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The Resonant Drag Instability (RDI): Acoustic Modes

Hopkins, Philip F. and Squire, Jonathan (2018) The Resonant Drag Instability (RDI): Acoustic Modes. Monthly Notices of the Royal Astronomical Society, 480 (2). pp. 2813-2838. ISSN 0035-8711. doi:10.1093/mnras/sty1982.

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Recently, Squire & Hopkins 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 μ. 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 (ω^2=c^2_sk^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 all dust-to-gas ratios μ and their growth rates depend only weakly on μ around resonance, as ∼μ^(1/3) or ∼μ^(1/2) (depending on wavenumber). The behaviour changes depending on whether the drift velocity is larger or smaller than the sound speed cs. In the supersonic regime, a ‘resonant’ instability appears with growth rate increasing without limit with wavenumber, even for vanishingly small μ 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 behaviour 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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Hopkins, Philip F.0000-0003-3729-1684
Squire, Jonathan0000-0001-8479-962X
Additional Information:© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2018 July 18. Received 2018 July 13; in original form 2017 July 7. Published: 25 July 2018. We would like to thank our referee, Andrew Youdin, as well as E. S. Phinney and E. Quataert for helpful discussions. Support for PFH and JS was provided by an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G, and NSF Collaborative Research Grant #1411920 and CAREER grant #1455342. JS was funded in part by the Gordon and Betty Moore Foundation through Grant GBMF5076 to Lars Bildsten, Eliot Quataert, and E. Sterl Phinney.
Group:TAPIR, Astronomy Department
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Gordon and Betty Moore FoundationGBMF5076
Subject Keywords:instabilities – turbulence – planets and satellites: formation – ISM: kinematics and dynamics – galaxies: formation
Issue or Number:2
Record Number:CaltechAUTHORS:20170713-154123249
Persistent URL:
Official Citation:Philip F Hopkins, Jonathan Squire; The resonant drag instability (RDI): acoustic modes, Monthly Notices of the Royal Astronomical Society, Volume 480, Issue 2, 21 October 2018, Pages 2813–2838,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79098
Deposited By: Joy Painter
Deposited On:14 Jul 2017 14:44
Last Modified:15 Nov 2021 17:45

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