Aspects of heliospheric turbulence - intermittency, stationarity and Alfvénicity

1. Aspects of heliospheric turbulence - intermittency, stationarity and Alfvénicity André Balogh* Imperial College London with Silvia Perri* University of Calabria, Cosenza, Italy IAFA-2011 Alpbach *both previously at International Space Science Institute, Bern Switzerland

2. Topics Solar wind turbulence studies need to take into account the fundamentally bimodal nature of the solar wind Ulysses observations of relevant turbulence phenomena during the sampling of fast and slow solar wind and the transitions between these streams The Taylor hypothesis: an exercise in assessing the “frozen-in” approximation Cross-helicity, residual energy and Alfvénicity: assessing what observations can tell us

3. The bimodal solar wind • Fast solar wind (> 600 km/s) originates in large coronal holes and is relatively uniform (in speed, density, temperature) • Slow solar wind (< 500 km/s) originates in the hot corona and is highly variable (in speed, density, temperature) • The origin of solar wind streams can be determined by the coronal freezing in temperature that fixes the ionization distribution of heavier ions (e.g. oxygen). • Determining the origin of the solar wind from composition measurements is essential for recognising the different turbulent characteristics of fast, slow and mixed solar wind regimes.

4. Ulysses: the best laboratory for the study of solar wind turbulence The projection of the Ulysses orbit on the solar meridional plane

5. Magnetic fluctuations during transition between fast and slow solar wind flow The projection of the Ulysses orbit on the solar meridional plane

6. Differences in magnetic variances and cross-helicity between fast and slow solar wind • Variances in magnetic field magnitude and its radial component change little (on average) between solar wind streams • There is a significant reduction in the variance of the transverse magnetic field components in slow and mixed velocity streams • The normalized cross-helicity corresponds to the high level of correlation between the transverse components of the magnetic field and plasma velocity

7. Magnetic field variances during transitions from fast to slow solar wind regimes Variances of the transverse magnetic field components are generally larger in the fast wind; variances always present a very bursty character. Transition 1 Transition 2

8. Alfvénic fluctuations in the slow and fast solar wind Fast wind: correlated Slow wind: decorrelated? Not really Fast wind: anticorrelated Slow wind: decorrelated? Yes, mostly

9. The different nature of magnetic fluctuations in the fast and slow solar wind • The analysis of the PDFs of the magnetic field increments during the two transitions showed that the 4-th order moment of the distributions, i.e., the flatness, increases as the time lag decreases. • The fast streams are found to be less intermittent than the slow ones, in agreement with previous results (a dependence of the intermittency on the regions of origin of the wind flows in the solar corona (Bruno et al. 2003; Yordanova et al. 2009). • No significant differences were found among the PDFs of the increments of the magnetic field components at small scales in the different types of solar wind.

10. The different nature of magnetic fluctuations in the fast and slow solar wind – a conclusion Slow wind 27 day interval 7 day interval Fast wind 1 day interval

11. The Taylor hypothesis and the “frozen-in approximation The condition derived by Matthaeus & Goldstein (1982) for satisfying the “frozen-in” approximation is: is the solar wind flow (radial) speed is the Alfvén speed is the average magnetic field is the average solar wind density is the magnetic field of an eddy of a given scale

12. Testing for the “frozen-in” approximation Equivalent to evaluate and assess if Conclusion: the condition is generally satisfied, although rvb is less than 10 ~50% of the time, particularly in mixed speed solar wind streams.

13. Alfvénic fluctuations in the solar wind: definition of parameters SW velocity vector fluctuations averaged over time t Magnetic field vector fluctuations averaged over time t Total energy in fluctuations Normalized cross-helicity: measure of correlation between magnetic and velocity fluctuations Residual energy: measure of difference in velocity and magnetic fluctuations energy Alfvén ratio: ratio of velocity and magnetic fluctuations energy

14. Alfvénic fluctuations in the solar wind: an early identification of complexity • The Alfvén ratio* rA was expected to fluctuate around 1, but has been found instead to be consistently < 1. • The corresponding value of the normalized residual energy sR has been observed to be consistently < 0 • The cross-helicity (measuring the correlation between velocity and magnetic fluctuations) is high during Alfvénic intervals, but remains * Concept introduced in Matthaeus & Goldstein, JGR 87, 6011-6028, 1982; graphs adapted from their Figures 6 and 8

15. Ulysses observations 1: Mid-heliolatitude Corotating Interaction Region 5.0 AU, 15oS • Corotating Interaction Region at 5 AU: • Region X: High level of cross helicity in the high speed wind (~0.8), Alfvén ratio (~0.6) relatively high • Region Y: Alfvén ratio even higher (~ 3) in rarefaction region, cross helicity ~ 0 Y X Histograms of the cross helicity and residual energy

16. Ulysses observations 2: High-heliolatitude pure high-speed solar wind 2.2 AU, 79oS • Nominally purely Alfvenic solar wind from the polar coronal hole: • High and constant cross-helicity (~0.75), • But sR remains uniformly ~ -0.5 (rA ~ 0.3) Histograms of the cross helicity and residual energy

17. Ulysses observations 3: Mid-heliolatitude rarefaction region • Rarefaction region at 4 AU: • Low and variable level of cross helicity • Alfvén ratio highly variable • Result similar to “standard” view of parameters in the ecliptic 4.0 AU, 28oN Histograms of the cross helicity and residual energy

18. CIRs: fluctuations and magnetic fluctuation power • Total magnetic variance varies over ~ 5 orders of magnitude in CIRs • Magnetic fluctuation power is correlated to the stream structure and compression regions • Alfvén ratio remains consistently low (~0.3) • Brief intervals of sR ~ 0 occur during some of the rarefaction regions Total magnetic variance (unnormalized): 2279 hourly samples

19. “Daily occurrence frequency F of sC (top panel) and sR (bottom panel) hourly values for days 240 (1996) to 14 (1997), during the Ulysses’s second distant mid-latitude phase. In both panels a white line shows the solar wind velocity magnitude V.” From B. Bavassano, N. A. Schwadron, E. Pietropaolo, and R. Bruno, Alfvenic turbulence in solar wind originating near coronal hole boundaries: heavy-ion effects? Ann. Geophys., 24, 785–789, 2006 Alfvénicity in high-latitude, mixed speed streams 3383 hourly samples

20. Is the large negative residual energy term due to the underestimation of the conversion to Alfvénunits? “Overestimation” of magnetic fluctuation energy could result from incomplete conversion into Alfvén units (correction factor F proposed by Barnes, 1979; assessed by several authors since then) • Sources of correction parameters: • Pressure anisotropies of ion species – occasionally can be significant; systematically not sufficiently significant • Differential streaming - occasionally can be significant; systematically not sufficiently significant • Pick-up ion effects – had been proposed at high heliolatitudes, but could be effective only at large (>5 or >10 AU ?) heliocentricc distances

21. Recent theoretical work on the less than expected value of the Alfvén ratio • The current theoretical consensus is to develop or modify turbulence propagation models to reproduce the behaviour of the cross-helicity and residual energy in the solar wind observations. • These efforts have been at least moderately successful (once enough flexible parameters have been included in the modelling) • Fully developed MHD turbulence requires zero cross helicity ~ equal power in inward and outward propagating waves. Within 5 AU this is not (consistently) the case. • Inclusion of the contributions of convected structures (Bruno et al., Tu and Marsch, Bavassano et al.) has provided a promising phenomenological model. However, the observed (very inconsistent) variability of the parameters with heliospheric and solar wind parameters has made a systematic joint treatment of waves and structures highly complicated. • N. Yokoia and F. Hamba, An application of the turbulent magnetohydrodynamic residual-energy equation model to the solar wind, Phys. Plasmas 14, 112904, 2007 • R. Bruno, et al., Magnetically dominated structures as an important component of the solar wind turbulence, Ann. Geophys., 25, 1913–1927, 2007 • B. Breech, et al., Turbulence transport throughout the heliosphere, J. Geophys. Res., 113, A08105, doi:10.1029/2007JA012711, 2008 • G.M. Webb et al., Alfvén simple waves: Euler potentials and magnetic helicity, Astrophys. J., 725, 2128-2151, 2010 • J. J. Podesta, On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence, Phys. Plasmas 18, 012907, 2011

22. Concluding remarks • The solar wind is bimodal: the fast wind is fundamentally different from the slow wind • The nature of magnetic fluctuations is different in the two kinds of solar wind – it is likely that the interactions that lead to the turbulent cascade affect at least the inertial range • The use of the “frozen-in” hypothesis is reasonably justified at the MHD scales – but care must be exercised when solar wind dynamics leads to evolving structures propagating through the solar wind • The puzzle of the generally negative value of the residual energy parameter is a symptom of a lack of understanding what we mean by turbulence in the solar wind. This problem MUST be resolved.