Polarized radiation from an accretion shock in accreting millisecond pulsars using exact Compton scattering formalism

Pulse profiles of accreting millisecond pulsars can be used to determine neutron star (NS) parameters, such as their masses and radii, and therefore provide constraints on the equation of state of cold dense matter. Information obtained by the Imaging X-ray Polarimetry Explorer (IXPE) can be used to decipher pulsar inclination and magnetic obliquity, providing ever tighter constraints on other parameters. In this paper, we develop a new emission model for accretion-powered millisecond pulsars based on thermal Comptonization in an accretion shock above the NS surface. The shock structure was approximated by an isothermal plane-parallel slab and the Stokes parameters of the emergent radiation were computed as a function of the zenith angle and energy for different values of the electron temperature, the Thomson optical depth of the slab, and the temperature of the seed blackbody photons. We show that our Compton scattering model leads to a significantly lower polarization degree of the emitted radiation compared to the previously used Thomson scattering model. We computed a large grid of shock models, which can be combined with pulse profile modeling techniques both with and without polarization included. In this work, we used the relativistic rotating vector model for the oblate NS in order to produce the observed Stokes parameters as a function of the pulsar phase. Furthermore, we simulated the data to be produced by IXPE and obtained constraints on model parameters using nested sampling. The developed methods can also be used in the analysis of the data from future satellites, such as the enhanced X-ray Timing and Polarimetry mission.Comment: Accepted to A&A on 11 August 202

First detection of X-ray polarization from the accreting neutron star 4U 1820-303

This paper reports the first detection of polarization in the X-rays for atoll-source 4U 1820-303, obtained with the Imaging X-ray Polarimetry Explorer (IXPE) at 99.999% confidence level (CL). Simultaneous polarimetric measurements were also performed in the radio with the Australia Telescope Compact Array (ATCA). The IXPE observations of 4U 1820-303 were coordinated with Swift-XRT, NICER, and NuSTAR aiming to obtain an accurate X-ray spectral model covering a broad energy interval. The source shows a significant polarization above 4 keV, with a polarization degree of 2.0(0.5)% and a polarization angle of -55(7) deg in the 4-7 keV energy range, and a polarization degree of 10(2)% and a polarization angle of -67(7) deg in the 7-8 keV energy bin. This polarization also shows a clear energy trend with polarization degree increasing with energy and a hint for a position-angle change of about 90 deg at 96% CL around 4 keV. The spectro-polarimetric fit indicates that the accretion disk is polarized orthogonally to the hard spectral component, which is presumably produced in the boundary/spreading layer. We do not detect linear polarization from the radio counterpart, with a 99.97% upper limit of 50% at 7.25 GHz

THE COMPARISON OF ALGORITHMS OF RECOGNITION OF IMAGES HOPFILD’S NEURAL NETWORKS

Основным достоинством искусственных нейронных сетей (ИНС) в задачах распознавания состоит в их функционировании подобно человеческому мозгу. В работе рассмотрены вопросы распознавания изображений нейронными сетями Хопфилда, выполнен сравнительный анализ распознавания изображений методом проекций и по правилу Хебба. Для этих целей разработана программа на языке C# в среде Microsoft Visual Studio 2012. В ходе распознавания эталонных и искаженных образов изображений с разным уровнем зашумленности показал, что сети Хопфилда, обучаемые методом проекций способны запоминать и восстанавливать исходные образы со значительными искажениями до 25–30%.The main advantage of artificial neural networks (ANN) in recognition of the cottages, is in their functioning like a human brain. The paper deals with image recognition neuron Hopfield’s networks, a comparative analysis of the recognition images by a projection’s method and the Hebb’s rule. For these purposes, was developed program with C# in Microsoft Visual Studio 2012. In this article to recognition for images with different levels of distortion were used. The analysis of results of recognition of images has shown that the method of projections allows to restore strongly distorted images (level of distortions up to 25–30 percent

X-Ray Polarimetry of the Dipping Accreting Neutron Star 4U 1624–49

We present the first X-ray polarimetric study of the dipping accreting neutron star 4U 1624−49 with the Imaging X-ray Polarimetry Explorer. We report a detection of polarization in the nondip time intervals with a confidence level of 99.99%. We find an average polarization degree (PD) of 3.1% ± 0.7% and a polarization angle of 81° ± 6° east of north in the 2–8 keV band. We report an upper limit on the PD of 22% during the X-ray dips with 95% confidence. The PD increases with energy, reaching from 3.0% ± 0.9% in the 4–6 keV band to 6% ± 2% in the 6–8 keV band. This indicates the polarization likely arises from Comptonization. The high PD observed is unlikely to be produced by Comptonization in the boundary layer or spreading layer alone. It can be produced by the addition of an extended geometrically thin slab corona covering part of the accretion disk, as assumed in previous models of dippers, and/or a reflection component from the accretion disk

X-Ray Polarized View of the Accretion Geometry in the X-Ray Binary Circinus X-1

International audienceCir X-1 is a neutron star X-ray binary characterized by strong variations in flux during its eccentric ~16.6 day orbit. There are also strong variations in the spectral state, and it has historically shown both atoll and Z state properties. We observed the source with the Imaging X-ray Polarimetry Explorer during two orbital segments, 6 days apart, for a total of 263 ks. We find an X-ray polarization degree in these segments of 1.6% ± 0.3% and 1.4% ± 0.3% at polarization angles of 37° ± 5° and -12° ± 7°, respectively. Thus, we observed a rotation of the polarization angle by 49° ± 8° along the orbit. Because variations of accretion flow, and then of the hardness ratio, are expected during the orbit, we also studied the polarization binned in hardness ratio and found the polarization angle differing by 67° ± 11° between the lowest and highest values of the hardness ratio. We discuss possible interpretations of this result that could indicate a possible misalignment between the symmetry axes of the accretion disk and the Comptonizing region caused by the misalignment of the neutron star's angular momentum with respect to the orbital one

X-Ray Polarimetry of the Dipping Accreting Neutron Star 4U 1624–49

International audienceWe present the first X-ray polarimetric study of the dipping accreting neutron star 4U 1624‑49 with the Imaging X-ray Polarimetry Explorer. We report a detection of polarization in the nondip time intervals with a confidence level of 99.99%. We find an average polarization degree (PD) of 3.1% ± 0.7% and a polarization angle of 81° ± 6° east of north in the 2–8 keV band. We report an upper limit on the PD of 22% during the X-ray dips with 95% confidence. The PD increases with energy, reaching from 3.0% ± 0.9% in the 4–6 keV band to 6% ± 2% in the 6–8 keV band. This indicates the polarization likely arises from Comptonization. The high PD observed is unlikely to be produced by Comptonization in the boundary layer or spreading layer alone. It can be produced by the addition of an extended geometrically thin slab corona covering part of the accretion disk, as assumed in previous models of dippers, and/or a reflection component from the accretion disk

Discovery of strongly variable X-ray polarization in the neutron star low-mass X-ray binary transient XTE J1701−462

International audienceContext. After about 16 years since its first outburst, the transient neutron star low-mass X-ray binary XTE J1701−462 turned on again in September 2022, allowing for the first study of its X-ray polarimetric characteristics by a dedicated observing program with the Imaging X-ray Polarimeter Explorer (IXPE). Aims: Polarimetric studies of XTE J1701−462 have been expected to improve our understanding of accreting weakly magnetized neutron stars, in particular, the physics and the geometry of the hot inner regions close to the compact object. Methods: The IXPE data of two triggered observations were analyzed using time-resolved spectroscopic and polarimetric techniques, following the source along its Z-track of the color-color diagram. Results: During the first pointing on 2022 September 29, an average 2-8 keV polarization degree of (4.6 ± 0.4)% was measured, the highest value found up to now for this class of sources. Conversely, only a ∼0.6% average degree was obtained during the second pointing ten days later. Conclusions: The polarimetric signal appears to be strictly related to the higher energy blackbody component associated with the boundary layer (BL) emission and its reflection from the inner accretion disk, and it is as strong as 6.1% and 1.2% (> 95% significant) above 3-4 keV for the two measurements, respectively. The variable polarimetric signal is apparently related to the spectral characteristics of XTE J1701−462, which is the strongest when the source was in the horizontal branch of its Z-track and the weakest in the normal branch. These IXPE results provide new important observational constraints on the physical models and geometry of the Z-sources. Here, we discuss the possible reasons for the presence of strong and variable polarization among these sources

Discovery of a variable energy-dependent X-ray polarization in the accreting neutron star GX 5-1

International audienceWe report on the coordinated observations of the neutron star low-mass X-ray binary (NS-LMXB) GX 5−1 in X-rays (IXPE, NICER, NuSTAR, and INTEGRAL), optical (REM and LCO), near-infrared (REM), mid-infrared (VLT VISIR), and radio (ATCA). This Z-source was observed by IXPE twice in March-April 2023 (Obs. 1 and 2). In the radio band the source was detected, but only upper limits to the linear polarization were obtained at a 3σ level of 6.1% at 5.5 GHz and 5.9% at 9 GHz in Obs. 1 and 12.5% at 5.5 GHz and 20% at 9 GHz in Obs. 2. The mid-IR, near-IR, and optical observations suggest the presence of a compact jet that peaks in the mid- or far-IR. The X-ray polarization degree was found to be 3.7%±0.4% (at 90% confidence level) during Obs. 1 when the source was in the horizontal branch of the Z-track and 1.8%±0.4% during Obs. 2 when the source was in the normal-flaring branch. These results confirm the variation in polarization degree as a function of the position of the source in the color-color diagram, as for previously observed Z-track sources (Cyg X-2 and XTE 1701−462). Evidence of a variation in the polarization angle of ∼20° with energy is found in both observations, likely related to the different, nonorthogonal polarization angles of the disk and Comptonization components, which peak at different energies

Highly Significant Detection of X-Ray Polarization from the Brightest Accreting Neutron Star Sco X-1

The Imaging X-ray Polarimetry Explorer measured with high significance the X-ray polarization of the brightest Z-source, Sco X-1, resulting in the nominal 2–8 keV energy band in a polarization degree of 1.0% ± 0.2% and a polarization angle of 8° ± 6° at a 90% confidence level. This observation was strictly simultaneous with observations performed by NICER, NuSTAR, and Insight-HXMT, which allowed for a precise characterization of its broadband spectrum from soft to hard X-rays. The source has been observed mainly in its soft state, with short periods of flaring. We also observed low-frequency quasiperiodic oscillations. From a spectropolarimetric analysis, we associate a polarization to the accretion disk at <3.2% at 90% confidence level, compatible with expectations for an electron scattering dominated optically thick atmosphere at the Sco X-1 inclination of ∼44°; for the higher-energy Comptonized component, we obtain a polarization of 1.3% ± 0.4%, in agreement with expectations for a slab of Thomson optical depth of ∼7 and an electron temperature of ∼3 keV. A polarization rotation with respect to previous observations by OSO-8 and PolarLight, and also with respect to the radio-jet position angle, is observed. This result may indicate a variation of the polarization with the source state that can be related to relativistic precession or a change in the corona geometry with the accretion flow