scale-dependence of magnetic helicity in the solar wind
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 PresentationTRANSCRIPT
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
Dynamo produces bi-helical fieldDynamo produces bi-helical field
BAdkkH )(
Magnetic helicity spectrum
031 / bjuω
Pouquet, Frisch, & Leorat (1976)
Southernhemisphere
3
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
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
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)
6
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)
7
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
8
Measure 2-point correlation tensorMeasure 2-point correlation tensor
tuRR R 0Taylor hypothesis:
RRNRTR kkBkBkH /)(~
)(~
Im4)( *
u1 u2
9
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)
10
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)
11
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
12
Latitudinal scaling and trendLatitudinal scaling and trend
1. Antisymmetric about equator
2. Decline toward minum
13
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
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
15
Dynamos with exterior Dynamos with exterior CMEs? CMEs?W
arnecke, B
randen
burg, Mitra (2011, A
&A
, 534, A11)
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
17
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