The Resonant Drag Instability (RDI): Acoustic Modes
  Recently, Squire & Hopkins (2017) showed any coupled dust-gas mixture is
subject to a class of linear 'resonant drag instabilities' (RDI). These can
drive large dust-to-gas ratio fluctuations even at arbitrarily small
dust-to-gas mass ratios. Here, we identify and study both resonant and new
non-resonant instabilities, in the simple case where the gas satisfies neutral
hydrodynamics and supports acoustic waves ($\omega^{2}=c_{s}^{2}\,k^{2}$). The
gas and dust are coupled via an arbitrary drag law and subject to external
accelerations (e.g. gravity, radiation pressure). If there is any dust drift
velocity, the system is unstable. The instabilities exist for {\em all}
dust-to-gas ratios $\mu$ and their growth rates depend only weakly on $\mu$
around resonance, as $\sim\mu^{1/3}$ or $\sim \mu^{1/2}$ (depending on
wavenumber). The behavior changes depending on whether the drift velocity is
larger or smaller than the sound speed $c_{s}$. In the supersonic regime a
'resonant' instability appears with growth rate increasing without limit with
wavenumber, even for vanishingly small $\mu$ and values of the coupling
strength ('stopping time'). In the subsonic regime non-resonant instabilities
always exist, but their growth rates no longer increase indefinitely towards
small wavelengths. The dimensional scalings and qualitative behavior of the
instability do not depend sensitively on the drag law or equation-of-state of
the gas. The instabilities directly drive exponentially growing
dust-to-gas-ratio fluctuations, which can be large even when the modes are
otherwise weak. We discuss physical implications for cool-star winds,
AGN-driven winds and torii, and starburst winds: the instabilities alter the
character of these outflows and could drive clumping and/or turbulence in the
dust and gas.
