive hyper-giant companion star Wray 977 supplies mass to the neutron star via powerful stellar winds. We do not detect significant polarization in the phase-averaged data using spectro-polarimetric analysis, with the upper limit on the polarization degree (PD) of 2.3% (99% confidence level). Using the phase-resolved spectro-polarimetric analysis we get a significant detection of polarization (above 99% c.l.) in two out of nine phase bins and marginal detection in three bins, with a PD ranging between ~3% and ~10%, and a polarization angle varying in a very wide range from ~0 deg to ~160 deg. Using the rotating vector model we obtain constraints on the pulsar geometry using both phase-binned and unbinned analysis getting excellent agreement. Finally, we discuss possible reasons for a low observed polarization in GX 301-2.Comment: 10 pages, 10 figures, submitted to A&

X-ray Polarization at the Crossroads

We argue that measurements of X-ray polarization using the recently launched Imaging X-ray Polarimetry Explorer will answer many open questions about magnetars in particular the physical state of their surfaces, whether vacuum birefringence exists, and the nature of the hard X-ray emission from these objects. We outline the capabilities of the instrument, specific models and the results of simulations for the magnetar 4U~0142+61.Comment: 12 pages, 7 figures, Neutron Star Astrophysics at the Crossroads: Magnetars and the Multimessenger Revolution, Proceedings IAU Symposium No. 363, 2022, E. Troja & M. Baring, ed

Optimal Summary Statistics for X-ray Polarization

International audienceWe develop two new highly efficient estimators to measure the polarization (Stokes parameters) in experiments that constrain the position angle of individual photons such as scattering and gas-pixel-detector polarimeters, and analyse in detail a previously proposed estimator. All three of these estimators are at least fifty percent more efficient on typical datasets than the standard estimator used in the field. We present analytic estimates of the variance of these estimators and numerical experiments to verify these estimates. Two of the three estimators can be calculated quickly and directly through summations over the measurements of individual photons

The X-Ray Polarimetry View of the Accreting Pulsar Cen X-3

International audienceThe first X-ray pulsar, Cen X-3, was discovered 50 yr ago. Radiation from such objects is expected to be highly polarized due to birefringence of plasma and vacuum associated with propagation of photons in the presence of the strong magnetic field. Here we present results of the observations of Cen X-3 performed with the Imaging X-ray Polarimetry Explorer. The source exhibited significant flux variability and was observed in two states different by a factor of ~20 in flux. In the low-luminosity state, no significant polarization was found in either pulse phase-averaged (with a 3σ upper limit of 12%) or phase-resolved (the 3σ upper limits are 20%-30%) data. In the bright state, the polarization degree of 5.8% ± 0.3% and polarization angle of 49.°6 ± 1.°5 with a significance of about 20σ were measured from the spectropolarimetric analysis of the phase-averaged data. The phase-resolved analysis showed a significant anticorrelation between the flux and the polarization degree, as well as strong variations of the polarization angle. The fit with the rotating vector model indicates a position angle of the pulsar spin axis of about 49° and a magnetic obliquity of 17°. The detected relatively low polarization can be explained if the upper layers of the neutron star surface are overheated by the accreted matter and the conversion of the polarization modes occurs within the transition region between the upper hot layer and a cooler underlying atmosphere. A fraction of polarization signal can also be produced by reflection of radiation from the neutron star surface and the accretion curtain

The X-Ray Polarimetry View of the Accreting Pulsar Cen X-3

International audienceThe first X-ray pulsar, Cen X-3, was discovered 50 yr ago. Radiation from such objects is expected to be highly polarized due to birefringence of plasma and vacuum associated with propagation of photons in the presence of the strong magnetic field. Here we present results of the observations of Cen X-3 performed with the Imaging X-ray Polarimetry Explorer. The source exhibited significant flux variability and was observed in two states different by a factor of ~20 in flux. In the low-luminosity state, no significant polarization was found in either pulse phase-averaged (with a 3σ upper limit of 12%) or phase-resolved (the 3σ upper limits are 20%-30%) data. In the bright state, the polarization degree of 5.8% ± 0.3% and polarization angle of 49.°6 ± 1.°5 with a significance of about 20σ were measured from the spectropolarimetric analysis of the phase-averaged data. The phase-resolved analysis showed a significant anticorrelation between the flux and the polarization degree, as well as strong variations of the polarization angle. The fit with the rotating vector model indicates a position angle of the pulsar spin axis of about 49° and a magnetic obliquity of 17°. The detected relatively low polarization can be explained if the upper layers of the neutron star surface are overheated by the accreted matter and the conversion of the polarization modes occurs within the transition region between the upper hot layer and a cooler underlying atmosphere. A fraction of polarization signal can also be produced by reflection of radiation from the neutron star surface and the accretion curtain

X-ray polarimetry of the accreting pulsar GX 301−2

International audienceThe phase- and energy-resolved polarization measurements of accreting X-ray pulsars (XRPs) allow us to test different theoretical models of their emission, and they also provide an avenue to determine the emission region geometry. We present the results of the observations of the XRP GX 301−2 performed with the Imaging X-ray Polarimetry Explorer (IXPE). A persistent XRP, GX 301−2 has one of the longest spin periods known: ∼680 s. A massive hyper-giant companion star Wray 977 supplies mass to the neutron star via powerful stellar winds. We did not detect significant polarization in the phase-averaged data when using spectro-polarimetric analysis, with the upper limit on the polarization degree (PD) of 2.3% (99% confidence level). Using the phase-resolved spectro-polarimetric analysis, we obtained a significant detection of polarization (above 99% confidence level) in two out of nine phase bins and a marginal detection in three bins, with a PD ranging between ∼3% and ∼10% and a polarization angle varying in a very wide range from ∼0° to ∼160°. Using the rotating vector model, we obtained constraints on the pulsar geometry using both phase-binned and unbinned analyses, finding excellent agreement. Finally, we discuss possible reasons for a low observed polarization in GX 301−2

Polarized x-rays from a magnetar

We report on the first detection of linearly polarized x-ray emission from an ultra-magnetized neutron star with the Imaging X-ray Polarimetry Explorer (IXPE). The IXPE 35 observations of the anomalous x-ray pulsar 4U 0142+61 reveal a linear polarization degree of $(12\pm 1)\%$ throughout the IXPE 2--8 keV band. We detect a substantial variation of the polarization with energy: the degree is $(14\pm 1)\%$ at 2--4 keV and $(41\pm 7)\%$ at 5.5--8 keV, while it drops below the instrumental sensitivity around 4--5 keV, where the polarization angle swings by $\sim 90^\circ$. The IXPE observations give us completely new information about the properties of the neutron star surface and magnetosphere and lend further support to the presence of the quantum mechanical effect of vacuum birefringence.Comment: 32 pages, 9 figures, 3 table