Fundamental and Applied X-ray Astrophysics

Scientific results:

• We have developed a method for modeling the atmospheres of neutron stars heated by a stream of fast ions falling on them. The model gives an opportunity to refine the masses and radii of neutron stars.
• A method for determining the spectra of rapidly rotating neutron stars has been refined. We have modified a method for determining the fundamental parameters of  neutron stars from the spectral evolution of thermonuclear bursts at the stage of luminosity decline.
• A new method has been developed for direct approximation of the spectra of X-ray bursters with models of the atmospheres of  neutron stars and a procedure for interpolation of model spectra has been developed.
• As part of works to research the physical characteristics of strongly magnetized neutron stars, we for the first time found a change in the spectrum during transition from the luminous to the weak state of the object GX 304-1 and provided a theoretical interpretation of this phenomenon.
• From more than 2000 pulsars observed in the radio range we selected about 40 that also significantly radiate in the X-ray part of the electromagnetic spectrum. Using data from the NICER observatory, we selected 8 candidates that are most suitable for use as «reference» sources for X-ray navigation systems.
• We have developed and tested a technique for analyzing fast variability (pulse-to-pulse) in observations X-ray pulsars performed by various observatories. The technique allows to research the properties of ensembles of pulses and determine the phases of the pulse  profile in which non-stochastic variability is observed.
• A software package has been developed for the simultaneous complex analysis of   collective temporal characteristics (cross-correlation, power spectra, coherence, temporal delays) of data from several X-ray channels.
• Requirements have been formulated for an X-ray detector for neutron star research and navigation systems relying on X-ray pulsars, its main parameters have been determined.
• We have formulated and evaluated the feasibility of requirements for a system for supporting thermal regimes of X-ray detectors designed for the research of neutron stars and spacecraft navigation relying on X-ray  pulsars for spacecraft operating on near-Earth and high-apogee orbits.
• The Laboratory has developed a topology of the main IP blocks for an application-specific integrated circuit (ASIC) that comprise the spectrometry tract. We optimized the topology of IP-blocks on the basis of extracted parameters.
• Our researchers have united IP blocks into a single SDDASIC3 circuit. The compliance of the topology with design requirements has been verified. The design of the ASIC is being prepared for production.
• A draft of the design of an X-ray radiation detector has been developed. It relies on a matrix of silicon drift detectors.
• We have developed a model of the pure hydrogen atmosphere of the polar cap of a millisecond radio pulsar heated by a flow of ultra-relativistic electrons, so called reverse current of the magnetosphere. It was demonstrated that the angular distribution of heated models of the atmosphere can be significantly different from the normal distribution of outgoing radiation in standard models of the atmospheres of neutron stars. In particular, darkening towards the edge can change to brightening towards the edge. These effects should be accounted for when modeling the pulse  profiles of millisecond pulsars observed by the NICER tool and can significantly affect the determination of the radii of neutron stars obtained as a result of such modeling.
• The Laboratory has started developing a self-consistent model of an accretion column in classical pulsars with a strong magnetic field B = 10¹²…10¹³ Gs. Numerical code has been developed on the basis of Monte Carlo simulations of radiation transfer. The cross-sections of the main processes in a strong magnetic field have been tabulated. We built models of the dynamics and energetics of gas in a column. The spectra in the region of cyclotron resonance have been obtained. We researched the dependence of pulse transmitted to gas depending on its temperature in various magnetic fields. The physical nature of the fan chart of directions in supercritical pulsars has been explained.
• We have enhanced a Bayesian method for modeling the phase-resolved spectra of millisecond pulsars.
• Our researchers have developed a mathematical apparatus and software for the computation of the spectra from rapidly rotating neutron stars. It was demonstrated the way color adjustment and dilution factors change due to the rapid rotation. We proposed an improved «cooling down tail» model that accounts for the fast rotation of neutron stars. By applying it to the SAX J1810.8-2609 burster we obtained the value of the radius of the neutron star (at M☉=1.5 Solar mass) in the 11.5…12.0 km interval (68% reliability).
• We have proposed a simple formula that approximates precise computations of the bending of light rays in the Schwarzschild metric with a precision better than 0.06%.
• A Bayesian method has been developed for bounding the masses and radii of neutron stars with the use of both spectral and temporal information from accreting millisecond pulsars. The results indicate that the developed method works, and knowing the geometry of the source and the inclination of the observer from X-ray polarization leads to more precise boundaries for the mass and the radius of a neutron star.
• The Laboratory researched the fast variability of the pulses  profiles of     X-ray pulsars with the use of the previously developed methodology. The methodology was applied to an extensive set of systems for which archive measurement data from the RXTE and NuSTAR observatories. It was demonstrated that in X-ray pulsars strong pulse-to-pulse variability is observed, while the shape of the pulse strongly depends on the intensity of the pulse,including at short temporal scales.
• We have developed a mathematical apparatus that allows to determine the parameters of the location and motion of a spacecraft and to assess the uncertainty of these parameters from signals of X-ray pulsars. A program for observing several X-ray pulsars has been created. We started processing the accumulated observational data.
• The Laboratory has conducted works to install technological libraries of the semiconductor process XT018 produced by X-Fab into the Tanner CAD. We are transferring the electrical circuit designs of blocks of the SDDASIC3 chip from the Pyxis Schematic CAD to the Tanner S-Edit CAD.  We performed a transformation of the topology of the SDDASIC3 chip from the Pyxis Layout CAD to the Tanner L-Edit CAD.
• We have developed and manufactured a prototype for researching the sensitivity properties of the element of the detector and verifying the parameters of the first version of the application-specific integrated circuit SDDASIC3. A bench has been designed to research the parameters of sensitive elements and the application-specific integrated circuit. We debugged the remaining parts of the prototype and the bench. Configurations for programmable logical integrated circuits have been created. Software has been created for real-time microprocessor units PRU-ICSS of the ARM Cortex-A8 central processing unit of the bench’s control unit.
• Using direct and indirect methods, we managed to determine the intensity of the magnetic field in four X-ray pulsars, XTE J1829−098, IGR J19294+1816, RX J0812.4–3114 and SXP4.78.
• Variation of the period of pulsations in the GX 301−2 system at the scale of the orbital period allowed to discover, for the first time, the neutron star rotating in the direction  opposite to  its orbital motion.
• In a system with the accreting millisecond pulsar IGR J17591−2342 we managed to determine all the orbital parameters with high precision.
• Long-term monitoring of one of the slowest rotating pulsars, SXP1062, allowed to discover an unexpected significant acceleration of rotation of the neutron star and its interaction with dense absorbing matter while moving away from the companion star.
• For a very luminous transient, GROJ1744−28, it was found that the power  spectrum of its radiation is in sharp contrast with the canonical form, while the frequency of breaks turned out to be significantly higher than expected on the basis of an assessment of the magnetic field from the energy of the cyclotron line, which points at the fact that the accretion disk contains a region with a predominance of radiation pressure and the presence of strong quadrupole component in the magnetic field.
• The recent discovery of pulsating ultra-luminous X-ray radiation (ULX) demonstrated that the visible luminosity of accreting neutron starts can exceed the Eddington luminosity by a factor of hundreds. It was shown that the great amplification of luminosity due to the geometric collimation and the high amplitude of pulsations eliminate each other to a significant extent, and only an insignificant part of collimator ULX pulsars can demonstrate pulsation amplitudes higher than 10%. The discrepancy between this conclusion and current observations indicates that ULX pulsars cannot be strongly collimated and their visible luminosity is close to real.
• Using the developed software (the package for searching for, selecting and transmitting data, the package for stream-oriented data processing, searching for pulsations etc.), we analyzed data of monitoring observations of several rapidly rotating pulsars performed over the preceding two years by the NICER tool. We developed software for analyzing the luminosity curves of pulsars obtained in measurements by the ART-XC telescope. In particular, we developed a methodology for adjusting the onboard time to Coordinated Universal Time, or UTC (onboard block correction), and implemented a procedure for barycentering.
• As part of the project, we have planned and staged a number of experiments that allow to refine elements of the space navigation systems of the Russian X-ray telescope ART-XC named after Mikhail N. Pavlinskiy installed on the orbital space observatory «Spektr-RG». We organized and conducted 11 series of observations of a number of rapidly rotating X-ray pulsars by the ART-XC telescope. These observations, along with standard measurements of the parameters of the trajectory of the spacecraft, allowed to adjust the onboard clock to match UTC with millisecond precision. It was demonstrated that acceptable navigation parameters of the satellite can be calculated on the basis of solely data of measurements of pulsars, which proves the possibility of creating an autonomous spacecraft navigation system using X-ray pulsar signals. Drawing on data of observations by ART-XC, for each of the pulsars we not only demonstrated that it is possible  to determine the time of arrival of pulses with highest precision possible, but also obtained the laws of their rotation (ephemerides), thus laying the groundwork for creating and supporting the national database of X-ray pulsars suitable for the needs of autonomous navigation in space.
• In the process of our research to develop algorithms and software for determining the orbit of a spacecraft from signals of X-ray pulsars, we designed a mathematical apparatus that allows to determine the parameters of the position and motion of a spacecraft and evaluate the uncertainty of these parameters. In particular, we developed: an algorithm for computing pulse arrival time (PAT) for the problem of determining the orbit of a spacecraft, an algorithm for computing the mean value of PAT from several periods of the X-ray radiation signal from a pulsar  determining the orbit of a spacecraft, an algorithm and software for determining the orbit of a spacecraft from measurements of the value of PAT, we modeled measurements of PAT and conducted computational experiments to determine the orbit of a spacecraft.
• To research a multi-element detector of X-ray radiation based on silicon drift detectors (SDD), we developed a prototype of a detector.
• The Laboratory has conducted tests of a prototype of the sensing element of  a detector for the assessment of possible directions of further work to improve the characteristics of samples of the detector necessary to solve the project’s objectives. For the E52410007.00.00 SDD, which is part of the bench, we developed and manufactured the E52410007.37.00 that allows to conduct testing of ASIC and silicon drift detectors (SDD) in a dry nitrogen atmosphere that prevents the negative effects of the environment on sensitive elements. With the use of the E52410010.00.00 bench, we conducted testing of the SDDASIC3 circuit in conjunction with the SDD.
• Our researchers have modeled the thermal X-ray spectrum of the PSR B0656+14 pulsar using various models describing the radiating surface of the magnetized neutron star. The observed phase-averaged spectrum was obtained by the eROSITA X-ray telescope installed onboard the «Spektr–RG» space observatory. We used three models of the radiating surface. Within the first model, we suggested that the surface of the neutron star is covered with a thick hydrogen shell and the local spectra of the pulsar is described by the spectra of hydrogen magnetized models of the atmospheres. The second reviewed hypothesis suggests that the neutron star is covered with a condensed metallic surface. The third model includes, apart from a condensed surface, polar caps covered with geometrically thin hydrogen atmospheres near the magnetic poles.
• We have researched the periodic variability for a large set of accreting neutron stars and intermediate polars. In particular, we studied the relationship between the frequency of breaks in their power spectra and the strength of their magnetic fields. We conducted a detailed research of multi-wave observations of a number of X-ray pulsars (4U 1901+03, V 0332+53, 2S 1845-024, SXP 1323, PSR B1259-63) with the purpose of determining the physical parameters of both the neutron star and the binary system as a whole. Our researchers managed to show that the measured frequency of breaks in the spectrum of power of the Her X-1 pulsar correspond to a dipole magnetic field of several 1e11 Gs, i. e. almost by an order of magnitude less than the intensity of the magnetic field corresponding to cyclotron energy. This discrepancy was explained by the presence of strong multipole components of the magnetic field of a neutron star. In the case of 4U 1901+03, we for the first time managed to demonstrate that the wideband X-ray spectrum of a pulsar can be well described using a model of two-component continuum without an absorption line at a power of 10 keV, which casts doubts on the interpretation of this feature as a cyclotron line. in the V 0332+53 pulsar we, for the first time, discovered coherent pulsations of both the fluorescence line of iron at an energy of 6.4 keV and the K-edge of neutral iron at an energy of 7.1 keV. Optical observations of the pulsar 2S 1845-024 allowed to classify the companion star in the system as OB supergiants which is located at a distance of about 14 kpc. Relying on the rate of acceleration of the rotation period of the  SXP 1323 source we evaluated the high value of the strength of its magnetic field — B~(1-6)e13 Gs. In the case of gamma-loud binary system with the PSR B1259-63 radio pulsar, we found a significant delay of burst in the GeV range, which was explained within the an emission cone model.
• A numerical model has been created that computes reflection of X-ray radiation of the accretion column from the atmosphere of a neutron star. The model locally computes radiation transfer using the Monte Carlo method, accounting for such elementary processes as magnetic Compton scattering, braking and cyclotron radiation and absorption. To obtain the spectra visible to a remote observer, we factored in the propagation of radiation accounting for the effects of the general theory of relativity in the application of the Schwarzschild metric. It turned out that a significant role in the formation of the spectrum is played by true absorption of radiation in the atmosphere due to braking processes. As a result of absorption, the spectrum of reflected radiation becomes significantly harder in comparison with the spectrum of the falling radiation, and an absorption feature forms in the spectrum that has a complex structure. Reflection reduces the degree of linear polarization, though insignificantly. It turns out to be critical for the assessment of polarization to consider the effect of the magnetosphere on the propagation of polarized photons.
• We have developed a numerical model of radiation transfer in the low luminosity state of X-ray pulsars. The model is based on Monte Carlo simulations of radiation transfer and iterative search for the temperature and density profiles in the atmosphere of a neutron star. Using the produced model, we are able to obtain the spectrum and polarization of radiation for a remote observer. Relying on this model, we managed to confirm the existence of an overheated surface layer in the atmospheres of neutron stars at low accretion rates and to reproduce the observed spectra of some X-ray pulsars in low luminosity states.
• The Laboratory has been continuing experiments to refine the elements of an autonomous space navigation system under conditions of real space. We planned and staged 13 series of observations of rapidly rotating X-ray pulsars, after which scientific data was processed with the use of algorithms developing at previous stages. We conducted tests of the carrier frequency of the time stamp of the ART-XC telescope to determine the degree of its desynchronization with regards to the onboard time scale on long time intervals. The conducted observations were added to the database of ephemerides and pulse profiles of pulsars that can be used as reference objects in an X-ray navigation system. The most important result was that we managed to register pulsations of one of the most rapidly rotating pulsars, PSR B1821-24, using the ART-XC telescope (with a period of about 3 ms) and recover its pulse profile. Thus we have demonstrated that the temporal resolution of the telescope and its sensitivity to the flow allow to refine almost all the elements of the autonomous navigation system, which demonstrates the fact that Russian technologies are now already sufficiently compliant with the requirements set for the technical implementation of the project of an autonomous navigation system based on X-ray pulsars.
• The Laboratory has developed algorithms and software for determining the parameters of motion of a spacecraft on flight trajectories to planets of the Solar system according to signals from X-ray pulsars factoring in additional disturbances in motion of spacecraft. The presented algorithm for processing navigation measurements ensures simultaneous refinement of the kinematic vector of the state of a spacecraft and the deviation of the time scale. We have described a mathematical bench for bulk imitation modeling of spacecraft trajectories with the use of X-ray navigation in the onboard control circuit.
• Our researchers have proposed a concept of two X-ray radiation detectors based on a matrix of silicon drift detectors with SDDplus and SDDexFet elements. We designed a spectrometry channel for processing signals from SDDplus cells for the SDDASIC4 information system. We started designing a spectrometry channel for processing signals from SDDexFet cells, which is also planned to be refined using SDDASIC4.  
• We have refined the concept of a space experiment to demonstrate the functioning of the elements of an X-ray navigation system. Several variations of the X-ray detection equipment have been tested, as well as systems of mirrors, capillary collimators focusing X-ray radiation onto the receiver. The final variation of the instrument will be formed depending on the availability of the necessary elements and the readiness levels of a number of critical technologies.

• Two employees of the Laboratory have completed internships at the University of Turku (Finland).
• One Doctor of Sciences dissertation and two Candidate of Sciences dissertations have been prepared and defended.

Collaborations:

• University of Turku (Finland). joint research of rapidly rotating neutron stars and the atmospheres of radio pulsars.
• University of Tübingen (Germany): joint research of X-ray pulsars and the atmospheres of neutron stars.
• Leiden University (the Netherlands): joint research of processes in strong magnetic fields.
• Nordic Optical Telescope (Spain), South African Astronomical Observatory (South Africa): joint research of compact objects based on data of ground and space observations