Radiography in high mass X-ray binaries -- Micro-structure of the stellar wind through variability of the column density

In high mass X-ray binaries (HMXBs), an accreting compact object orbits a high mass star which loses mass through a dense and inhomogeneous wind. Using the compact object as an X-ray backlight, the time variability of the absorbing column density in the wind can be exploited in order to shed light on the micro-structure of the wind and obtain unbiased stellar mass loss rates for high mass stars. We explore the impact of clumpiness on the variability of the column density with a simplified wind model. In particular, we focus on the standard deviation of the column density and the characteristic duration of enhanced absorption episodes, and compare them with analytical predictions based on the porosity length. We identified the favorable systems and orbital phases to determine the wind micro-structure. The coherence time scale of the column density is shown to be the self-crossing time of a clump in front of the compact object. We provide a recipe to get accurate measurements of the size and of the mass of the clumps, purely based on the observable time variability of the column density. The coherence time scale grants direct access to the size of the clumps while their mass can be deduced separately from the amplitude of the variability. If it is due to unaccreted passing-by clumps, the high column density variations in some HMXBs requires high mass clumps to reproduce the observed peak-to-peak amplitude and coherence time scales. These clump properties are hardly compatible with the ones derived from first principles. Alternatively, other components could contribute to the variability of the column density: larger orbital scale structures produced by a mechanism still to be identified, or a dense environment in the immediate vicinity of the accretor such as an accretion disk, an outflow or a spherical shell around the magnetosphere of the accreting neutron star.