2017MNRAS.467.2585E

Classical supergiant X-ray binaries host a neutron star orbiting a supergiant OB star and display persistent X-ray luminosities of 10³⁵-10³⁷ erg s^–1. The stellar wind from the massive companion is believed to be the main source of matter accreted by the compact object. With this first paper, we introduce a ballistic model to evaluate the influence of the orbital effects on the structure of the accelerating winds that participate to the accretion process. Thanks to the parametrization we retained the numerical pipeline we designed, we can investigate the supersonic flow and the subsequent observables as a function of a reduced set of characteristic numbers and scales. We show that the shape of the permanent flow is entirely determined by the mass ratio, the filling factor, the Eddington factor and the α-force multiplier that drives the stellar wind acceleration. Provided scales such as the orbital period are known, we can trace back the observables to evaluate the mass accretion rates, the accretion mechanism, the shearing of the inflow and the stellar parameters. We discuss the likelihood of wind-formed accretion discs around the accretors in each case and confront our model to three persistent supergiant X-ray binaries (Vela X-1, IGR J18027-2016, XTE J1855-026).