An empirical view of the extended atmosphere and inner envelope of the asymptotic giant branch star R Doradus. II. Constraining the dust properties with radiative transfer modelling

Abstract

Mass loss in oxygen-rich asymptotic giant branch (AGB) stars remains poorly understood, as the dust detected around them appears too transparent to drive winds through absorption alone. The current paradigm invokes outflows driven by photon scattering on relatively large grains ($\sim0.3\,μ$m), but whether such grains exist in sufficient quantities remains uncertain. We test whether the dust around the oxygen-rich AGB star R~Doradus can drive its wind by combining polarimetric constraints, elemental abundance limits, and force-balance calculations. We examine Fe-free silicates (MgSiO$_3$), alumina (Al$_2$O$_3$), and Fe-bearing silicates (MgFeSiO$_4$) to evaluate whether any species can produce enough radiative pressure under realistic conditions. Using high-angular-resolution polarimetric observations from SPHERE/ZIMPOL at the VLT, we model the circumstellar dust with RADMC-3D and explore a broad parameter space in grain size, density structure, and wavelength-dependent stellar radius. For models consistent with the observations, we assess wind feasibility using updated gas-density profiles, elemental depletion constraints, and radiation-pressure thresholds. Although several dust configurations reproduce the observed scattering patterns, none generate sufficient radiative force at realistic gas-to-dust ratios, even under maximal elemental depletion. Our results for R~Doradus indicate that photon scattering on dust cannot by itself launch the wind, implying that additional mechanisms must contribute.

Figures (10)

• Figure 1: Polarisation degree maps (top row) and normalised total intensity maps (bottom row) of R Dor observed with VLT/SPHERE-ZIMPOL at three wavelengths: 0.65 $\mu$m (left), 0.75 $\mu$m (middle), and 0.82 $\mu$m (right). The red contours in the bottom right of each panel show the instrument PSF at the 10% and 50% intensity levels (see Appendix \ref{['sec:PSF']} for the complete PSF maps).
• Figure 2: Radial profiles of the polarisation degree (top row) and normalised total intensity (bottom row) for R Dor at three wavelengths: 0.65 µ m (left), 0.75 µ m (middle), and 0.82 µ m (right). The profiles are averaged over 360 degrees. The green curves with error bars represent the observational data. The red curves show one of the acceptable models obtained in Fig. \ref{['fig:chi2min_pyr-mg100_DHS']}, while the blue shading indicates the density of overlapping acceptable models.
• Figure 3: Dust and gas properties around R Dor considering MgSiO$_3$ dust using DHS scattering theory. Left panel: Density profiles showing the gas density (dashed black line with grey uncertainty region) from khouri_empirical_2024 and dust densities for different grain sizes (coloured lines) corresponding to models that fit the observational constraints. The gas density exhibits a transition at $1.6 \times R_{887}$khouri_empirical_2024. Right panel: Gas-to-dust (GTD) ratios derived from the density profiles. The hatched area (GTD $\leq$ 420) represents unrealistic values where more silicon would be locked in dust than expected in the stellar atmosphere. The red horizontal band shows constraints from SiO-depletion measurements van_de_sande_chemical_2018. The background colour gradient indicates the percentage of available silicon locked in dust grains, from 1% (light blue) to 100% (dark blue).
• Figure 4: Radiative-to-gravitational force ratio ($\Gamma$) as a function of radius for MgSiO$_3$ dust grains calculated using DHS scattering theory. Different coloured lines represent dust grain sizes. The green shaded area ($\Gamma > 1$) indicates regions where radiation pressure exceeds gravity. The hatched area ($\Gamma < 1$) represents regions where radiation pressure alone is insufficient to overcome gravity.
• Figure 5: Radiative-to-gravitational force ratio ($\Gamma$) vs gas-to-dust mass ratio for dust models fitting the polarisation observations. Squares and circles denote inner and outer regions ($R \lessgtr 1.6 R_{887}$ from khouri_empirical_2024); colours indicate grain sizes. Five zones are shown, based on physical viability: (A) $\Gamma > 1$ but $>100\%$ elemental depletion is impossible; (B) $\Gamma < 1$ and $>100\%$ and depletion is impossible; (C) $<100\%$ depletion but $\Gamma < 1$, representing insufficient radiation pressure; (D) $\Gamma > 1$ with high but possible depletion inconsistent with observations; and (E) $\Gamma > 1$ with observed depletion levels, the ideal wind-driving zone. The horizontal line marks $\Gamma = 1$.