Characterising the post-red supergiant binary system AFGL 4106 and its complex nebula with SPHERE/VLT

Context. Mass loss in evolved massive stars plays a critical role in shaping their circumstellar environments and enriching the interstellar medium. In binary systems, stellar interactions can further complicate this process, affecting stellar evolution, stellar yields, and nebular morphology. Aims. We aim to characterise the physical and morphological properties of the binary system AFGL 4106, which is composed of two evolved massive stars. Understanding its mass-loss processes and circumstellar environment offers insight into the late stages of stellar evolution in massive binary systems. Methods. We obtained high-angular-resolution, high-contrast imaging using VLT/SPHERE with ZIMPOL (optical) and IRDIS (near-infrared) across multiple filters. We used aperture photometry to extract the spectral energy distributions (SEDs) of each star and applied radiative-transfer modelling to study the system and its surrounding dusty environment. Results. The observations resolve both components of the binary and unveil a complex, dusty nebula featuring asymmetric structures and cavities. SED fitting yields stellar temperatures of T-1 = 6723 +/- 196 K and T-2 = 3394 +/- 264 K, along with bolometric luminosities of L-1 = (7.9 +/- 0.18)x10(4) L-circle dot and L-2 = (3.8 +/- 0.11)x10(4) L-circle dot. These values support the classification of the primary as being in a post-red-supergiant (post-RSG) phase and the secondary as an active red supergiant (RSG). The luminosity ratio, combined with the inferred radii, indicates that both stars are at close yet distinct stages of their evolution. The binary is surrounded by an extended shell whose asymmetric morphology and large-scale features suggest interaction with the stellar winds and interstellar medium (ISM), and possibly the presence of a third, undetected companion. Conclusions. These observations provide the first resolved view of AFGL 4106 s system and its dusty envelope. Our analysis sets constraints on the physical properties and evolutionary status of the system. This work contributes to our understanding of mass-loss processes in massive binaries and the shaping of nebulae around evolved stars.