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Keywords = X-ray pulsars

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23 pages, 9259 KB  
Article
Timing and Spectral Analysis of the 2024 Outburst of 2S 1553-542 with NuSTAR and NICER
by Haifan Zhu, Wei Wang, Wen Yang, Mariano Méndez, Chenxu Gao, Ziyi Xu and Pengfu Tian
Galaxies 2026, 14(4), 76; https://doi.org/10.3390/galaxies14040076 - 29 Jul 2026
Viewed by 257
Abstract
We report a timing and spectral study of the 2024 outburst of the Be/X-ray binary pulsar 2S 1553-542 using NuSTAR and NICER observations. From the NuSTAR light curve, we measure a pulse period of 9.285022±0.000001 s. The energy-resolved pulse profiles are [...] Read more.
We report a timing and spectral study of the 2024 outburst of the Be/X-ray binary pulsar 2S 1553-542 using NuSTAR and NICER observations. From the NuSTAR light curve, we measure a pulse period of 9.285022±0.000001 s. The energy-resolved pulse profiles are dominated by a single peak and show a wing-like structure most clearly in the 12–22 keV band. The pulsed fraction remains above 60% and increases with energy. The phase-averaged NuSTAR spectrum is described by an absorbed blackbody plus cutoff power-law continuum, together with an iron emission line and a cyclotron absorption feature. Using the cyclabs model, we obtain a cyclotron energy of Ecyc24.1 keV, corresponding to a magnetic field strength of B3×1012 G. Phase-resolved spectroscopy shows that the continuum and cyclotron-line parameters vary with pulse phase, and that the line becomes poorly constrained around the pulse-wing phase. We also searched the short NICER GTIs for transient mHz variability using wavelet analysis and a CEEMDAN-based Hilbert–Huang transform. Localized excesses near ∼10 mHz and ∼20 mHz are found, but the short exposures, COI effects, red-noise fluctuations, and the lack of a well-constrained Fourier peak limit their significance. We therefore treat them as candidate mHz variability rather than firm mHz QPO detections. Full article
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17 pages, 8665 KB  
Article
Optimization of Film Thickness Uniformity of X-Ray Telescope Mirror Based on Off-Axis Biaxial Rotation Coating Method
by Haibo Zhu, Yu Yang, Liansheng Li, Zhiwu Mei, Yongqiang Shi, Hongyu Wu and Qingyong Zhou
Coatings 2026, 16(7), 820; https://doi.org/10.3390/coatings16070820 - 10 Jul 2026
Viewed by 369
Abstract
Pulsar detection holds significant value in spacecraft autonomous navigation, space-based time reference establishment, and space science research. The X-ray telescope is a crucial instrument for pulsar detection, and its focusing mirror—the most critical component—exhibits detection performance directly influenced by the film thickness uniformity. [...] Read more.
Pulsar detection holds significant value in spacecraft autonomous navigation, space-based time reference establishment, and space science research. The X-ray telescope is a crucial instrument for pulsar detection, and its focusing mirror—the most critical component—exhibits detection performance directly influenced by the film thickness uniformity. This paper proposes an off-axis biaxial rotation coating method and derives, for the first time, a theoretical model of film thickness distribution on a cylindrical substrate based on classical thin-film deposition theory. Using this model, we systematically analyze the influence of key coating parameters—namely the distances a and b from the evaporation source to the vertical rotation axis and to the horizontal rotation axis, respectively—on thickness uniformity. By optimizing the coating process parameters, the thickness uniformity on the cylindrical substrate is significantly improved. When parameters a and b are within certain ranges and satisfy a specific relationship, a film with thickness uniformity better than 1% can be obtained. Coating experiments are carried out on a mandrel cylinder, and the measured film thickness distribution shows good agreement with theoretical predictions, with a maximum deviation of only 1.2%, thereby validating the accuracy of the proposed model. This work provides a rapid, non-iterative approach for determining coating parameters, significantly improving efficiency and reducing costs. Full article
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20 pages, 9094 KB  
Article
High Signal-to-Noise Ratio Method Without Phase Deviation for X-Ray Pulsar Profile Acquisition
by Zewei Zhang, Haiyan Fang, Weimin Bao and Xiaoping Li
Aerospace 2026, 13(7), 611; https://doi.org/10.3390/aerospace13070611 - 3 Jul 2026
Viewed by 221
Abstract
High-quality X-ray pulsar observation profiles are vital for investigating both their physical properties and navigation applications. Conventional profile extraction relies on epoch folding, whose performance is constrained by observation duration and bin size, often leading to poor-quality profiles or even failure under extremely [...] Read more.
High-quality X-ray pulsar observation profiles are vital for investigating both their physical properties and navigation applications. Conventional profile extraction relies on epoch folding, whose performance is constrained by observation duration and bin size, often leading to poor-quality profiles or even failure under extremely low-photon conditions. This paper proposes a novel method that directly extracts high-quality profile frequency spectra merely by statistical analysis of photon sequences followed by the reconstruction of time domain waveforms. Monte Carlo simulations and real observational data demonstrate that the proposed method exhibits higher correlation coefficients and signal-to-noise ratios than those obtained using traditional epoch folding, and also outperforms the Fourier-series-based frequency cutoff method. Moreover, comparable profile quality can be achieved using an order of magnitude fewer photons than required by epoch folding. The lower the photon count, the more significant the improvement, making the method especially suitable for small-area detectors and resource-constrained observation scenarios. Full article
(This article belongs to the Section Astronautics & Space Science)
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33 pages, 3136 KB  
Article
A Waterfall-Plot-Based Multi-Criteria Framework for X-Ray Pulsar Time-Delay Estimation in Multi-Scenario Celestial Remote Sensing and Navigation
by Tianhao Xie, Xin Ma, Wei Yu, Peiling Cui, Xiaolin Ning, Jianli Li and Rong Zhang
Remote Sens. 2026, 18(11), 1693; https://doi.org/10.3390/rs18111693 - 23 May 2026
Viewed by 545
Abstract
To improve the accuracy and stability of X-ray pulsar time-delay estimation for multi-scenario celestial remote sensing and navigation, this paper proposes a time-delay estimation method based on a waterfall-plot multi-criteria framework and develops an end-to-end simulation framework for multi-scenario applications. First, a pulsar [...] Read more.
To improve the accuracy and stability of X-ray pulsar time-delay estimation for multi-scenario celestial remote sensing and navigation, this paper proposes a time-delay estimation method based on a waterfall-plot multi-criteria framework and develops an end-to-end simulation framework for multi-scenario applications. First, a pulsar profile waterfall-plot model is built, and principal component analysis is performed to characterize candidate periodic structures. The contribution rate of the principal eigenvalue is used to describe the overall significance of the candidate period, and the projection variance of the first principal component is used to measure the prominence of the candidate pattern in the principal subspace. Second, support vector regression is used to fit the peak track of the waterfall plot, and a regression slope is used to describe the geometric stability of the candidate period. These three indicators are fused for pulsar period and time-delay estimation. Tests based on Insight-HXMT satellite observation data show that, compared with the χ2 and Z2 test methods, our method improves time-delay estimation accuracy by 68.68% and 50.43%, respectively. Multi-scenario navigation simulations indicate positioning improvements of approximately 0.83 km, 3.04 km, and 1.05 km in the Earth-orbiting, Earth–Moon transfer, and Mars approach scenarios, respectively. These results suggest that the proposed framework can improve pulsar time-delay estimation and may provide useful measurement support for celestial remote sensing and navigation. Full article
(This article belongs to the Section Satellite Missions for Earth and Planetary Exploration)
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16 pages, 1822 KB  
Article
Beaming of Polarized Radiation in Subcritical X-Ray Pulsars
by Ivan D. Markozov, Alexander Y. Potekhin, Alexander D. Kaminker and Alexander A. Mushtukov
Particles 2026, 9(2), 49; https://doi.org/10.3390/particles9020049 - 5 May 2026
Viewed by 493
Abstract
Radiation of X-ray pulsars is powered by accretion on the neutron star surface from a binary companion under the influence of a strong magnetic field. We study the beaming of this radiation in the case of subcritical X-ray pulsars, where it is formed [...] Read more.
Radiation of X-ray pulsars is powered by accretion on the neutron star surface from a binary companion under the influence of a strong magnetic field. We study the beaming of this radiation in the case of subcritical X-ray pulsars, where it is formed in the accretion channel close to the neutron star surface. We solve equations of the hydrodynamics and radiative transfer of two coupled polarization modes in the accretion channel numerically, taking into account resonant Compton scattering and vacuum polarization. The beaming patterns are obtained for different accretion rates, photon energies, and polarizations, as well as for different models of the neutron star surface radiation. The calculated beaming patterns are converted into light curves for both the intensity and polarization, taking into account the effects of General Relativity. These beaming patterns and light curves are found to be strongly affected by the resonant Compton scattering for photon energies comparable with the electron cyclotron energy. In particular, the angular redistribution of radiation near the cyclotron resonance may reduce the light-curve modulation amplitude, which is consistent with observational indications of a suppressed pulsed fraction at these energies. Full article
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19 pages, 10559 KB  
Article
Radio Observations of Microquasars with FAST
by Botao Li and Wei Wang
Astronomy 2026, 5(1), 6; https://doi.org/10.3390/astronomy5010006 - 6 Mar 2026
Viewed by 929
Abstract
We report six radio observations of four microquasars—SS 433, GRS 1915+105, Cyg X-3 and MAXI J1820+070—conducted between 2022 and 2025 with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) using its pulsar backend, achieving a time resolution of 98.304 μs across an effective [...] Read more.
We report six radio observations of four microquasars—SS 433, GRS 1915+105, Cyg X-3 and MAXI J1820+070—conducted between 2022 and 2025 with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) using its pulsar backend, achieving a time resolution of 98.304 μs across an effective feed range of 1.04–1.45 GHz. A major focus of this work is the development of a standardized calibration pipeline for microquasar observations, including RFI mitigation, flux density, and polarization calibration, as well as multi-beam correlation inspections. Using On–Off mode and cross-beam verification, radio activity was detected in SS 433, GRS 1915+105 and Cyg X-3, while MAXI J1820+070 remained inactive. Both SS 433 and GRS 1915+105 show low linear polarization degrees of only a few percent. No credible quasi-periodic oscillations (QPOs) were detected in the 0.01–100 Hz range, suggesting that radio QPOs within this frequency range are relatively rare compared to those observed in the X-ray band. We therefore highlight the importance of future monitoring with high–time-resolution and high–sensitivity radio telescopes such as FAST, which will be crucial for revealing the correlation between jet and accretion processes and for uncovering the physical origin of QPOs. Full article
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36 pages, 3703 KB  
Review
Millihertz Quasi-Periodic Oscillations in Accreting X-Ray Pulsars
by Wen Yang and Wei Wang
Universe 2026, 12(1), 7; https://doi.org/10.3390/universe12010007 - 27 Dec 2025
Cited by 2 | Viewed by 1160
Abstract
Accreting neutron stars exhibit pulsed X-rays and complex temporal variability across multi-wavelengths and different timescales. This variability could be driven by various physical processes including instability or inhomogeneous motions within the accretion flow, thermonuclear bursts on the neutron star surface. In this review, [...] Read more.
Accreting neutron stars exhibit pulsed X-rays and complex temporal variability across multi-wavelengths and different timescales. This variability could be driven by various physical processes including instability or inhomogeneous motions within the accretion flow, thermonuclear bursts on the neutron star surface. In this review, we present a concise overview of the observational features for millihertz (mHz) quasi-periodic oscillations (QPOs) at a frequency range of ∼1–1000 mHz observed in light curves of X-ray pulsars for both low-mass X-ray binaries and high-mass X-ray binaries, based on recent X-ray missions, e.g., NICER, Insight-HXMT and NuSTAR. We further summarize current theoretical interpretations, discuss remaining challenges and propose potential directions for future studies to advance the understanding of the nature and physical origin of these QPOs. Full article
(This article belongs to the Section Compact Objects)
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11 pages, 2887 KB  
Article
INTEGRAL/ISGRI Post 2024-Periastron View of PSR B1259-63
by Aleksei Kuzin, Denys Malyshev, Maria Chernyakova, Brian van Soelen and Andrea Santangelo
Universe 2025, 11(8), 254; https://doi.org/10.3390/universe11080254 - 31 Jul 2025
Cited by 1 | Viewed by 682
Abstract
PSR B1259-63/LS 2883 is a well-studied gamma-ray binary hosting a pulsar in a 3.4-year eccentric orbit around a Be-type star. Its non-thermal emission spans from radio to TeV energies, exhibiting a significant increase near the periastron passage. This paper is dedicated to the [...] Read more.
PSR B1259-63/LS 2883 is a well-studied gamma-ray binary hosting a pulsar in a 3.4-year eccentric orbit around a Be-type star. Its non-thermal emission spans from radio to TeV energies, exhibiting a significant increase near the periastron passage. This paper is dedicated to the analysis of INTEGRAL observations of the system following its last periastron passage in June 2024. We aim to study the spectral evolution of this gamma-ray binary in the soft (0.3–10 keV) and hard (30–300 keV) X-ray energy bands. We performed a joint analysis of the data taken by INTEGRAL/ISGRI in July–August 2024 and quasi-simultaneous Swift/XRT observations. The spectrum of the system in the 0.3–300 keV band is well described by an absorbed power law with a photon index of Γ=1.42±0.03. We place constraints on potential spectral curvature, limiting the break energy Eb>30 keV for ΔΓ>0.3 and cutoff energy Ecutoff>150 keV at a 95% confidence level. For one-zone leptonic emission models, these values correspond to electron distribution spectral parameters of Eb,e>0.8 TeV and Ecutoff,e>1.7 TeV, consistent with previous constraints derived by H.E.S.S. Full article
(This article belongs to the Section Compact Objects)
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6 pages, 228 KB  
Article
Stellar Wind Parameters of Massive Stars in Accretion-Powered High-Mass X-Ray Binary Pulsars
by Nina Beskrovnaya, Nazar Ikhsanov and Vitaliy Kim
Galaxies 2025, 13(2), 37; https://doi.org/10.3390/galaxies13020037 - 5 Apr 2025
Cited by 3 | Viewed by 1499
Abstract
The process of mass exchange between the components of High-Mass X-ray Binary (HMXB) systems with neutron stars undergoing wind-fed accretion is discussed. The X-ray luminosity of these systems allows us to evaluate the mass capture rate by the neutron star from the stellar [...] Read more.
The process of mass exchange between the components of High-Mass X-ray Binary (HMXB) systems with neutron stars undergoing wind-fed accretion is discussed. The X-ray luminosity of these systems allows us to evaluate the mass capture rate by the neutron star from the stellar wind of its massive companion and set limits on the relative velocity between the neutron star and the wind. We found that the upper limit to the wind velocity in the orbital plane during the high state of the X-ray source is in the range of 120–1000 kms1, which is by a factor of 2–4 lower than both the terminal wind velocity and the speed of the wind flowing out from the polar regions of massive stars for all the objects under investigation. This finding is valid not only for the systems with Be stars, but also for the systems in which the optical components do not exhibit the Be phenomenon. We also show that the lower limit to the radial wind velocity in these systems can unlikely be smaller than a few percent of the orbital velocity of the neutron star. This provides us with a new constraint on the mass transfer process in the outflowing disks of Be-type stars. Full article
(This article belongs to the Special Issue Circumstellar Matter in Hot Star Systems)
12 pages, 784 KB  
Article
Image Deconvolution to Resolve Astronomical X-Ray Sources in Close Proximity: The NuSTAR Images of SXP 15.3 and SXP 305
by Sayantan Bhattacharya, Dimitris M. Christodoulou and Silas G. T. Laycock
Algorithms 2025, 18(4), 191; https://doi.org/10.3390/a18040191 - 27 Mar 2025
Viewed by 1582
Abstract
The broad point spread function of the NuSTAR telescope makes resolving astronomical X-ray sources a challenging task, especially for off-axis observations. This limitation has affected the observations of the high-mass X-ray binary pulsars SXP 15.3 and SXP 305, in which pulsations are detected [...] Read more.
The broad point spread function of the NuSTAR telescope makes resolving astronomical X-ray sources a challenging task, especially for off-axis observations. This limitation has affected the observations of the high-mass X-ray binary pulsars SXP 15.3 and SXP 305, in which pulsations are detected from nearly overlapping regions without spatially resolving these X-ray sources. To address this issue, we introduce a deconvolution algorithm designed to enhance NuSTAR’s spatial resolution for closely spaced X-ray sources. We apply this technique to archival data and simulations of synthetic point sources placed at varying separations and locations, testing the algorithm’s efficacy in source detection and differentiation. Our study confirms that on some occasions when SXP 305 is brighter, SXP 15.3 is also resolved, suggesting that some prior non-detections may have resulted from imaging limitations. This deconvolution technique represents a proof of concept test for analyzing crowded fields in the sky with closely spaced X-ray sources in future NuSTAR observations. Full article
(This article belongs to the Special Issue Machine Learning Algorithms for Image Understanding and Analysis)
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13 pages, 2538 KB  
Article
From Be X-Ray Binaries to Double Neutron Stars: Exploring the Spin and Orbital Evolution
by Yungang Zhou, Dehua Wang and Chengmin Zhang
Universe 2025, 11(2), 51; https://doi.org/10.3390/universe11020051 - 6 Feb 2025
Viewed by 1360
Abstract
We explore the evolutionary link between Galactic Be X-ray binaries (BeXBs) and Galactic field double neutron stars (DNSs) based on the properties of the NS spin period—P and binary orbital period—Porb. First, both BeXB and DNS sources show positive [...] Read more.
We explore the evolutionary link between Galactic Be X-ray binaries (BeXBs) and Galactic field double neutron stars (DNSs) based on the properties of the NS spin period—P and binary orbital period—Porb. First, both BeXB and DNS sources show positive correlation trends in P versus Porb relation (PPorb diagram), which may relate to the influence of the accretion evolution. Secondly, the two types of sources exhibit similar bi-modal P/Porb distributions with the gaps of P40 s/Porb60 days for BeXBs and P50 ms/Porb1 day for DNSs, respectively. We propose a possibility that Galactic BeXBs may transfer the bi-modal P/Porb classifications to Galactic field DNSs during the evolution process. Furthermore, based on the bi-modal gaps, we infer the contraction factors of P (by 1800) and Porb (by 160) valuesin the evolution from Galactic BeXBs to Galactic field DNSs. We find that the scaled P or Porb values of Galactic BeXBs share the similar bi-modal distributions to that of Galactic field DNSs, and these results can offer a reference to trace the classification and evolution between the two types of sources. Full article
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18 pages, 2484 KB  
Article
Augmentation Method for X-Ray Pulsar Navigation Using Time Difference of Arrival and Range Measurement, Based on Polarization Encoded Pulse Position Modulation
by Rong Jiao and Hua Zhang
Aerospace 2025, 12(2), 113; https://doi.org/10.3390/aerospace12020113 - 31 Jan 2025
Viewed by 2462
Abstract
This paper addresses the use of the position difference between the reference satellite and the target spacecraft to improve X-ray pulsar navigation (XPNAV) for Earth orbit spacecraft. This is achieved by first installing an X-ray detector on the reference satellite whose position is [...] Read more.
This paper addresses the use of the position difference between the reference satellite and the target spacecraft to improve X-ray pulsar navigation (XPNAV) for Earth orbit spacecraft. This is achieved by first installing an X-ray detector on the reference satellite whose position is accurately known. The position measurement error of the reference satellite, known as the correction value, is sent to the spacecraft through the X-ray communication (XCOM) link. It is hoped that the accuracy of the spacecraft state measurement can be improved by offsetting common errors of measurement. X-ray ranging observation between the reference satellite and the target spacecraft, obtained from XCOM, can accomplish high precision in distance measurements, which can supply precise information for XPNAV. A novel pulse position modulation (PPM) polarization encode and modulation mode is used to achieve difference time transmission and range measurement simultaneously. Through the information fusion of the difference timing observation and the ranging observation, the positioning accuracy of the spacecraft is improved further. With the aim of estimating the spacecraft’s errors in location and speed, an adaptive divided difference filter (ADDF) is applied to eliminate nonlinearity. Several simulation cases are designed to verify the proposed method. Numerical simulations show that, compared with the traditional timing observation, the difference timing and ranging method can improve the position estimation accuracy by 27% and the velocity estimation accuracy by 22%. Full article
(This article belongs to the Section Astronautics & Space Science)
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31 pages, 1808 KB  
Review
X-Ray Views of Galactic Accreting Pulsars in High-Mass X-Ray Binaries
by Shan-Shan Weng and Long Ji
Universe 2024, 10(12), 453; https://doi.org/10.3390/universe10120453 - 10 Dec 2024
Cited by 9 | Viewed by 3158
Abstract
Accreting X-ray pulsars, located in X-ray binaries, are neutron stars with magnetic fields as strong as B101213 G. This review offers a concise overview of the accretion and radiation processes of X-ray pulsars and summarizes their rich observational [...] Read more.
Accreting X-ray pulsars, located in X-ray binaries, are neutron stars with magnetic fields as strong as B101213 G. This review offers a concise overview of the accretion and radiation processes of X-ray pulsars and summarizes their rich observational features, particularly focusing on complex and variable temporal phenomena, spectral properties, and evolution, the new window for X-ray polarimetry and multi-wavelength advances. We also briefly discuss other related systems, i.e., gamma-ray binaries and pulsating ultraluminous X-ray sources. Full article
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25 pages, 6785 KB  
Article
Intelligent QLFEKF Integrated Navigation for the SSBE Cruise Phase Based on X-Ray Pulsar/Solar and Target Planetary Doppler Information Fusion
by Wenjian Tao, Jinxiu Zhang, Jianing Song, Qin Lin, Zebin Chen, Hui Wang, Jikun Yang and Jihe Wang
Remote Sens. 2024, 16(23), 4465; https://doi.org/10.3390/rs16234465 - 28 Nov 2024
Cited by 4 | Viewed by 2117
Abstract
The Solar System Boundary Exploration (SSBE) mission is the focal point for future far-reaching space exploration. Due to the SSBE having many scientific difficulties that need to be studied, such as a super long space exploratory distance, a super long flight time in [...] Read more.
The Solar System Boundary Exploration (SSBE) mission is the focal point for future far-reaching space exploration. Due to the SSBE having many scientific difficulties that need to be studied, such as a super long space exploratory distance, a super long flight time in orbit, and a significant communication data delay between the ground and the probe, the probe must have sufficient intelligence to realize intelligent autonomous navigation. Traditional navigation schemes have been unable to provide high-accuracy autonomous intelligent navigation for the probe independent of the ground. Therefore, high-accuracy intelligent astronomical integrated navigation would provide new methods and technologies for the navigation of the SSBE probe. The probe of the SSBE is disturbed by multiple sources of solar light pressure and a complex, unknown environment during its long cruise operation while in orbit. In order to ensure the high-accuracy position state and velocity state error estimation for the probe in the cruise phase, an autonomous intelligent integrated navigation scheme based on the X-ray pulsar/solar and target planetary Doppler velocity measurements is proposed. The reinforcement Q-learning method is introduced, and the reward mechanism is designed for trial-and-error tuning of state and observation noise error covariance parameters. The federated extended Kalman filter (FEKF) based on the Q-learning (QLFEKF) navigation algorithm is proposed to achieve high-accuracy state estimations of the autonomous intelligence navigation system for the SSBE probe cruise phase. The main advantage of the QLFEKF is that Q-learning combined with the conventional federated filtering method could optimize the state parameters in real-time and obtain high position and velocity state estimation (PVSE) accuracy. Compared with the conventional FEKF integrated navigation algorithm, the PVSE navigation accuracy of the federated filter integrated based the Q-learning navigation algorithm is improved by 55.84% and 37.04%, respectively, demonstrating the higher accuracy and greater capability of the raised autonomous intelligent integrated navigation algorithm. The simulation results show that the intelligent integrated navigation algorithm based on QLFEKF has higher navigation accuracy and is able to satisfy the demands of autonomous high accuracy for the SSBE cruise phase. Full article
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14 pages, 1795 KB  
Review
X-ray Polarimetry of X-ray Pulsars
by Juri Poutanen, Sergey S. Tsygankov and Sofia V. Forsblom
Galaxies 2024, 12(4), 46; https://doi.org/10.3390/galaxies12040046 - 7 Aug 2024
Cited by 24 | Viewed by 3345
Abstract
Radiation from X-ray pulsars (XRPs) was expected to be strongly linearly polarized owing to a large difference in their ordinary and extraordinary mode opacities. The launch of IXPE allowed us to check this prediction. IXPE observed a dozen X-ray pulsars, discovering pulse-phase dependent [...] Read more.
Radiation from X-ray pulsars (XRPs) was expected to be strongly linearly polarized owing to a large difference in their ordinary and extraordinary mode opacities. The launch of IXPE allowed us to check this prediction. IXPE observed a dozen X-ray pulsars, discovering pulse-phase dependent variation of the polarization degree (PD) and polarization angle (PA). Although the PD showed rather erratic profiles resembling flux pulse dependence, the PA in most cases showed smooth variations consistent with the rotating vector model (RVM), which can be interpreted as a combined effect of vacuum birefringence and dipole magnetic field structure at a polarization-limiting (adiabatic) radius. Application of the RVM allowed us to determine XRP geometry and to confirm the free precession of the NS in Her X-1. Deviations from RVM in two bright transients led to the discovery of an unpulsed polarized emission likely produced by scattering off the accretion disk wind. Full article
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