Scale-dependence of magnetic helicity in the solar wind

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Scale-dependence of magnetic Scale-dependence of magnetic helicity in the solar wind helicity in the solar wind Axel Brandenburg (Nordita/Stockholm) Kandaswamy Subramanian (IUCAA, Pune) Andre Balogh (ISSI and Imperial) Melvyn Goldstein (NASA Goddard, Greenbelt) Kemel+12 Kemel+12 Brandenburg+1 Brandenburg+1 3 Warnecke+11 Warnecke+11 K äpylä äpylä +12 +12 assume isotropy to get helicity spectrum

description

Scale-dependence of magnetic helicity in the solar wind.  a ssume isotropy to get helicity spectrum. Axel Brandenburg (Nordita/Stockholm) Kandaswamy Subramanian (IUCAA, Pune) Andre Balogh (ISSI and Imperial) Melvyn Goldstein (NASA Goddard, Greenbelt). Kemel+12. K äpylä +12. Warnecke+11. - PowerPoint PPT Presentation

Transcript of Scale-dependence of magnetic helicity in the solar wind

Page 1: Scale-dependence of magnetic  helicity  in the solar wind

Scale-dependence of magnetic Scale-dependence of magnetic helicity in the solar windhelicity in the solar wind

Axel Brandenburg (Nordita/Stockholm)Kandaswamy Subramanian (IUCAA, Pune)Andre Balogh (ISSI and Imperial)Melvyn Goldstein (NASA Goddard, Greenbelt)

Kemel+12Kemel+12

Brandenburg+13Brandenburg+13Warnecke+11Warnecke+11KKäpylääpylä+12+12

assume isotropy to get helicity spectrum

Page 2: Scale-dependence of magnetic  helicity  in the solar wind

Dynamo produces bi-helical fieldDynamo produces bi-helical field

BAdkkH )(

Magnetic helicity spectrum

031 / bjuω

Pouquet, Frisch, & Leorat (1976)

Southernhemisphere

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Helicity fluxes to alleviate Helicity fluxes to alleviate catastrophic quenchingcatastrophic quenching

Bra

nden

burg

(20

05, A

pJ)

1046 Mx2/cycle

FBJBA 2d

d

t

AB BJ

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Magnetic helicity fluxMagnetic helicity flux

• EMF and resistive terms still dominant

• Fluxes import at large Rm ~ 1000

• Rm based on kf

• Smaller by 2

4

m22d

dF BJBBA ε

t

f22d

dF bjBba ε

t

Page 5: Scale-dependence of magnetic  helicity  in the solar wind

Magnetic helicity fluxMagnetic helicity flux

• EMF and resistive terms still dominant

• Fluxes import at large Rm ~ 1000

• Rm based on kf

• Smaller by 2

5

m22d

dF BJBBA ε

t

f22d

dF bjBba ε

t

Gauge-invariant in steady state!

Del Sordo, Guerrero, Brandenburg (2013, MNRAS 429, 1686)

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This is how it looks like…This is how it looks like…Coronal mass ejections from helical structuresCoronal mass ejections from helical structures

Gibson et al. (2002)

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Helicity from solar windHelicity from solar wind

)()( xBxBM jiij

)(

)(ˆˆ)(

kHki

kEkkkM

kijk

jiijij

)()( xBxBM jiij

)()()( rxxr jiij BBM

Matthaeus et al. (1982) Measure correlation function

In Fourier space, calculatemagnetic energy and helicity spectra

Should be done with Ulysses data away from equatorial plane

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Measure 2-point correlation tensorMeasure 2-point correlation tensor

tuRR R 0Taylor hypothesis:

RRNRTR kkBkBkH /)(~

)(~

Im4)( *

u1 u2

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Ulysses: scaling with distanceUlysses: scaling with distance

022 2/4 BuRL RM

* Fairly isotropic* Falls off faster than R-2

* Need to compensate before R averaging

Power similar to US consumptionEnergy density similar to ISM

Vector helium magnetometer2 sec resolution10 pT sensitivity (0.1 G)

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Noisy helicity Noisy helicity from Ulyssesfrom Ulysses

• Taylor hypothesis

• Roundish spectra

• Southern latitude with opposite sign

• Positive H at large k

Brandenburg, Subramanian, Balogh,Goldstein (2011, ApJ 734, 9)

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Bi-helical fields from UlyssesBi-helical fields from Ulysses

• Taylor hypothesis• Broad k bins• Southern latitude

with opposite sign• Small/large distances• Positive H at large k• Break point with

distance to larger k

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Latitudinal scaling and trendLatitudinal scaling and trend

1. Antisymmetric about equator

2. Decline toward minum

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ComparisonComparison

• Field in solar wind is clearly bi-helical

• ...but not as naively expected

• Need to compare with direct and mean-field simulations

• Recap of dynamo bi-helical fields

Helicity LS SS

Dynamo + -

Solar wind - +

Southernhemisphere

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14Strong fluctuations, but positive in north

War

nec

ke, B

rand

enbu

rg, M

itra

(20

11, A

&A

, 534

, A11

)Shell dynamos with ~CMEsShell dynamos with ~CMEs

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Dynamos with exterior Dynamos with exterior CMEs? CMEs?W

arnecke, B

randen

burg, Mitra (2011, A

&A

, 534, A11)

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To carry negative flux: need positive gradientTo carry negative flux: need positive gradient

f2f

m2m

22d

d

22d

d

FBJB

FBJB

t

t

t

h

t

h

Brandenburg, Candelaresi, Chatterjee(2009, MNRAS 398, 1414)

Sign reversal makes sense!

ff hh F

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ConclusionsConclusions

• Magnetic helicity measurable

• High latitudes ( Ulysses)

• Expect bi-helical

• Bi-helical fields in dynamo & solar wind• + sign in wind by turbulent diffusion

• also found in CME-like simulations