Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

Постоянный URI для этого сообществаhttps://cris.qyzpu.edu.kz/handle/123456789/1

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Автор: search.filters.author.Aray MuratkhanЕсть файлы: Да

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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.