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

2 Introduction Ulysses Data Multifractal analysis Results - Radial dependence of multifractality - Latitudinal dependence of multifractality Conclusions Outline

AuthorsDataMethodsResults Marsch and Liu [1993] wind speed magnetic field components Helios Structure function scaling fast solar wind is less intermittent than slow wind Bruno et al. [2003] magnetic field components Helios Flatness Factorthe intermittency of the fast wind increases with the increase of the distance ( AU) from the Sun Intermittency in the ecliptic plane

AuthorsDataMethodConclusions Ruzmaikin et al. [JGR, 1995] 10 second averages of MF (Br, Bt, Bn) Min ( ) at 3.9 AU, 46ᵒ Fast solar wind Structure function scaling Time scales: 60s-3600s Bi – 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 ( ) 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 ( ) Max ( ) Fast solar wind Slow solar wind Structure function scaling P-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

AuthorsDataMethodConclusions Pagel and Balogh [JGR, 2003] 20 second averaged MF (Br, Bt, Bn) Min ( ) Fast solar wind Castaing distribution Range of considered scales s in the polar coronal fast intermittency increases with increasing the radial distance from the Sun difference between the radial and transverse magnetic field components, the transverse magnetic field components are significantly more non-Gaussian than radial Yordanova et al. [ JGR, 2009] 20 second averaged MF (Br, Bt, Bn) Min ( ) Pure fast wind Fast stream Pure slow Slow stream Spectral analysis (Br, Bt, Bn, B) Flatness factor (Br, Bt, Bn)

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 ( ) Radial Velocity v R Oxygen Ion Ratio O 7+ /O 6+ Magnetic Compressibility* Proton Temperature T p Proton Density n p Slow Solar Wind (SW) Fast Solar Wind (FW) Ulysses shock list (1996 – 2002) v R > t V O 7+ /O 6+ < t O7+ /O6+ Compressibility < t Compr T p > t Tp n p < t n v R < t V O 7+ /O 6+ > t O7+ /O6+ Compressibility > t Compr T p < t Tp n p > t n Data without CMEs and interplanetary shocks The Ulysses CME list ( ) prepared by Gosling and D. Reisenfeld. Ulysses shock list prepared by J. Gosling and R. Forsyth (only for years ) D1MAXSW : 1999, 2000, 2001 D3MINSW : 2007 and 2008 D5MINSW : 1997, Idea of Ulysses Data Selection

Thresholds Table: 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 ( ) D3MINSW ( ) D5MINSW ( ) Slow solar wind Fast solar wind Data base Number of cases: 130 time intervals Data size: 2 -7 days Parameter: |B|, B R, B T, B N Instrument : VHM-FGM Reference system: RTN Data resolution: 0.5 Hz [Bruno and Carbone, 2005]

Multifractal Formalism Multifractal spectrum Degree of Multifractality

Multifractal analysis 1) Measure 2) Partition Function

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 ( , ) and solar maximum ( ), correspondingly.

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 attention Credits: NASA This work was supported by the European Community's Seventh Framework Programme ([FP7/ ]) under Grant agreement no /STORM.