Dusty winds and the Resonant Drag Instability Jono Squire — GalFresca With Phil Hopkins Squire+Hopkins arXiv:1706.05020 + Stefania Moroianu (Cambridge) Eric Moseley (Caltech) Hopkins+Squire arXiv:1707.02997
RDI Basics GAS
RDI Basics GAS DUST
RDI Basics GAS DUST speed w drift
RDI Basics GAS DUST speed w drift Gas drag on dust F dust
RDI Basics GAS DUST speed w drift Gas drag on dust F dust Dust backreaction on gas F gas
RDI Basics Wave in the gas
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed?
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance Instability
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance Instability i 1 / 2 ± iµ 1 / 2 h ρ d ) ( k T D − 1 ( ξ L F T (1) drag C v ξ R F ) γ =
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance Instability i 1 / 2 ± iµ 1 / 2 h ρ d ) ( k T D − 1 ( ξ L F T (1) drag C v ξ R F ) γ = Dust to gas mass ratio
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance Instability i 1 / 2 ± iµ 1 / 2 h ρ d ) ( k T D − 1 ( ξ L F T (1) drag C v ξ R F ) γ = Fluid modes Dust to gas mass ratio
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance Instability Coupling of dust to gas i 1 / 2 ± iµ 1 / 2 h ρ d ) ( k T D − 1 ( ξ L F T (1) drag C v ξ R F ) γ = Fluid modes Dust to gas mass ratio
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance Instability Drag on the dust Coupling of dust to gas i 1 / 2 ± iµ 1 / 2 h ρ d ) ( k T D − 1 ( ξ L F T (1) drag C v ξ R F ) γ = Fluid modes Dust to gas mass ratio
RDI Basics Wave in the gas w drift = v dust − u gas = wave speed? Wave is stationary in the dust frame — resonance Instability Drag on the dust Coupling of gas to dust Coupling of dust to gas i 1 / 2 ± iµ 1 / 2 h ρ d ) ( k T D − 1 ( ξ L F T (1) drag C v ξ R F ) γ = Fluid modes Dust to gas mass ratio
RDI Basics Gas wave can be: w drift > c s Squire+Hopkins arXiv:1706.05020
RDI Basics Gas wave can be: • Sound wave — RDI if w drift > c s Squire+Hopkins arXiv:1706.05020
RDI Basics Gas wave can be: • Sound wave — RDI if w drift > c s • MHD waves (slow/fast waves) Squire+Hopkins arXiv:1706.05020
RDI Basics Gas wave can be: • Sound wave — RDI if w drift > c s • MHD waves (slow/fast waves) • Buoyancy oscillations Squire+Hopkins arXiv:1706.05020
RDI Basics Gas wave can be: • Sound wave — RDI if w drift > c s • MHD waves (slow/fast waves) • Buoyancy oscillations • Epicyclic oscillations Squire+Hopkins arXiv:1706.05020
RDI Basics Gas wave can be: • Sound wave — RDI if w drift > c s • MHD waves (slow/fast waves) • Buoyancy oscillations • Epicyclic oscillations • ……. Squire+Hopkins arXiv:1706.05020
RDI Basics Gas wave can be: This talk • Sound wave — RDI if w drift > c s • MHD waves (slow/fast waves) • Buoyancy oscillations • Epicyclic oscillations • ……. Squire+Hopkins arXiv:1706.05020
Source of w drift Radiation pressure on dust drives winds:
Source of w drift Radiation pressure on dust drives winds: AGN w drift ∼ 100 c s
Source of w drift Radiation pressure on dust drives winds: AGN Starbursts/GMCs/star forming disks w drift ∼ 100 c s w drift ∼ 10 c s
Source of w drift Radiation pressure on dust drives winds: Cool star winds w drift ∼ c s
Source of w drift Radiation pressure on dust drives winds: Cool star winds Supernovae ejecta w drift ∼ c s w drift ∼ c s
Source of w drift Pressure support of gas drives w dridt in Protoplanetary disks w drift ⌧ c s
Source of w drift Pressure support of gas drives w dridt in Protoplanetary disks But lots of other waves… w drift ⌧ c s Epicycles (streaming instability), Brunt-Vaisala, MHD, Hall MHD… Youdin & Goodman (2005)
Acoustic RDI (sound waves) from radiation pressure d v dt = − v − u gas Dust equation + a rad t s Hopkins+Squire arXiv:1707.02997
Acoustic RDI (sound waves) from radiation pressure d v dt = − v − u gas Dust equation + a rad t s Radiative acceleration Hopkins+Squire arXiv:1707.02997
Acoustic RDI (sound waves) from radiation pressure Dust drag d v dt = − v − u gas Dust equation + a rad t s Radiative acceleration Hopkins+Squire arXiv:1707.02997
Acoustic RDI (sound waves) from radiation pressure Dust drag d v dt = − v − u gas Dust equation + a rad t s Radiative acceleration t s determined by grain size, gas density (Epstein drag) big grains free stream small grains stop quickly a rad determined by F λ , λ / R d , m d Hopkins+Squire arXiv:1707.02997
d u gas u gas � v = � ρ d Dust drags gas � r p dt t s ρ gas w drift ∼ a rad t s
d u gas u gas � v = � ρ d Dust drags gas � r p dt t s ρ gas w drift ∼ a rad t s 3.5 3.0 w drift 2.5 v 2.0 t s 1.5 u gas 1.0 0.5 1 2 3 4 5 6 7 Equilibrium with constant acceleration
RDI condition — dust streaming matches wave w drift cos( θ ) = c s
RDI condition — dust streaming matches wave w drift cos( θ ) = c s E.g., w drift = 2 c s w drift Dust streaming θ = 60 � θ c s Sound wave Dust “sees” a stationary wave
RDI condition — dust streaming matches wave s Growth rate keeps � � ω ⇡ kc s + µ 1 / 2 1 + i c s η k 1 / 2 � � � 1 � increasing with k � � h t s i 1 + ζ 2 �
Instability is fastest growing at resonant angle 10 (maximum over all k) 1 0.1 0.01 0.001 (no resonance) but still exists for subsonic w s
see Hopkins+Squire arXiv:1707.02997 Acoustic RDI is robust: • Arbitrary drag law (Epstein, Coulomb etc.,) and dust size • Any streaming velocity • Arbitrary gas equation of state • Any dust-to-gas mass ratio • Gas pressure support • Spectrum of grain sizes s � � ω ⇡ kc s + µ 1 / 2 1 + i c s η k 1 / 2 � � � 1 � � � h t s i 1 + ζ 2 �
Nonlinear evolution — what happens? with GIZMO periodic with 128 3 gas/dust Stefania Moroianu (Cambridge) Eric Moseley (Caltech)
Resonant mode matters ρ d = 0 . 01 even in nonlinear turbulence ρ g w drift ≈ 3 c s Time y z drift c s drift cos θ = x x w drift
Resonant mode matters ρ d = 0 . 01 even in nonlinear turbulence ρ g w drift ≈ 3 c s Time y z drift c s drift cos θ = x x w drift
ρ d = 0 . 01 w drift ≈ 10 c s Dust can decouple completely! ρ g y z drift drift c s cos θ = x x w drift
ρ d = 0 . 01 w drift ≈ 10 c s Dust can decouple completely! ρ g y z drift drift c s cos θ = x x w drift
Range of grain sizes
Range of grain sizes • Does the instability exist? (Yes!)
Range of grain sizes • Does the instability exist? (Yes!) dM • E ff ect of dust size spectrum, e.g., ∼ R 0 . 5 d d ln R d
Range of grain sizes • Does the instability exist? (Yes!) dM • E ff ect of dust size spectrum, e.g., ∼ R 0 . 5 d d ln R d • Acceleration
Range of grain sizes • Does the instability exist? (Yes!) dM • E ff ect of dust size spectrum, e.g., ∼ R 0 . 5 d d ln R d • Acceleration a rad ∼ const. λ > R d w drift ∼ R 1 / 2 d
Range of grain sizes • Does the instability exist? (Yes!) dM • E ff ect of dust size spectrum, e.g., ∼ R 0 . 5 d d ln R d • Acceleration a rad ∼ const. λ > R d w drift ∼ R 1 / 2 d a rad ∼ 1 /R d λ < R d w drift ∼ const.
ρ d = 0 . 1 ρ g Big grains Medium z drift GAS DUST Small x w drift ≈ 1 . 5 c s y drift GAS DUST x
ρ d = 0 . 1 ρ g Big grains Medium z drift GAS DUST Small x w drift ≈ 1 . 5 c s y drift GAS DUST x
Conclusions • Dust-driven winds/outflows are likely unstable to RDI • Can grow very fast (formally 𝛿→ ∞ as k → ∞ ) • Drives large dust-to-gas fluctuations and turbulence • Important for AGN, star-forming regions, cool stars, SNe ejecta? • Implications for grain collisions/growth?
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