Origin of the X-ray off-states in Vela X-1

$Context$: Vela X-1 is the prototype of the classical sgHMXB systems. Recent continuous and long monitoring campaigns revealed a large hard X-rays variability amplitude with strong flares and off-states. This activity has been interpreted invoking clumpy stellar winds and/or magnetic gating mechanisms. $Aims$: We are probing if the observed behaviour could be explained by unstable hydrodynamic flows close to the neutron star rather than the more exotic phenomena. $Methods$: We have used the hydrodynamic code VH-1 to simulate the flow of the stellar wind with high temporal resolution and to compare the predicted accretion rate with the observed light-curves. $Results$: The simulation results are similar to the observed variability. Off-states are predicted with a duration of 5 to 120 minutes corresponding to transient low density bubbles forming around the neutron star. Oscillations of the accretion rate with a typical period of $\sim$ 6800 sec are generated in our simulations and observed. They correspond to the complex motion of a bow shock, moving either towards or away from the neutron star. Flares are also produced by the simulations up to a level of $10^{37}$ erg/s. $Conclusions$: We have qualitatively reproduced the hard X-ray variations observed in Vela X-1 with hydrodynamic instabilities predicted by a simple model. More sophisticated phenomena, such as clumpy winds or the magnetic gating mechanism, are not excluded but not required to explain the basic phenomenology.