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Radiative Rayleigh-Taylor instabilities

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.

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Radiative Rayleigh-Taylor instabilities

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  1. Radiative Rayleigh-Taylor instabilities Emmanuel Jacquet (ISIMA 2010) Mentor: Mark Krumholz (UCSC)

  2. Outline • Introduction and motivation • Fundamentals and generalities • The (very) optically thin limit • The (very) optically thick limit • Conclusion

  3. I. Introduction and motivation

  4. Classical Rayleigh-Taylor instability • Two immiscible liquids in a gravity field • If denser fluid above  unstable (fingers).

  5. 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.

  6. Motivation 2: HII regions • Neutral H swept by ionized H • Radiative flux in the ionized region  RT instabilities? And more!

  7. II. Fundamentals and generalities

  8. The general setting Width Δz of interface ignored. z=0+ - - - - z=0-

  9. Equations of non-relativistic RHD gas Radiation Energy Rate of 4-momentum transfer from radiation to matter Momentum

  10. 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:

  11. 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.

  12. Boundary conditions z>0 • Normal flux continuity at interface in its rest frame: • From momentum flux continuity: • Perturbations vanish at infinity. z<0 ≈ 0

  13. III. The (very) optically thin limit

  14. Absorption and reradiation in an optically thin medium • Higher opacity for UV photons  dominate force Hard photon attenuation Radiative equilibrium visible near infrared

  15. So we should solve: Let us simplify… with: ?

  16. Discontinuity in sound speed. Assume ρ-independent opacity and constant F in each region  constant T and effective gravity field: Constant 2x2 matrix A: Isothermal media with a chemical discontinuity eff

  17. Instability criterion 1 • (Pure) instability condition: • Dispersion relation: • Growth rates: 2 Ex. of unstable configuration with:

  18. IV. The (very) optically thick limit

  19. Optically thick limit • Radiation Planckian at gas T (LTE) • Radiation conduction approximation. • Total (non-mechanical) energy equation: • Conditions:

  20. Meet A again: with:

  21. Adiabatic approximation • Rewrite energy equation as: • If we neglect Δs=0. • …under some condition: with

  22. « Reduced » set of equations with:

  23. Perturbations evanescent on a scale height • A traceless  must be eigenmode of A: • Pressure continuity:

  24. Rarefied lower medium • Dispersion relation: in full: • In essence: • Really a bona fide Rayleigh-Taylor instability! Unstable if g>0

  25. Domain of validity No temperature locking Convective instability? Not local Not optically thick Window if: Not adiabatic E=x=1

  26. 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…

  27. Summary: role of radiation in Rayleigh-Taylor instabilities & Co. Characteristic length/photon mean free path >> 1 << 1 1 OPTICALLY THIN adiabatic isothermal OPTICALLY THICK Flux sips in rarefied regions: buoyant photon bubbles (e.g. Blaes & Socrates 2003) Radiation as effective gravity (« equivalence principle violating ») Radiation modifies EOS, with radiation force lumped in pressure gradient

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