Intermittency beyond the ecliptic plane Anna Wawrzaszek, Marius Echim, Wiesław M. Macek, Roberto Bruno Mamaia, 6-13 September 2015 (1) Space Research Centre.

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

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http://storm-fp7.eu/

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• 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.