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The Imaging X-ray Polarimetry Explorer (IXPE) has confirmed that X-ray polarimetry is a valuable tool in astronomy, providing critical insights into the emission processes and the geometry of compact objects. IXPE was designed to be sensitive in the 2–8 keV energy range for three primary reasons: (1) celestial X-ray sources are bright within this range, (2) the optics are effective, and (3) most sources across various classes were expected to exhibit some level of polarization. Indeed, IXPE is a great success, and its discoveries are necessitating the revision of many theoretical models for numerous sources. However, one of IXPE’s main limitations is its relatively narrow energy band, coupled with rapidly declining efficiency. In this paper, we will demonstrate the benefits of devising a mission focused on a broader energy band (0.1–79 keV). This approach leverages current technologies that align well with theoretical expectations and builds on the successes of IXPE.

Accreting stellar-mass black holes represent unique laboratories for studying matter and radiation under the influence of extreme gravity. They are highly variable sources going through different accretion states, showing various components in their X-ray spectra from the thermal emission of the accretion disc dominating in the soft state to the up-scattered Comptonisation component from an X-ray corona in the hard state. X-ray polarisation measurements are particularly sensitive to the geometry of the X-ray scatterings and can thus constrain the orientation and relative positions of the innermost components of these systems. The IXPE mission has observed about a dozen stellar-mass black holes with masses up to 20 solar masses in X-ray binaries with different orientations and in various accretion states. The low-inclination sources in soft states have shown a low fraction of polarisation. On the other hand, several sources in soft and hard states have revealed X-ray polarisation higher than expected, which poses significant challenges for theoretical interpretation, with 4U 1630–47 being one of the most puzzling sources. IXPE has measured the spin of three black holes via the measurement of their polarisation properties in the soft emission state. In each of the three cases, the new results agree with the constraints from the spectral observations. The polarisation observations of the black hole X-ray transient Swift J1727.8–1613 across its entire outburst has revealed that the soft-state polarisation is much weaker than the hard-state polarisation. Remarkably, the observations furthermore show that the polarisation of the bright hard state and that of the 100 times less luminous dim hard state are identical within the accuracy of the measurement. For sources with a radio jet, the electric field polarisation tends to align with the radio jet, indicating the equatorial geometry of the X-ray corona, e.g., in the case of Cyg X–1. In the unique case of Cyg X–3, where the polarisation is perpendicular to the radio jet, the IXPE observations reveal the presence and geometry of obscuring material hiding this object from our direct view. The polarisation measurements acquired by the IXPE mission during its first 2.5 years have provided unprecedented insights into the geometry and physical processes of accreting stellar-mass black holes, challenging existing theoretical models and offering new avenues for understanding these extreme systems.

In this paper we present the science potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission for studies of strongly magnetized objects. We will focus on the physics and astrophysics of strongly magnetized objects, namely magnetars, accreting X-ray pulsars, and rotation powered pulsars. We also discuss the science potential of eXTP for QED studies. Developed by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is expected to be launched in the mid 2020s.

Measurements of the angular momentum (spin) of astrophysical black holes are extremely important, as they provide information on the black hole formation and evolution. We present simulated observations of a X-ray binary system with the Imaging X-ray Polarimetry Explorer (IXPE), with the aim to study the robustness of black hole spin and geometry measurements using X-ray polarimetry. As a representative example, we used the parameters of GRS 1915+105 in its former unobscured, soft state. In order to simulate the polarization properties, we modeled the source emission with a multicolor blackbody accounting for thermal radiation from the accretion disk, including returning radiation. Our analysis shows that the polarimetric observations in the X-ray waveband will be able to estimate both spin and inclination of the system with a good precision (without returning radiation we obtained for the lowest spin \\(\\Delta a \\leq 0.4\\) (0.4/0.998 \\(\\sim\\) 40%) for spin and \\(\\Delta i \\leq 30^\\circ\\) (30\\(^\\circ\\)/70\\(^\\circ\\) \\(\\sim\\) 43%) for inclination, while for the higher spin values we obtained \\(\\Delta a \\leq 0.12\\) (\\(\\sim\\) 12%) for spin and \\(\\Delta i \\leq 20^\\circ\\) (\\( \\sim \\) 29%) for inclination, within 1\\( \\sigma \\) errors). When focusing on the case of returning radiation and treating inclination as a known parameter, we were able to successfully reconstruct spin and disk albedo in \\(\\Delta a \\leq 0.15\\) (\\(\\sim\\) 15%) interval and \\(\\Delta\\) albedo \\(\\leq 0.45\\) (45%) intervals within 1\\( \\sigma \\) errors. We conclude that X-ray polarimetry will be a useful tool to constrain black hole spins, in addition to timing and spectral-fitting methods.

The launch of the Imaging X-ray Polarimetry Explorer (IXPE) on 2021 December 9 has opened a new window in X-ray astronomy. We report here the results of the first IXPE observation of a weakly magnetized neutron star, GS 1826-238, performed on 2022 March 29-31 when the source was in a high soft state. An upper limit (99.73% confidence level) of 1.3% for the linear polarization degree is obtained over the IXPE 2-8 keV energy range. Coordinated INTEGRAL and NICER observations were carried out simultaneously with IXPE. The spectral parameters obtained from the fits to the broad-band spectrum were used as inputs for Monte Carlo simulations considering different possible geometries of the X-ray emitting region. Comparing the IXPE upper limit with these simulations, we can put constraints on the geometry and inclination angle of GS 1826-238.

We report on an observational campaign on the bright black hole X-ray binary Swift J1727.8\\(-\\)1613 centered around five observations by the Imaging X-ray Polarimetry Explorer (IXPE). These observations track for the first time the evolution of the X-ray polarization of a black hole X-ray binary across a hard to soft state transition. The 2--8 keV polarization degree decreased from \\(\\sim\\)4\\% to \\(\\sim\\)3\\% across the five observations, but the polarization angle remained oriented in the North-South direction throughout. Based on observations with the Australia Telescope Compact Array (ATCA), we find that the intrinsic 7.25 GHz radio polarization aligns with the X-ray polarization. Assuming the radio polarization aligns with the jet direction (which can be tested in the future with higher spatial resolution images of the jet), our results imply that the X-ray corona is extended in the disk plane, rather than along the jet axis, for the entire hard intermediate state. This in turn implies that the long (\\(\\gtrsim\\)10 ms) soft lags that we measure with the Neutron star Interior Composition ExploreR (NICER) are dominated by processes other than pure light-crossing delays. Moreover, we find that the evolution of the soft lag amplitude with spectral state does not follow the trend seen for other sources, implying that Swift J1727.8\\(-\\)1613 is a member of a hitherto under-sampled sub-population.

How astrophysical systems translate the kinetic energy of bulk motion into the acceleration of particles to very high energies is a pressing question. SS 433 is a microquasar that emits TeV gamma-rays indicating the presence of high-energy particles. A region of hard X-ray emission in the eastern lobe of SS 433 was recently identified as an acceleration site. We observed this region with the Imaging X-ray Polarimetry Explorer and measured a polarization degree in the range 38% to 77%. The high polarization degree indicates the magnetic field has a well ordered component if the X-rays are due to synchrotron emission. The polarization angle is in the range -12 to +10 degrees (east of north) which indicates that the magnetic field is parallel to the jet. Magnetic fields parallel to the bulk flow have also been found in supernova remnants and the jets of powerful radio galaxies. This may be caused by interaction of the flow with the ambient medium.

We report the first detection of the X-ray polarization of the bright transient Swift J1727.8-1613 with the Imaging X-ray Polarimetry Explorer. The observation was performed at the beginning of the 2023 discovery outburst, when the source resided in the bright hard state. We find a time- and energy-averaged polarization degree of 4.1%+/-0.2% and a polarization angle of 2.2+/-1.3 degrees (errors at 68% confidence level; this translates to about 20-sigma significance of the polarization detection). This finding suggests that the hot corona emitting the bulk of the detected X-rays is elongated, rather than spherical. The X-ray polarization angle is consistent with that found in sub-mm wavelengths. Since the sub-mm polarization was found to be aligned with the jet direction in other X-ray binaries, this indicates that the corona is elongated orthogonal to the jet.

We report on an X-ray polarimetric observation of the high-mass X-ray binary LMC X-1 in the high/soft state, obtained by the Imaging X-ray Polarimetry Explorer (IXPE) in October 2022. The measured polarization is below the minimum detectable polarization of 1.1 per cent (at the 99 per cent confidence level). Simultaneously, the source was observed with the NICER, NuSTAR and SRG/ART-XC instruments, which enabled spectral decomposition into a dominant thermal component and a Comptonized one. The low 2-8 keV polarization of the source did not allow for strong constraints on the black-hole spin and inclination of the accretion disc. However, if the orbital inclination of about 36 degrees is assumed, then the upper limit is consistent with predictions for pure thermal emission from geometrically thin and optically thick discs. Assuming the polarization degree of the Comptonization component to be 0, 4, or 10 per cent, and oriented perpendicular to the polarization of the disc emission (in turn assumed to be perpendicular to the large scale ionization cone detected in the optical and radio bands), an upper limit to the polarization of the disc emission of 0.5, 1.7, or 3.6 per cent, respectively, is found (at the 99 per cent confidence level).