NOVEL CELESTIAL NAVIGATION FOR SATELLITE USING X-RAY PULSARS

The X-ray pulsar-based navigation is a novel technology for the satellite autonomous navigation. The position and the velocity of the satellite are deterimined by using the pulse phases detected at the satellite and predicted by the pulse timing models. With the detected pulse phase, the satellite position with respect to the Earth center can be calculated along the line-of-sight to the pulsar. Using three pulsars, the satellite position in the in- ertial frame can be resolved. The extended Kalman filter （EKF） algorithm is designed to incorporate the range measurements with the satellite dynamics. Simulation verification shows that the proposed algorithm can accu- rately determine the satellite orbit, with the position error less than 100 m. Furthermore, the factors influencing the navigation performance are also discussed.

Denoising of X-ray pulsar observed profile using biorthogonal lifting wavelet transform

In X-ray pulsar-based navigation, strong X-ray background noise leads to a low signal-to-noise ratio（SNR） of the observed profile, which consequently makes it very difficult to obtain an accurate pulse phase that directly determines the navigation precision. This signifies the necessity of denoising of the observed profile. Considering that the ultimate goal of denoising is to enhance the pulse phase estimation, a profile denoising algorithm is proposed by fusing the biorthogonal lifting wavelet transform of the linear phase characteristic with the thresholding technique. The statistical properties of X-ray background noise after epoch folding are studied. Then a wavelet-scale dependent threshold is introduced to overcome correlations between wavelet coefficients. Moreover, a modified hyperbola shrinking function is presented to remove the impulsive oscillations of the observed profile. The results of numerical simulations and real data experiments indicate that the proposed method can effectively improve SNR of the observed profile and pulse phase estimation accuracy, especially in short observation durations. And it also outperforms the Donoho thresholding strategy normally used in combination with the orthogonal discrete wavelet transform.

Effects of dynamo magnetic fields on observational properties of accreting millisecond X-ray pulsars

In this paper,we have investigated accreting millisecond X-ray pulsars,which are rapidly rotating neutron stars in low-mass X-ray binaries.These systems exhibit coherent X-ray pulsations that arise when the accretion flow is magnetically channeled to the stellar surface.Here,we have developed the fundamental equations for an accretion disk around accreting millisecond X-ray pulsars in the presence of a dynamo generated magnetic field in the inner part of the disk.We have also formulated the numerical method for the structure equations in the inner region of the disk and the highest accretion rate is enough to form the inner region of the disk,which is overpowered by radiation pressure and electron scattering.Finally,we have examined our results with the effects of dynamo magnetic fields on accreting millisecond X-ray pulsars.

In-Orbit Calibration and Data Analysis of China＇s First Grazing Incidence Focusing X-Ray Pulsar Telescope

The grazing incidence focusing X-ray pulsar telescope(iFXPT), as the main payload of the X-ray Pulsar Navigation Test Satellite(XPNAV-1), will have great significance on China's space scientific exploration and X-ray pulsar navigation. With PSR B0531+21(Crab Pulsar) as the observation target, the pulsar profile has been recovered based on the data obtained by iFXPT, realizing the main objective of "observing" PSR B0531+21 for the first time in China. This payload mainly consists of the Wolter-I X-ray optics, silicon drift detector, magnetic deflector, electronics, high-energy particle shield and high-stability structures. Currently, the iFXPT, with its good in-orbit performance, has obtained a considerable observation data. The effective area, sensitivity and energy response have been calibrated both on ground and in-orbit, demonstrating a high degree of consistency. Meanwhile, the in-orbit observation data and information for pulsar navigation has also been analyzed simultaneously. As a result, the feasibility of the exploration scheme and the performance of the telescope have been fully validated.

Spectral Properties of Anomalous X-ray Pulsars

We examine the spectra of the persistent emission from anomalous X-ray pulsars (AXPs) and their variation with the spin-down rate . Based on an accretion-powered model, the influences of both the magnetic field and the mass accretion rate on the spectral properties of AXPs are addressed. We then investigate the relation between the spectral property of AXPs and mass accretion rate . The result shows that there exists a linear correlation between the photon index and the mass accretion rate: the spectral hardness increases with increasing . A possible emission mechanism for the explanation of the spectral properties of AXPs is also discussed.

X-ray pulsar signal detection using photon interarrival time

The distribution probability of the photon interarrival time （PIT） without signal initial phases is derived based on the Poisson model of X-ray pulsar signals, and a pulsar signal detection algorithm employing the PIT sequence is put forward. The joint probability of the PIT sequence is regarded as a function of the distribution probability and used to compare a constant radiation intensity model with the nonhomogeneous Poisson model for the signal detection. The relationship between the number of detected photons and the probabilities of false negative and positive is studied, and the success rate and mean detection time are estimated based on the number of the given photons. For the spacecraft velocity data detection, the changes of time of photon arrival （TOPA） and PIT caused by spacecraft motion are presented first, then the influences on detection are analyzed respectively. By using the analytical pulse profile of PSR B0531＋21, the simulation of the Xray pulsar signal detection is implemented. The simulation results verify the effectiveness of the proposed method, and the contrast tests show that the proposed method is suitable for the spacecraft velocity data detection.

Understanding the X-ray spectrum of anomalous X-ray pulsars and soft gamma-ray repeaters

Hard X-rays above 10 keV are detected from several anomalous X-ray pul- sars （AXPs） and soft gamma-ray repeaters （SGRs）, and different models have been proposed to explain the physical origin within the frame of either a magnetar model or a fallback disk system. Using data from Suzaku and INTEGRAL, we study the soft and hard X-ray spectra of four AXPs/SGRs： 1RXS J 170849-400910, 1E 1547.0- 5408, SGR 1806-20 and SGR 0501＋4516. It is found that the spectra could be well reproduced by the bulk-motion Comptonization （BMC） process as was first suggested by Triimper et al., showing that the accretion scenario could be compatible with X- ray emission from AXPs/SGRs. Simulated results from the Hard X-ray Modulation Telescope using the BMC model show that the spectra would have discrepancies from the power-law, especially the cutoff at -200 keV. Thus future observations will allow researchers to distinguish different models of the hard X-ray emission and will help us understand the nature of AXPs/SGRs.

A Two-Temperature Supernova Fallback Disk Model for Anomalous X-ray Pulsars

We present a case study of the relevance of the radially pulsational instability of a two-temperature accretion disk around a neutron star to anomalous X-ray pulsars (AXPs). Our estimates are based on the approximation that such a neutron star disk with mass in the range of 10-6-10-5 M⊙ is formed by supernova fallback. We derive several peculiar properties of the accretion disk instability: a narrow interval of X-ray pulse periods; lower X-ray luminosities; a period derivative and an evolution time scale. All these results are in good agreement with the observations of the AXPs.

Hard X-ray emission cutoff in the anomalous X-ray pulsar 4U 0142+61 detected by INTEGRAL

The anomalous X-ray pulsar 4U 0142＋61 has been studied with obser- vations from INTEGRAL. The hard X-ray spectrum in the range 18-500 keV for 4U 0142＋61 was derived using nearly nine years of INTEGRAL/IBIS data. We ob- tained the average hard X-ray spectrum of 4U 0142＋61 with all available data. The spectrum of 4U 0142＋61 can be fitted with a power law that includes an exponen- tial high energy cutoff. This average spectrum is well fitted by a power law with r ,~ 0.51 ± 0.11 plus a cutoff energy at 128.6 ± 17.2 keV. The hard X-ray flux of the source from 20-150 keV showed no significant variations （within 20%） from 2003- 2011. The spectral profiles have some variability over the nine years such that the photon index varies from 0.3-1.5 and the cutoff energies from 110-250 keV. The de- tection of the high energy cutoff around 130 keV shows some constraints on the radia- tion mechanisms of magnetars and possibly probes the differences between magnetar and accretion models for this special class of neutron stars. Future HXMTobservations could provide stronger constraints on the hard X-ray spectral properties of this source and other magnetar candidates.

On the magnetic fields of ultraluminous X-ray pulsars

So far quite a few ultraluminous X-ray(ULX) pulsars have been discovered.In this work,we construct a super-Eddington,magnetic accretion disk model to estimate the dipole magnetic field of eight ULX pulsars based on their observed spin-up variations and luminosities.We obtain two branches of dipole magnetic field solutions.They are distributed in the range of B-(0.156-64.5) × 10^(10) G and-(0.275-79.0) × 10^(13) G corresponding to the low-and high-B solutions respectively.The low magnetic field solutions correspond to the state that the neutron stars are far away from the spin equilibrium,and the high magnetic field solutions are close to the spin equilibrium.The ultra-strong magnetic fields derived in Be-type ULX pulsars imply that the accretion mode in Be-type ULX pulsars could be more complicated than in the persistent ULX pulsars and may not be accounted for by the magnetized accretion disk model.We suggest that the transition between the accretor and the propeller regimes may be used to distinguish between the low-and high-B magnetic field solutions in addition to the detection of the cyclotron resonance scattering features.

Formation of accreting millisecond X-ray pulsars

Accreting millisecond X-ray pulsars(AMXPs) are an important subclass of low-mass X-ray binaries(LMXBs), in which coherent millisecond X-ray pulsations can be observed during outburst states.They have dual characteristics of LMXBs and millisecond pulsars, providing a direct confirmation for the recycling scenario. However, their formation is not well understood. In this work, we simulate the evolution of LMXBs with the MESA code to explore the formation and evolution of AMXPs. Based on the binary evolutionary model of LMXBs and the model of accretion disk instability, we find that most of the observed AMXPs can be produced from LMXBs with orbital periods at the onset of Roche lobe overflow close to the bifurcation period and their observed properties can be explained by our models. The AMXPs with main sequence(MS) donors ultimately evolve into AMXPs with extremely low-mass He white dwarf donors.Moreover, our results indicate that these AMXPs with MS donors are likely to have donor stars near the terminal-age main sequence.

Determination of the magnetic fields of Magellanic X-ray pulsars

The 80 high-mass X-ray binary （HMXB） pulsars that are known to reside in the Magellanic Clouds （MCs） have been observed by the XMM-Newton and Chandra X-ray telescopes on a regular basis for 15 years, and the XMM-Newton and Chandra archives contain nearly complete information about the duty cycles of the sources with spin periods Ps 〈 100 s. We have reprocessed the archival data from both observatories and we combined the output products with all the published observations of 31 MC pulsars with Ps 〈 100 s in an attempt to investigate the faintest X-ray emission states of these objects that occur when accretion to the polar caps proceeds at the smallest possible rates. These states determine the so-called propeller lines of the accreting pulsars and yield information about the magnitudes of their surface magnetic fields. We have found that the faintest states of the pulsars segregate into five discrete groups which obey to a high degree of accuracy the theoretical relation between spin period and X-ray luminosity. So the entire population of these pulsars can be described by just five propeller lines and the five corresponding magnetic moments （0.29, 0.53, 1.2, 2.9 and 7.3, in units of 1030 G cma）.

Temporal variations and spectral properties of the Be/X-ray pulsar GRO J1008–57 studied by INTEGRAL

The spin period variations and hard X-ray spectral properties of the Be/Xray pulsar GRO J1008-57 are studied with INTEGRAL observations during two out- bursts in 2004 June and 2009 March. The pulsation periods of -93.66 s in 2004 and - 93.73 s in 2009 are determined. Pulse profiles of GRO J1008-57 during out- bursts are strongly energy dependent with a double-peaked profile from 3-7 keV and a single-peaked profile in hard X-rays above 7 keV. Combined with previous measure- ments, we find that GRO J1008-57 has undergone a spin-down trend from 1993 - 2009 with a rate of - 4.1 × 10^-5 s d^-1, and could have changed into a spin-up trend after 2009. We find a relatively soft spectrum in the early phase of the 2009 outburst with cutoff energy ~ 13keV. Above a hard X-ray flux of - 10^-9 erg cm^-2 s^-1, the spectra of GRO J1008-57 during outbursts need an enhanced hydrogen absorption with column density ~ 6 x 1022 cm-2. The observed dip-like pulse profile of GRO J1008-57 in soft X-ray bands could be caused by this intrinsic absorption. Around the outburst peaks, a possible cyclotron resonance scattering feature at - 74 keV is detected in the spectra of GRO J1008-57 which is consistent with the feature that was reported in MAXI/GSC observations, making the source a neutron star with the highest known magnetic field （- 6.6 × 10^12 G） among accreting X-ray pulsars. This marginal feature is supported by the present detections in GRO J1008-57 following the correlation between the fundamental line energies and cutoff energies in accret- ing X-ray pulsars. Finally we discovered two modulation periods at - 124.38 d and 248.78d using RXTE/ASM light curves of GRO J1008-57. Two flare peaks ap- pearing in the folded light curve had different spectral properties. The normal outburst lasting 0,1 of an orbital phase had a hard spectrum and could not be significantly de- tected below 3 keV. The second flare lasting ten days showed a very soft spectrum without significant detections above 5 keV. GRO J1008-57 is a good candidate of an accreting system with an equatorial circumstellar disk around the companion star. The neutron star passing the disk of the Be star near periastron and apastron produces two X-ray flares. The soft spectral properties in the secondary flares still need further detailed studies with soft X-ray spectroscopy.

Review of X-ray pulsar spacecraft autonomous navigation

This article provides a review on X-ray pulsar-based navigation(XNAV).The review starts with the basic concept of XNAV,and briefly introduces the past,present and future projects concerning XNAV.This paper focuses on the advances of the key techniques supporting XNAV,including the navigation pulsar database,the X-ray detection system,and the pulse time of arrival estimation.Moreover,the methods to improve the estimation performance of XNAV are reviewed.Finally,some remarks on the future development of XNAV are provided.

Investigation of bubbles escape behavior from low basicity mold flux for high-Mn high-Al steels using 3D X-ray microscope

During the continuous casting process of high-Mn high-Al steels,various types of gases such as Ar need to escape through the top of the mold.In which,the behavior of bubbles traversing the liquid slag serves as a restrictive link,closely associated with viscosity and the thickness of liquid slag.In contrast to two-dimensional surface observation,three-dimensional(3D)analysis method can offer a more intuitive,accurate,and comprehensive information.Therefore,this study employs a 3D X-ray microscope(3D-XRM)to obtained spatial distribution and 3D morphological characteristics of residual bubbles in mold flux under different basicity of liquid slag,different temperatures,and different holding times.The results indicate that as basicity of slag increases from 0.52 to 1.03,temperature increases from 1423 to 1573 K,the viscosity of slag decreases,the floating rate of bubbles increases.In addition,when holding time increases from 10 to 30 s,the bubbles floating distance increases,and the volume fraction and average equivalent sphere diameter of the bubbles solidified in the mold flux gradually decreases.In one word,increasing the basicity,temperature,and holding time leading to an increase in the removal rate of bubbles especially for the large.These findings of bubbles escape behavior provide valuable insights into optimizing low basicity mold flux for high-Mn high-Al steels.

A fast pulse phase estimation method for X-ray pulsar signals based on epoch folding

X-ray pulsar-based navigation （XPNAV） is an attractive method for autonomous deep- space navigation in the future. The pulse phase estimation is a key task in XPNAV and its accuracy directly determines the navigation accuracy. State-of-the-art pulse phase estimation techniques either suffer from poor estimation accuracy, or involve tile maximization of generally non- convex object function, thus resulting in a large computational cost. In this paper, a fasl pulse phase estimation method based on epoch folding is presented. The statistical properties of the observed profle obtained through epoch folding are developed. Based on this, we recognize the joint prob- ability distribution of the observed profile as the likelihood function and utilize a fast Fourier transform-based procedure to estimate the pulse phase. Computational complexity of the proposed estimator is analyzed as well. Experimental results show that the proposed estimator significantly outperforms the currently used cross-correlation （CC） and nonlinear least squares （NLS） estima- tors, while significantly reduces the computational complexity compared with NLS and maxinmm likelihood （ML） estimators.

Pulse phase and doppler frequency estimation of X-ray pulsars under conditions of spacecraft and binary motion and its application in navigation

The pulse phase and doppler frequency estimation of X-ray pulsars in dynamic situations and its application in navigation is a problem that has not been fully investigated. In this paper, solutions are proposed to solve this problem under conditions of spacecraft and binary motion. A high-precision doppler frequency (velocity) measurement model as well as a phase (range) measurement model is established. The averaged maximum-likelihood estimator is developed for the dynamic pulse phase estimation. The pulse phase tracking technique is used in the doppler frequency determination. The tracking filter is redesigned and compared with the existing algorithms. The comparison verifies the advantage of the filter algorithm presented in this pa- per. Unlike traditional views, it is found that in dynamic situations, shorter observation interval lengths will result in higher-accuracy phase and frequency estimates as the tracking filter outputs. A photon-level integrated numerical simulation is performed. Simulation results testify to the validity of the proposed phase and doppler frequency estimation scheme, and show that incorporation of velocity measurements as well as the range ones into the navigation estimator will improve the navigation steady-state performance.

A new maximum-likelihood phase estimation method for X-ray pulsar signals

X-ray pulsar navigation(XPNAV) is an attractive method for autonomous navigation of deep space in the future. Currently, techniques for estimating the phase of X-ray pulsar radiation involve the maximization of the general non-convex object functions based on the average profile from the epoch folding method. This results in the suppression of useful information and highly complex computation. In this paper, a new maximum likelihood(ML) phase estimation method that directly utilizes the measured time of arrivals(TOAs) is presented. The X-ray pulsar radiation will be treated as a cyclo-stationary process and the TOAs of the photons in a period will be redefined as a new process, whose probability distribution function is the normalized standard profile of the pulsar. We demonstrate that the new process is equivalent to the generally used Poisson model. Then, the phase estimation problem is recast as a cyclic shift parameter estimation under the ML estimation, and we also put forward a parallel ML estimation method to improve the ML solution. Numerical simulation results show that the estimator described here presents a higher precision and reduces the computational complexity compared with currently used estimators.

Fast period estimation of X-ray pulsar signals using an improved fast folding algorithm

An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival,which is the measurement of X-ray pulsar navigation.Epoch folding is a classical period estimation method in the time domain;however,its computational complexity grows as the number of trail periods increases.In order to reduce the computational complexity,this paper improves the fast folding algorithm through segment correlation and amplitude accumulation,which is based on the post-order traversal of a binary tree.Compared with epoch folding,the improved fast folding algorithm can achieve a similar accuracy at the cost of a lower computational burden.Compared with the original fast folding algorithm,the improved algorithm can be applied to detectors with a much smaller effective area.The performance of the method is investigated by simulation data and observation data from the Neutron star Interior Composition Explorer(NICER).

X-ray pulsar-based navigation using pulse phase and Doppler frequency measurements

In order to eliminate the impact of the Doppler effects caused by the motion of the spacecraft on the X-ray pulsar-based navigation, an innovative navigation method using the pulse phase and Doppler frequency measurements of the X-ray pulsars is proposed. Given the initial estimate of the spacecraft's state,the real-time photon arrival model is established at the spacecraft with respect to the spacecraft's position and velocity predicted by the orbit dynamic model and their estimation errors. On this basis, a maximum likelihood estimation algorithm directly using the observed photon event timestamps is developed to extract a single pair of pulse phase and Doppler frequency measurements caused by the spacecraft's state estimation error. Since the phase estimation error increases as the observation time increases, we propose a new measurement updating scheme of referring the measurements to the middle time of an observation interval. By using the ground-based simulation system of X-ray pulsar signals, a series of photon-level simulations are performed. The results testify to the feasibility and real-timeliness of the proposed navigation method, and show that the incorporation of the Doppler measurement as well as the pulse phase into the navigation filter can improve the navigation accuracy.