511 th WE-Heraeus-Seminar From the Heliosphere into the Sun SailingagainsttheWind Collection of presentations Edited by Hardi Peter (peter@mps.mpg.de) Physikzentrum Bad Honnef, Germany January 31 February 3, 2012 http://www.mps.mpg.de/meetings/heliocorona/
On the Origin of the 1/f Spectrum in the Heliosphere A. Verdini 1 R. Grappin 2,3 M. Velli 4,5 1. Royal Observatory of Belgium 2. LUTH, Meudon 3. LPP, Polytechnique 4. Università di Firenze 5. Jet Propulsion Laboratory
Helios [Bruno & Carbone 2005] Nature of the 1/f part: WKB evolution, freezed spectrum [Bavassano et al. 1982, Marsch & Tu 1990] Evolution with distance: turbulence vs expansion [Tu et al. 1984, Tu 1988, Tu & Marsch 1995] ORIGIN? From phot. or corona B [Matthaeus & Goldstein 1986, Close et al. 2004 Matthaeus et al. 2007] From MHD turbulence [Dmitruk et al. 2007, 2011] From SW Turbulence + expansion [Velli et al 1993] Corona ringing in Sub-Alfvénic SW [Hollweg & Isenberg 2007]
RMHD model for AW RMHD: NL only among k to B 0 2D shell model for perp NL (Re~10 5 ) Propagation in fixed U(r),V a (r),a(r) (not self consistent, but it is a SW model) k 1/A 1/2 : follows flux tube expansion Open boundaries (Input z 0 + at the phot.) Free parameters: z 0+, k 0, T f (t NL0 =1/ k 0 z 0+ ) z + =u-b/ρ 1/2 (outward) z - =u+b/ρ 1/2 (inward) z 0+ =10 km/s k 0 = 2π/16Mm, T f =600 s => T f /t NL0 2
Snapshot of z +,z - (run A) INPUT [Grappin SW model] km/s V a U X A n (10 8 cm -3 ) R/R -1 R/R -1 A X A A(r) OUTPUT km/s z + z + z - z - X A X A R/R -1 R/R
Perp. and Parallel spectra R>X A E b, E u Perp E u,parallel E b, Parallel k -5/3 1/f 1/f forcing k increases k increases t NL (k )=1/k u k RMHD parallel spectra <=> freq.spectra (k )=1/ ν=1/k V A Better use z ± to compute t NL Test the Critical Balance condition (k )? = t NL (k )
STRONG or WEAK cascade? [Verdini & Grappin submitted] A) Homogeneous RMHD forced in the weak regime =T f => becomes Strong t NL time WEAK <t NL STRONG t NL t NL critical balance Plenty of energy beyond CB limit
STRONG or WEAK cascade? [Verdini & Grappin submitted] A) Homogeneous RMHD forced in the weak regime =T f => becomes Strong t NL time WEAK <t NL STRONG t NL t NL B) In the solar wind t NL± (r) A 1/2 /z t NL+ > t - NL k 0 =1/T f V A (the forcing) +
t NL (r) vs (r) for z + & z - + ~ CONST => Same as forcing - t NL - => critical balance T f STRONG t NL < z - z + critical balance 2k 0 16k 0 64k 0 z + => WEAK z - => STRONG r increases 1R =>19R WEAK t NL > t NL
1/f generation REFLECTION T.R. LOW CORONA V A >>U HIGH CORONA U V A V + ~V - V + >>V - ~0 X A SOLAR WIND WEAK z + WEAK z+ WEAK z - STRONG z - z + z - z +
The resulting 1/f spectrum E b f -1 1/f =>Large-scale eddies E u z + WEAK cascade z - STRONG cascade f -2 Recycling=> in E b @TR z + -z - => z - goes in b E + input HOW MUCH SOLID?
Increasing Turb. Strength Increasing T f /t NL0, f -1 is partially or totally lost E + spectrum changes in its way out (z + strong cascade) 2 x z 0 + 10 x T f E b ~OK E b ~OK? E u E u f -1 f -1 E + input E + input
Conclusion The 1/f spectrum can be generated by turbulence in the sub-alfvénic solar wind if turbulence is weak enough Weak means T f /t NL0 1 (small wave amplitude and wide frequency spectra at the photosphere): not far from the expected conditions at the surface Reflection at the photosphere may change the spectrum entering the corona (the effective T f ) Considering self consistent model may change 1/f In the heliosphere: the E ± spectra evolve self-similarly because of expansion B 0 turns, a geometric model can explain the observed break as a superposition of parallel and perpendicular spectra (work in progress)
STRONG or WEAK cascade? A) Homogeneous RMHD 3 timescales =1/k V A, t NL, t cor 0 =T f forced in the weak regime => becomes Strong (k) t NL (k) t cor everywhere time WEAK <t NL STRONG t NL t NL B) In the solar wind t NL± (r) A 1/2 /z t NL+ > t - NL k 0 =1/T f V A (the forcing) + We start with 0 /t NL0 >1