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

Outline I.Introduction and motivation II.Fundamentals and generalities III.The (very) optically thin limit IV.The (very) optically thick limit V.Conclusion

I. Introduction and motivation

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

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.

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

II. Fundamentals and generalities

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

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

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:

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.

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

III. The (very) optically thin limit

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

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

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

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

IV. The (very) optically thick limit

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

Meet A again: with:

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

« Reduced » set of equations with:

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

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

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

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 ka). Tentative only…

Summary: role of radiation in Rayleigh- Taylor instabilities & Co. Characteristic length/photon mean free path 1 OPTICALLY THICK OPTICALLY THINadiabatic isothermal << 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)