radiative rayleigh-taylor instabilities
DESCRIPTION
Radiative Rayleigh-Taylor instabilities. Emmanuel Jacquet (ISIMA 2010) Mentor: Mark Krumholz (UCSC). Outline. Introduction and motivation Fundamentals and generalities The (very) optically thin limit The (very) optically thick limit Conclusion. I. Introduction and motivation. - PowerPoint PPT PresentationTRANSCRIPT
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Radiative Rayleigh-Taylor instabilities
Emmanuel Jacquet (ISIMA 2010)
Mentor: Mark Krumholz (UCSC)
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Outline
I. Introduction and motivation
II. Fundamentals and generalities
III. The (very) optically thin limit
IV. The (very) optically thick limit
V. Conclusion
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I. Introduction and motivation
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Classical Rayleigh-Taylor instability
• Two immiscible liquids in a gravity field
• If denser fluid above unstable (fingers).
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Motivation 1: massive star formation
• Radiation force/gravity ~ Luminosity/Mass of star.
• >1 for M>~20-30 solar masses.
• But accretion goes on… (Krumholz et al. 2009) : radiation flows around dense fingers.
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Motivation 2: HII regions
• Neutral H swept by ionized H
• Radiative flux in the ionized region RT instabilities?
And more!
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II. Fundamentals and generalities
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The general setting
Width Δz of interfaceignored.
z=0+- - - -z=0-
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Equations of non-relativistic RHD
gas
Radiation
Rate of 4-momentum transfer from radiation to matter
Energy
Momentum
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Linear analysis: the program (1/2)• Dynamical equations:
• Perturbation:
• Search for eigenmodes:
• Eulerian perturbation of a quantity Q:
• If Im(ω) > 0: instability!
• Lagrangian perturbation:
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Linear analysis: the program (2/2)
• Perturbation equations still contain z derivatives:
• Everything determined at z=0 so should dispersion relation.
• Importance of boundary conditions.
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Boundary conditions
• Normal flux continuity at interface in its rest frame:
• From momentum flux continuity:
• Perturbations vanish at infinity.
z>0
z<0
≈ 0
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III. The (very) optically thin limit
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Absorption and reradiation in an optically thin medium
• Higher opacity for UV photons dominate force
Radiative equilibrium
Hard photon attenuation
visible near infrared
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So we should solve:
Let us simplify…
with:
?
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Isothermal media with a chemical discontinuity
• Discontinuity in sound speed.• Assume ρ-independent opacity and constant
F in each region
constant T and effective gravity field:
• Constant 2x2 matrix A:
eff
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Instability criterion
• (Pure) instability condition:
• Dispersion relation:
• Growth rates:
Ex. ofunstableconfiguration
with:
1
2
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IV. The (very) optically thick limit
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Optically thick limit
• Radiation Planckian at gas T (LTE)
• Radiation conduction approximation.
• Total (non-mechanical) energy equation:
• Conditions:
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Meet A again:
with:
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Adiabatic approximation
• Rewrite energy equation as:
• If we neglect Δs=0.
• …under some condition:
with
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« Reduced » set of equations
with:
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Perturbations evanescent on a scale height
• A traceless must be eigenmode of A:
• Pressure continuity:
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Rarefied lower medium
• Dispersion relation: in full:
• In essence:
• Really a bona fide Rayleigh-Taylor instability!
Unstable if g>0
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Domain of validity
Not local
Not adiabatic
No temperature locking
Not optically
thick
E=x=1
Window if:
Convective instability?
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So what about massive star formation?• Flux may be too high for
« adiabatic RTI »
• But if acoustic waves unstable : « (RHD) photon bubbles » (Blaes & Socrates 2003)
• In dense flux-poor regions, « adiabatic RTI » takes over.
growth time a/g (i.e. 1-10 ka).
• Tentative only…
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Summary: role of radiation in Rayleigh-Taylor instabilities & Co.
Characteristic length/photon mean free path
1
OPTICALLY THICKOPTICALLY THIN adiabaticisothermal
<< 1 >> 1
Radiation modifies EOS, with radiation force lumped in pressure gradient
Radiation as effective gravity(« equivalence principle violating »)
Flux sips in rarefied regions: buoyant photon bubbles (e.g. Blaes & Socrates 2003)