Abstract
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.