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The Connection between Alfvénic Turbulence and the FIP Effect

Martin Laming, Naval Research Laboratory, Washington DC 20375

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Abstract

The ``FIP Effect'' is the elemental abundance anomaly observed in the solar corona and slow speed solar wind, whereby elements with First Ionization Potential (FIP) less than about 10 eV (e.g. Mg, Si, Fe) are enhanced in abundance by a factor of about 3. Elements with FIP higher than 10 eV (e.g. C, N, O) are essentially unchanged. This fractionation is assumed to occur in the solar chromosphere, since the low FIP elements are predominantly ionized here, while the high FIP elements are neutral. The abundance enhancement is currently explained by the upward action of the ponderomotive force on chromospheric ions, but not neutrals, as Alfvén waves generated in the corona reflect from the steep chromospheric density gradients at each footpoint. The fractionation so produced is almost independent of ion mass as observed, and is stronger for closed coronal loops than for open field lines, also as observed.I will describe some recent results from models of the FIP effect, including the role of slow mode waves generated by the ponderomotive force of coherent Alfvén waves in saturating the abundance enhancement. Work supported by NASA Contract NNGH05HL39I, and by basic research funds of the Office of Naval Research.

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Correlation with First Ionization Potential(Coronal abundance enhancement of elements with FIP < ~10 eV,

from von Steiger et al. 2000)

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Summary of Model

• FIP Effect due to action of ponderomotive force in chromosphere acting on ions, not neutrals.

• (J + J) x (B + B) J x B + J x B +J x B + J x B gives origin of ponderomotive force

• Ponderomotive acceleration; a = (qi

2/4mi2i

2) x d(E┴2)/dz,

is independent of ion mass m in magnetic plasma and independent of charge, but only acts on charged particles.

• Fractionation is approximately mass independent, occurs at top of chromosphere, but is sensitive to turbulence level.

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FIP Effect Model

• Coronal loop acts as resonant cavity for Alfvén waves (Hollweg 1984).

• Alfvén waves can have either chromospheric or coronal origin.

• Use non-WKB analysis to evaluate ponderomotive force in different B-field geometries.

Waves resonant with loop positive FIP effect Waves off resonance (i.e. reflected back into chromosphere) Inverse FIP effect

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Simulations

• Vernazza, Avrett & Loeser (1982 VALC), Avrett & Loeser (2008) model chromospheres.

• Fully mixed chromosphere in absence of FIP effect, with upward flow 100-1000 cm/s.

• Compute photoionization-recombination equilibrium for various elements with incident (absorbed) coronal spectrum.

• Solve momentum equations for ions and neutrals with ponderomotive acceleration to derive fractionation (following Schwadron, Fisk & Zurbuchen 1999).

• Need to be careful with ion-neutral collision cross sections for scattering and charge exchange.

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Fractionation = exp aeff /i /vs2 dz

• aeff /i =(ion fraction) x (accel.) x (collision freqs)• vs

2=kT/mi + vturb2 + vSM

2 = (thermal speed)2 + (microturbulence)2 + (slow modes assoc. with Alfvén waves)2

• Laming (2004) vSM = 0; Laming (2009) vSM = vAlf (i.e. isotropic turbulence). Real answer lies between these two limits

• To all orders, cubic equation in vSM gives vSM~vAlf2 in linear

regime, vSM~vAlf, vSM~vAlf2/3, vSM~const. at higher amplitudes

• Will check and investigate further with numerical simulations (Dahlburg & Laming 20??), but for the time being proceed with semi-analytic means; solve quartic equation at each step for equipartition between Alfvén and slow mode waves .

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Results for 100,000 km loop, with 3 Alfven waves incident from chromosphere on right hand side, B=7.1G.

I. Middle loop section.

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Results for 100,000 km loop, with 3 Alfven waves incident from chromosphere on right hand side, B=7.1G.

II. Left hand side chromosphere, with FIP fractionation.

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Results for 100,000 km loop, with 3 Alfven waves incident from chromosphere on right hand side, B=7.1G.

III. Right hand side chromosphere, smaller fractionation.

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FIP Effect in Slow Wind (taken from von Steiger with new model points rel. to O added)

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Coronal Hole to 500,000 km altitude, B-field from Banaskiewicz et al. 1998, A&A, 337, 940; waves from Cranmer & van Ballegooijen

(2005), Verdini et al. (2009), Chandran & Hollweg (2009)

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Coronal Hole chromosphere … minimal FIP fractionation as observed in fast solar wind

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Conclusions

• Coronal origin for Alfvén waves preferred? Need resonance with loop geometry.

• Fractionations shown above correspond to coronal non thermal mass motions of order 30-100 kms-1. Possibly indicative of heating by Alfvén resonance? Or nanoflares? Needs horizontally structured magnetic loop.

• If observed slow mode waves are generated by ponderomotive force need coherent Alfvén waves Alfvén resonance?

• No significant fractionation in open field. Fractionated slow solar wind must have originated in closed magnetic loop, which subsequently opened up.

• Future work: Include wave damping/growth in non-WKB analysis, estimate Reynolds number, etc.

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References

• Avrett, E. H., & Loeser, R. 2008, ApJS, 175, 229• Chandran, B. D. G. & Hollweg, J. V. 2009, arXiv:0911.1068• Cranmer, S. R., & van Ballegooijen, A. A. 2005, ApJS, 156, 265• Hollweg, J. V. 1984, ApJ, 277, 392• Laming, J. M. 2004, ApJ, 614, 1063• Laming, J. M. 2009, ApJ, 695, 954• Schwadron, N. A., et al. 1999, ApJ, 521, 859• Verdini, A. et al. 2009, arXiv:0911.5221• Vernazza, J., Avrett, E. H., & Loeser, R. 1981, ApJS, 45, 635• von Steiger, R., et al. 2000, JGR, 105, 27217

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Slow Mode Amplitudeproportional to Alfvén wave amplitude squared, as expected