The Acoustic Resonant Drag Instability with a Spectrum of Grain Sizes

Abstract

We study the linear growth and nonlinear saturation of the "acoustic Resonant Drag Instability" (RDI) when the dust grains, which drive the instability, have a wide, continuous spectrum of different sizes. This physics is generally applicable to dusty winds driven by radiation pressure, such as occurs around red-giant stars, star-forming regions, or active galactic nuclei. Depending on the physical size of the grains compared to the wavelength of the radiation field that drives the wind, two qualitatively different regimes emerge. In the case of grains that are larger than the radiation's wavelength -termed the constant-drift regime -the grain's equilibrium drift velocity through the gas is approximately independent of grain size, leading to strong correlations between differently sized grains that persist well into the saturated nonlinear turbulence. For grains that are smaller than the radiation's wavelength -termed the non-constant-drift regime -the linear instability grows more slowly than the single-grainsize RDI and only the larger grains exhibit RDI-like behavior in the saturated state. A detailed study of grain clumping and grain-grain collisions shows that outflows in the constant-drift regime may be effective sites for grain growth through collisions, with large collision rates but low collision velocities.

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

“…We note that the simulations HD-Q and MHD-Q are identical with the simulations discussed in (Squire et al 2021).…”

“…Generally, we find that in the case of a grain size independent acceleration (HD-Q, MHD-Q) the scatter in the instabilities across different sightlines is dominated by the largest grains in the MRN-spectrum. Physically, this arises because the largest grains are drifting the fastest causing a stronger contribution to the RDIs (Squire et al 2021). Vice versa in the cases with a grain size dependent acceleration we find that the scatter in the smallest grains is larger and the instabilities are dominated by the smallest grains in the MRN-spectrum.…”

“…8 is independent of 𝜖 d ) with trans-sonic |w 𝑠 | ∼ 1.5 𝑐 𝑠 , so the initial modes have the same acoustic-RDI resonant angle, which appears strongly at early times as the characteristic angle of the sheets; the non-linear evolution being more trans-sonic produces less coherent filaments with a more "patchy" morphology. Morphology, growth rate and resulting turbulence are discussed in more detail in Squire et al (2021). The MHD and MHD-Q cases are driven by a more complicated mix of modes, since with MHD and charged grains many more RDI families (resonances with gyro motion, Alfvén or slow or fast magnetosonic waves) are available.…”