How to disentangle geometry and mass-loss rate from AGB-star spectral energy distributions -- The case of EP Aqr

High-angular-resolution observations of asymptotic giant branch (AGB) stars often reveal non-spherical morphologies for the gas and dust envelopes. We aim to make a pilot study to quantify the impact of different geometries (spherically symmetric, spiral-shaped, and disc-shaped) of the dust component of AGB envelopes on spectral energy distributions (SEDs), mass estimates, and subsequent mass-loss rate (MLR) estimates. We also estimate the error made on the MLR if the SED is fitted by an inappropriate geometrical model. We use the 3D Monte-Carlo-based radiative-transfer code RADMC-3D to simulate emission from dusty envelopes with different geometries (but fixed spatial extension). We compare these predictions with each other, and with the SED of the AGB star EP Aqr that we use as a benchmark since its envelope is disc-like and known to harbour spiral arms, as seen in CO. The SEDs involving the most massive envelopes are those for which the different geometries have the largest impact, primarily on the silicate features at 10 and 18 um. These different shapes originate from large differences in optical depths. Massive spirals and discs appear akin to black bodies. Optically thick edge-on spirals and discs (with dust masses of 1e-4 and 1e-5 Msun) exhibit black-body SEDs that appear cooler than those from face-on structures and spheres of the same mass, while optically thick face-on distributions appear as warmer emission. We find that our more realistic models, combined spherical and spiral distributions, are 0.1 to 0.5 times less massive than spheres with similar SEDs. More extreme, less realistic scenarios give that spirals and discs are 0.01 to 0.05 times less massive than corresponding spheres. This means that adopting the wrong geometry for an AGB circumstellar envelope may result in a MLR that is incorrect by as much as 1 to 2 orders of magnitude when derived from SED fitting.