On the optical properties of resonant drag instabilities: variability of asymptotic giant branch and R Coronae Borealis stars

In dusty cool-star outflow or ejection events around asymptotic giant branch (AGB) or R Coronae Borealis or RCB-like stars, dust is accelerated by radiation from the star and coupled to the gas via collisional drag forces. It has recently been shown that such dust-gas mixtures are unstable to a super-class of instabilities called the resonant drag instabilities (RDIs), which promote dust clustering. We therefore consider idealized simulations of the RDIs operating on a spectrum of dust grain sizes subject to radiative acceleration (allowing for different grain optical properties), coupled to the gas with a realistic drag law, including or excluding the effects of magnetic fields and charged grains, and calculate for the first time how the RDIs could contribute to observed variability. We show that the RDIs naturally produce significant variations (spatially and temporally) ($\sim 10\!-\!20{{\ \rm per\ cent}}$ 1 σ-level) in the extinction, corresponding to $\sim 0.1\!-\!1\,$mag level in the stellar types above, on time-scales of order months to a year. The fluctuations are surprisingly robust to the assumed size of the source as they are dominated by large-scale modes, which also means their spatial structure could be resolved in some nearby systems. We also quantify how this produces variations in the line-of-sight grain size-distribution. All of these variations are similar to those observed, suggesting that the RDIs may play a key role driving observed spatial and temporal variability in dust extinction within dusty outflow/ejection events around cool stars. We further propose that the measured variations in grain sizes could directly be used to identify the presence of the RDIs in close by systems with observations.