Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

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    Empirical Determination of β-Law Wind Acceleration Profiles in High-Mass X-Ray Binaries
    (Multidisciplinary Digital Publishing Institute, 2026-02-28)
    Zhantay Muratkhan
    ;
    Manas Khassanov
    ;
    A.S. Taukenova
    ;
    Saken Toktarbay
    Stellar winds in high-mass X-ray binaries (HMXBs) are strongly modified by the presence of an accreting neutron star, yet the impact of X-ray photoionisation on the wind–acceleration profile remains difficult to quantify observationally. In this work, we combine the measured wind velocities at the neutron star orbital radius with spectroscopic terminal velocities in order to infer empirical β-law parameters for six well-studied HMXBs. By inverting the β-law, we reconstruct the individual acceleration curves v(r) and obtain revised estimates of the wind-acceleration parameters b and β for each system. A suggestive trend emerges from the reconstructed profiles: systems with lower terminal velocities tend to exhibit systematically larger acceleration indices β, consistent with the interpretation that dense, slowly accelerating winds may be more strongly affected by X-ray photoionisation. A secondary, weaker pattern is suggested between the orbital separation a/R* and β, although, for our small sample, it is not statistically significant, suggesting that compact systems experience a more pronounced suppression of wind acceleration in the vicinity of the neutron star. Taken together, these indicative relations provide a coherent observational picture linking the global wind–velocity scale to the local radiative environment. The resulting acceleration profiles and system-to-system correlations offer a practical empirical foundation for modelling wind-fed accretion in HMXBs. The parameter set derived here can be directly incorporated into studies of quasi-spherical accretion, torque evolution, and the dynamical influence of X-ray photoionisation in massive 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.