Supergiant fast X-ray transients (SFXTs) are X-ray binary systems with a supergiant companion and likely a neutron star, which show a fast ($sim 10^3$ s) and high variability with a dynamic range up to $10^{5-6}$. Given their extreme properties, they are considered among the most valuable laboratories to test accretion models. Recently, the orbital parameters of a member of this class, IGR J08408-4503, were obtained from optical observations. We used this information, together with X-ray observations from previous publications and new results from X-ray and optical data collected by INTEGRAL and presented in this work, to study the accretion mechanisms at work in IGR J08408-4503. We found that the high eccentricity of the compact object orbit and the large size of the donor star imply Roche lobe overflow (RLO) around the periastron. It is also likely that a fraction of the outer layers of the photosphere of the donor star are lost from the Lagrangian point $L_2$ during the periastron passages. On the basis of these findings, we discuss the flaring variability of IGR J08408-4503 assuming the presence of an accretion disc. We point out that IGR J08408-4503 may not be the only SFXT with an accretion disc fueled by RLO. These findings open a new scenario for accretion mechanisms in SFXTs, since most of them have so far been based on the assumption of spherically symmetric accretion.
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