A numerical investigation of wind accretion in persistent Supergiant   X-ray Binaries I - Structure of the flow at the orbital scale
  Classical Supergiant X-ray Binaries host a neutron star orbiting a supergiant OB star and display persistent X-ray luminosities of 10$^{35}$ to 10$^{37}$ erg/s. 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 characterize the structure of the wind at the orbital scale as it accelerates, from the stellar surface to the vicinity of the accretor. Thanks to the parametrization we retained and 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 $\alpha$-force multiplier which 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 confront our model to three persistent Supergiant X-ray Binaries (Vela X-1, IGR J18027-2016, XTE J1855-026) and discuss the likelihood of wind-formed accretion discs around the accretors in each case, further investigated in a following paper. 
I. El Mellah and F. Casse
astro-ph.HE