We use high-angular-resolution images obtained with SPHERE/ZIMPOL to study the photosphere, the warm molecular layer, and the inner wind of the close-by oxygen-rich AGB star R Doradus. We present observations in filters V, cntH$alpha$, and cnt820 and investigate the surface brightness distribution of the star and of the polarised light produced in the inner envelope. Thanks to second-epoch observations in cntH$alpha$, we are able to see variability on the stellar photosphere. We find that in the first epoch the surface brightness of R Dor is asymmetric in V and cntH$alpha$, the filters where molecular opacity is stronger, while in cnt820 the surface brightness is closer to being axisymmetric. The second-epoch observations in cntH$alpha$ show that the morphology of R Dor changes completely in a timespan of 48 days to a more axisymmetric and compact configuration. The polarised intensity is asymmetric in all epochs and varies by between a factor of 2.3 and 3.7 with azimuth for the different images. We fit the radial profile of the polarised intensity using a spherically symmetric model and a parametric description of the dust density profile, $rho(r)=rho_circ r^{-n}$. On average, we find exponents of $- 4.5 pm 0.5$ that correspond to a much steeper density profile than that of a wind expanding at constant velocity. The dust densities we derive imply an upper limit for the dust-to-gas ratio of $sim 2times10^{-4}$ at 5.0 $R_star$. Given the uncertainties in observations and models, this value is consistent with the minimum values required by wind-driving models for the onset of a wind, of $sim 3.3times10^{-4}$. However, if the steep density profile we find extends to larger distances from the star, the dust-to-gas ratio will quickly become too small for the wind of R Dor to be driven by the grains that produce the scattered light.
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