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.

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.

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 $\beta$-law parameters for six well-studied HMXBs. By inverting the $\beta$-law, we reconstruct the individual acceleration curves $v\left(r\right)$ and obtain revised estimates of the wind-acceleration parameters b and $\beta$ for each system. A suggestive trend emerges from the reconstructed profiles: systems with lower terminal velocities tend to exhibit systematically larger acceleration indices $\beta$, 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 $\beta$, 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.