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 MuratkhanТема: search.filters.subject.high-mass X-ray binaries

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    Analytical constraints on generalized β -velocity laws in X-ray-illuminated HMXBs
    (Oxford University Press, 2026-03-20)
    Saken Toktarbay
    ;
    Aray Muratkhan
    ;
    N. Myrzakulov
    ;
    Zhantay Muratkhan
    ABSTRACT We derive analytic constraints on the parameters of the generalized $\beta$-velocity law used to describe radiation-driven winds from OB (O- and B-type) supergiants in wind-fed X-ray binaries. Starting from the radial equation of motion with Castor–Abbott–Klein (CAK) line driving, gas pressure, and X-ray irradiation, we perform an asymptotic analysis of the near-base region and show that a monotonic CAK-type acceleration requires the exponent of the velocity law to satisfy a robust lower bound $\beta _{\min }=1/2$. A separate condition follows from requiring the $\beta$-law to connect smoothly to the subsonic layers: the wind speed at the stellar surface must be at least comparable to the isothermal sound speed, which yields a conservative upper limit on the onset parameter, $b \lesssim 1-\left(a_{\rm s}/v_\infty \right)^{1/\beta }$,and implies $b_{\max } \approx 0.95$–0.99 for typical OB-star parameters. We include the effects of X-ray photoionization and attenuation in an approximate way by introducing an effective force-multiplier slope $\alpha _{\rm eff}$ and an optical-depth parameter controlling the weakening of X-ray inhibition. A scaling analysis shows that strong irradiation favours larger $\beta$ and can lead to the loss of monotonic acceleration, providing an effective system-dependent upper limit on the acceleration index. To assess the consistency of these bounds, we integrate a simplified momentum equation and fit the resulting accelerating solutions with a generalized $\beta$-law. The best-fitting pairs $(b,\beta)$ lie within the analytically allowed domain and occupy the range $\beta \approx 0.6$–1.2, in good agreement with empirical determinations for several persistent high-mass X-ray binaries. Our results provide physically motivated constraints on velocity-law parameters that can guide wind modelling and the interpretation of spectroscopic diagnostics in irradiated massive-star winds.
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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.