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Intermittency beyond the ecliptic plane
Anna Wawrzaszek , Marius Echim , Wiesław M. Macek , Roberto Bruno
Mamaia, 6-13 September 2015
(1) Space Research Centre PAS, Warsaw, Poland
(2) The Belgian Institute for Space Aeronomy, Brussels, Belgium(3) Institute for Space Astrophysics and Planetology, Roma, Italy
1 2 3
http://storm-fp7.eu/
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2
• Introduction • Ulysses Data • Multifractal analysis• Results - Radial dependence of multifractality - Latitudinal dependence of multifractality• Conclusions
Outline
Authors Data Methods Results
Marsch and Liu [1993]
wind speed magnetic field componentsHelios
Structure function scaling
fast solar wind is less intermittent than slow wind
Bruno et al. [2003]
magnetic field componentsHelios
Flatness Factor the intermittency of the fast wind increases with the increase of the distance (0.3-0.9 AU) from the Sun
Intermittency in the ecliptic plane
Authors Data Method Conclusions
Ruzmaikin et al. [JGR, 1995]
10 second averages of MF (Br, Bt, Bn) Min (1993 -1994)at 3.9 AU, 46ᵒ
Fast solar wind
Structure function scalingTime scales: 60s-3600sBi – fractal model
High level of intermittency in the MF fluctuations
Three intervals Horbury et al. [JGR, 1996]
1,2 second MF vector (Br, Bt, Bn) Min (1993- 1994)
Fast solar wind
Structure function scaling 80s-320s
Small gaps linearly interpolated
Small scale fluctuations are significantly intermittent for all components
Pagel and Balogh [JGR, 2002]
10 second averaged MF (Br, Bt, Bn)
Min (1994-1995)Max (2000-2001)Fast solar windSlow solar wind
Structure function scalingP-model
magnetic field components present a high level of intermittency throughout minimum and maximum slow wind has a lower level of intermittency compared with the fast flow T and R components show very similar level of intermittency while the R component values are slightly lower
Intermittency beyond the ecliptic
Intermittency beyond the ecliptic
Authors Data Method Conclusions
Pagel and Balogh[JGR, 2003]
20 second averaged MF (Br, Bt, Bn)
Min (1994 -1996)
Fast solar wind
Castaing distribution
Range of considered scales 40-200 s
in the polar coronal fast intermittency increases with increasing the radial distance from the Sundifference between the radialand transverse magnetic field components, the transverse magnetic field components are significantly more non-Gaussian than radial
Yordanova et al.[ JGR, 2009]
20 second averagedMF (Br, Bt, Bn) Min (1992-1997)Pure fast windFast streamPure slowSlow stream
Spectral analysis(Br, Bt, Bn, B)
Flatness factor (Br, Bt, Bn)
slow wind measured at AU, is more intermittent than fast wind slow wind and does not present radial evolution.
D1MAXSW : 1999, 2000, 2001
D3MINSW : 2007 and 2008
D5MINSW : 1997, 1998
The main aim : to choose the „pure” states of the slow and fast solar wind for studying the intermittency
CME list (1992-2008)
Radial Velocity vR
Oxygen Ion Ratio O7+ /O6+
Magnetic Compressibility*
Proton Temperature Tp
Proton Density np
Slow Solar Wind(SW)
Fast Solar Wind (FW)
Ulysses shock list (1996 – 2002)
vR > tV
O7+ /O6+< t O7+ /O6+
Compressibility < t Compr
Tp> tTp
np < tn
vR < tV
O7+ /O6+ > t O7+ /O6+
Compressibility > t Compr
Tp < tTp
np > tn
Data without CMEs and
interplanetary shocks
The Ulysses CME list (1992-2008) prepared by Gosling and D. Reisenfeld.
http://swoops.lanl.gov/cme_list.html
Ulysses shock list prepared by J. Gosling and R. Forsyth (only for years 1996-2002)
http://www.sp.ph.ic.ac.uk/Ulysses/shocklist.txt
D1MAXSW : 1999, 2000, 2001D3MINSW : 2007 and 2008D5MINSW : 1997, 1998.
Idea of Ulysses Data Selection
ThresholdsTable: The threshold values for the five solar wind parameters used during data selection
d-days
Solar maximum
Shock
CME
Fast solar wind
Slow solar wind
Ulysses Data D1MAXSW
(1999-2001)D3MINSW
(2007-2008)D5MINSW
(1997-1998)
Slow solar wind 28 3 6 37
Fast solar wind 38 43 12 93
Data base
Number of cases: 130 time intervals
Data size: 2 -7 days
Parameter: |B|, BR , BT , BN
Instrument : VHM-FGM
Reference system: RTN
Data resolution: 0.5 Hz [Bruno and Carbone, 2005]
singularity strength
the fractal dimension of the subsets with local scaling indices
Multifractal Formalism
Multifractal spectrum
-Degree of Multifractality
Multifractal analysis
probability that the portion of fluctuation is transferred to an segment of size
denotes magnetic field component (BR, BT, BN ) or the magnitude of magnetic field |B| separated from a position by a distance .
1) Measure
2) Partition Function
The scaling of the partition function in dependence on scale.
Selection of the Scaling Range
The optimal scaling range chosen for the final analysis.
Saucier and Muller (1999)
Conditions proposed by Meneveau and Sreenivasan, (1991) as minimal requirements of multifractality.
3) Legendre Transform
Multifractal Spectrum
2-scale model [Macek and Szczepaniak, 2008]
P-model [Meneveau and Sreenivasan, 1987]
∆
4) Fit Model
5) Degree of multifractality
Radial Evolution of Multifractality/ Intermittency
Decrease of intermittency during the second minmum at distances from 1.4 to 2.6 AU.
Transverse magnetic field components are slightly more multifractal than radial
Intermittency- Latitudinal dependence
The existence of symmetry respect to the ecliptic plane confirms similar turbulent properties of the fast polar solar wind in the two hemispheres.
Intermittency in the fast wind decresases with the increase of latitudes. At solar poles we observe the smallest values of intermittency
Multifractality as function of both heliocentric distance and heliographic latitude.
Map of the degree of multifarctality (intermittency) determined for fast solar wind during solar minima (1997-1998, 2007-2008) and solar maximum (1999-2001), correspondingly.
ConclusionsSolar minimum (1997-1998)• slow solar wind measured at distances ~5 AU and close to the
equatorial plane presents higher level of intermittency than fast solar wind;
• intermittency in the slow solar wind at the ecliptic plane doesn’t show radial evolution.
Solar minimum (2007-2008)• fast solar wind at distances 1.4-2.6 AU and at wide range of
latitudes ( ) reveals decrease of intermittency;• the higher levels of intermittency comparing with results from
previous minimum are observed• fast solar wind beyond the ecliptic plane presents higher level of
intermittency than slow solar wind
Solar maximum (1999-2001)• in many cases we observe similar level of multifractality as
those determined for data from solar minimum
Conclusions
It seems that evolution of turbulence* beyond the ecliptic plane can be insufficient to maintain the level of intermittency.
For Ulysses magnetic field data we observe the highest degree of multifractality/intermittency at small distances from the Sun both in the slow and fast solar wind.
The existence of symmetry respect to the ecliptic plane confirms similar turbulent properties of the fast polar solar wind in the two hemispheres.
*of pure states of the solar wind (without CMEs, shocks)
Thank you for your attentionCredits: NASA
This work was supported by the European Community's Seventh Framework Programme ([FP7/2007-2013]) under Grant agreement no. 313038/STORM.