Inner dusty envelope of the AGB stars W~Hydrae, SW\,Virginis, and R~Crateris using SPHERE/ZIMPOL

Context. The asymptotic giant branch (AGB) marks the final evolutionary stage of stars with initial masses between similar to 0.8 and 8 M-circle dot. During this phase, stars undergo copious mass loss, which contributes significantly to the enrichment of the interstellar medium. The well-accepted mass-loss mechanism requires radiation pressure acting on dust grains that form in the density-enhanced and extended AGB stellar atmospheres. The details of the mass-loss process are not yet well understood, however. For oxygen-rich AGB stars, which are the focus of this study, the dust grains that drive the wind are expected to scatter visible light very efficiently because their sizes are relative large.Aims. We study the distribution of dust in the inner wind of oxygen-rich AGB stars to advance our understanding of the wind-driving process.Methods. We observed light scattered off dust grains that form around three oxygen-rich AGB stars (W Hya, SW Vir, and R Crt) with mass-loss rates between 10(-7) and 10(-6) M-circle dot yr(-1) using the extreme-adaptive-optics imager and polarimeter SPHERE/ZIMPOL with three filters centred at 0.65, 0.75 and 0.82 mu m. We compared the observed morphologies and the spectral dependence of the scattered light between the three sources and determined the radial profile, per image octant, of the dust density distribution around the closest target, W Hya.Results. We find the distribution of dust to be asymmetric for the three targets. A biconical morphology is seen for R Crt, with a position angle that is very similar to those inferred from interferometric observations of maser emission and of mid-infrared continuum emission. The cause of the biconical outflow cannot be inferred from the ZIMPOL data, but we speculate that it might be the consequence of a circumstellar disc or of the action of strong magnetic fields. The dust grains polarise light more efficiently at 0.65 mu m for R Crt and SW Vir and at 0.82 mu m for W Hya. This indicates that at the time of the observations, the grains around SW Vir and R Crt had sizes <0.1 mu m, while those around W Hya were larger, with sizes greater than or similar to 0.1 mu m. The asymmetric distribution of dust around R Crt makes the interpretation more uncertain for this star, however. We find that polarised light is produced already from within the visible photosphere of W Hya, which we reproduce using models with an inner dust shell that is optically thick to scattering. We fit radiative transfer models to the radial profile of the polarised light observed around W Hya and find a steep dust density profile, with steepness varying considerably with direction. We find the wind-acceleration region of W Hya to extend to at least similar to 7 R-star. This is in agreement with theoretical predictions of wind acceleration up to similar to 12 R-star, and highlights that ZIMPOL observations probe the crucial region around AGB stars where dust forms and is accelerated.