Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

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Thin accretion-disc transfer functions in the q-metric spacetime: quadrupolar lensing signatures
(Cornell University, 2026-09-07)
Saken Toktarbay
;
Manas Khassanov
;
Aray Muratkhan
;
Zhantay Muratkhan
;
Aliya Taukenova
We study geometrically thin equatorial disc images in the static, axisymmetric q-metric spacetime using backward ray tracing. The Schwarzschild solution is recovered at $q=0$; for the nonzero deformations considered here, $r=2M$ is a curvature singularity rather than an event horizon. For a distant nearly face-on observer, we construct the first three equatorial transfer functions $r_m(b;q)$. In the {Schwarzschild} limit, the resolved third-crossing interval contains the critical impact parameter $b=3\sqrt{3}M$. As $q$ increases from $-0.3$ to $0.3$, the branch center shifts from $b_{3,c}/M\simeq3.716$ to $6.702$. In units of the physical monopole mass $\mathcal M=(1+q)M$, it instead decreases from $b_{3,c}/\mathcal M\simeq5.309$ to $5.156$. Much of the displacement in metric-parameter units therefore reflects the changing monopole scale. At fixed $\mathcal M$, the inclined first-intersection maps show that the contour dimensions increase with $q$, with larger relative changes near the inner disc. A prescribed power-law emissivity and relativistic frequency-shift weighting yield direct images whose integrated flux differs from the Schwarzschild value by at most $2.4\%$. Between the endpoint models, the horizontal median-flux position increases by $8.8\%$ and the interquartile width by $14.5\%$. Within this emission prescription, the residual deformation dependence appears mainly as a displacement and broadening of the brightness distribution. Higher-order radiative contributions are not included.
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Adiabatic theory in Kerr spacetimes
(Springer Science+Business Media, 2024-05-01)
Kuantay Boshkayev
;
Gulmira Nurbakyt
;
Hernando Quevedo
;
Gulnara Suliyeva
;
Abylaikhan Tlemissov
Цитирования (OpenAlex) 3Цитирования (OpenCitations) 3
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Gravitational capture cross-section in Zipoy-Voorhees spacetimes
(Springer Science+Business Media, 2025-05-28)
S.B. Momynov
;
Kuantay Boshkayev
;
Hernando Quevedo
;
Farida Belissarova
;
A. Dalelkhankyzy
Цитирования (OpenAlex) 5Цитирования (OpenCitations) 4
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NUMERICAL STUDY OF ORBITAL STABILITY IN THE RELATIVISTIC RESTRICTED THREE-BODY PROBLEM
(2026-03-29)
Ayazhan Orazymbet
;
Aliya Taukenova
;
Daniya Utepova
;
Nurzada Beissen
;
N. Sandibayeva
This paper presents a numerical study of the relativistic restricted three-body problem within the framework of General Relativity. Using the Lagrangian and Hamiltonian formalisms, the equations of motion with relativistic corrections up to the order of 1/c2 were derived and solved numerically in Wolfram Mathematica. The developed model allows one to analyze orbital stability under small relativistic perturbations. Numerical simulations were performed using the Runge–Kutta integration method for three systems: “Earth–Sun–Moon,” “Earth–Sun– Mercury,” and an equal-mass configuration. The results confirm the stability of circular orbits and reproduce the observed relativistic precession of Mercury’s perihelion. For the equal-mass system, the calculations reveal a transition from quasi-periodic to chaotic motion, depending on the initial conditions. The study demonstrates the reliability and efficiency of the Mathematica environment for modeling nonlinear relativistic dynamics and shows that the proposed approach can be useful for further research in celestial mechanics and gravitational physics.
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COMPARATIVE ANALYSIS OF X-RAY LUMINOSITY OF PERSISTENT AND TRANSIENT HIGH-MASS X-RAY BINARIES
(2026-03-29)
Zhantay Muratkhan
;
Manas Khassanov
;
Aray Muratkhan
;
Aliya Taukenova
;
A. Sadu
High-mass X-ray binaries (HMXBs) are commonly divided into persistent sources, which emit X-rays steadily over long periods, and transient sources, which remain mostly in a quiescent state and exhibit episodic X-ray outbursts. The aim of this work is to statistically compare the X-ray luminosity properties of these two classes, focusing on the maximum luminosity and the luminosity variability range . For this purpose, catalog data for Galactic HMXB pulsars were used, including 18 persistent and 64 transient systems. The distributions of and were analyzed using histograms, box plots, cumulative distribution functions (CDFs), and the non-parametric Mann–Whitney test. It is shown that both classes reach similar values of on the order of – erg/s), with no statistically significant difference between their distributions. However, transient systems exhibit a much wider luminosity variability range, reaching increases of 4–5 orders of magnitude (up to ), whereas persistent sources typically show lower variability. This difference is statistically confirmed, with transients demonstrating significantly higher variability p ≈ 0.05). Thus, the main distinction between persistent and transient HMXBs lies not in their peak X-ray luminosity, but in their accretion regime. In persistent systems, the compact object continuously accretes matter from a relatively stable stellar wind of an OB supergiant, resulting in steady X-ray emission. In contrast, transient systems are characterized by intermittent accretion (for example, episodic mass capture from a Be-star circumstellar disc), which leads to their extreme luminosity variability.
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Correlation analysis of the wind acceleration parameter in high-mass X-ray binaries
(Al-Farabi Kazakh National University, 2026-06-19)
Zhantay Muratkhan
;
Saken Toktarbay
;
Aray Muratkhan
;
Aliya Taukenova
;
Nadeem Azhar
This work presents a correlation analysis of the wind acceleration parameter β in high-mass X-ray binaries (HMXBs). The aim of the study is to determine how β depends on the geometric and dynamical characteristics of the system, primarily on the ratio of the orbital radius to the stellar radius, a⁄R_* and on the terminal wind velocity v_∞. For this purpose, published values of R_*, a and v_∞ together with measured wind velocities in the vicinity of the neutron star, were used. Based on these data, the parameters of the β-velocity law were determined numerically. The resulting β values were then approximated using a linear regression, β≈k a⁄R_* +c, yielding a simple empirical relation. The results show that the linear correlation between β and the orbital-to-stellar radius ratio is weak (with a Pearson correlation coefficient r ≈ 0.22) and is accompanied by substantial scatter, indicating the influence of additional physical factors. The linear regression yields a small positive slope (k ≈ 0.14), which suggests only a weak tendency for β to increase with the orbital ratio. Because of the small sample size, this trend should be regarded as tentative. The proposed linear model allows β to be estimated without detailed spectroscopic analysis and may be useful as a rough empirical indicator of wind-accretion properties in HMXBs. The originality of this study lies in providing a simple empirical first-order assessment of the β parameter in HMXBs based on observed orbital and wind properties in systems where detailed spectroscopic constraints are limited. Key words: high-mass X-ray binaries (HMXBs), β-law (β-velocity profile), wind velocity profile, terminal wind velocity, orbital ratio a⁄R_* , correlation analysis.
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Vertical epicyclic stability and dissipative settling in a weakly deformed q-metric spacetime
(L. N. Gumilyov Eurasian National University, 2026-09-30)
Ayazhan Orazymbet
;
Aray Muratkhan
;
Aliya Taukenova
;
A. Dalelkhankyzy
We investigate the motion of massive test particles close to the equatorial plane of a weakly deformed q-metric spacetime. Working to first order in the dimensionless quadrupole parameter q, we derive the orbital angular velocity and the vertical epicyclic frequency for equatorial circular orbits while keeping the physical monopole mass fixed. The Schwarzschild limit is recovered at q = 0, whereas a nonzero quadrupole removes the degeneracy between the vertical and azimuthal frequencies already at O(q). A small phenomenological damping term is then introduced into the linearized vertical equation to describe the gradual approach of a perturbed orbit toward the equatorial plane. In the conservative case, the particle continues to oscillate about this plane without any decrease in amplitude. With damping, the amplitude decays exponentially. The quadrupolar deformation changes the vertical oscillation frequency and, consequently, the number of cycles completed before a specified settling threshold is reached. It does not, however, set the decay timescale, which follows from the adopted damping prescription. Since the coordinate-time damping coefficient is kept fixed in our numerical examples, the trajectories share the same exponential envelope but oscillate at different frequencies. The comparison with the exact q-metric also provides a direct check of the firstorder approximation. Over the sampled domain |q| ≤ 0.1 and 6 ≤ r/M ≤ 20, the relative error in the vertical frequency remains below 0.34%, while the corresponding frequency ratio is reproduced to better than 0.10%. These results show explicitly how the quadrupolar geometry modifies vertical orbital dynamics within a model in which dissipative settling is introduced independently.

Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

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