1. Predictions for the Outer Corona and Inner Heliosphere
Turbulence in the Solar Wind, from the Energy Containing Range to the Dissipation Range:
Predictions for the Outer Corona and Inner Heliosphere
Roberto Bruno
INAF-Istituto di Astrofisica e Planetologia Spaziali Rome, Italy,
Parker Solar Probe SWG Meeting Join with
Solar Orbiter, October 2-6, 2017, JHU-APL, Laurel, MD, USA

2. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Most of our knowledge about solar wind, in the inner heliosphere, derives from observations from the late 70’s performed by Helios 1 & 2 s/c.
About plasma measurements:
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

3. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Source regions of fast wind
polar coronal holes are the source regions of fast solar wind (Zirker 1977)
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
(McComas et al., 2003)

4. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Source regions of fast wind
polar coronal holes are the source regions of fast solar wind (Zirker 1977)
Source regions of slow wind
slow component of the solar wind comes from:
the edges of coronal holes (Wang & Sheeley, 1990, D’Amicis and Bruno, 2015), the flanks of equatorial streamers (Antonucci et al., 2005)
slowest wind from above the streamer cusp, roughly corresponding to the heliospheric current sheet (Bavassano et al., 1997, Antonucci et al., 2005,… )
transient reconnections in closed-field streamers (e.g.,Wu et al., 2000),
active regions (Hick et al., 1999).
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
(McComas et al., 2003)

5. ASW SI FW RR ASW An interplanetary, corotating high velocity stream
ASW…Ambient Solar Wind
SI……..Stream Interface
FW…..Fast Wind
RR……Rarefaction Region RR
ASW

6. Roberto Bruno, AOGS 2017, Singapore 6-11 August
ASW SI FW RR ASW
Mapping back to the Sun a corotating high velocity stream
Wilcox Solar Observatory source surface synoptic charts
ASW…Ambient Solar Wind
SI……..Stream Interface
FW…..Fast Wind
RR……Rarefaction Region
Roberto Bruno, AOGS 2017, Singapore 6-11 August

7. Roberto Bruno, AOGS 2017, Singapore 6-11 August
ASW SI FW RR ASW
An interplanetary, corotating high velocity stream
ASW: Ambient Solar Wind
SI: Stream Interaction region – leading edge
FW: Fast Wind region
RR: Rarefaction Region (slower wind region)
Alfvénic turbulence quickly drops when moving from FW to RR.
Large differences in the nature and amplitude of fluctuations
Roberto Bruno, AOGS 2017, Singapore 6-11 August

8. At 0.3 AU, strong Alfvénicity persists within slow wind regions bordering fast wind
Faster Alfvénic wind
Slower Alfvénic wind
Shaded area might correspond to the over-expanding region  slower wind flow
[D’Amicis &Bruno, 2015]
same level of Alfvénicity as in fast wind but smaller amplitude fluctuations

9. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Typical power spectrum of magnetic fluctuations in fast solar wind
high Reynolds number fc fb
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

10. Fast wind:
during the wind expansion (i.e. elapsed time)  low frequency break shifts to lower frequencies
Larger and larger scales are involved in the cascade process
Low frequency break R-1.5 (Bruno and Carbone 2005)

11. Fast wind:
during the wind expansion (i.e. elapsed time)  low frequency break shifts to lower frequencies
break location at 20Rs
Larger and larger scales are involved in the cascade process
Low frequency break R-1.5 (Bruno and Carbone 2005)
Around the Alfvén radius (~20Rs):
low frequency break ~310-2Hz
power density level (R-4) (Bavassano et al., 1982) about 2 decades higher than at 0.3AU
PSP will verify this estimate

12. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Slow wind:
Helios and Ulysses do not provide long enough intervals of slow wind to detect a clear f -1 scaling
f -1 possibly located at lower frequencies wrt fast wind
turbulence older than in fast wind
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

13. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Ongoing study on slow wind samples of long duration observed by WIND at 1 AU allows to locate the break
[Bruno & Telloni, 2017]
f -1 observed for f<10-4 Hz, about 1 decade lower than in fast wind.
break location
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

14. Ongoing study on slow wind samples of long duration observed by WIND at 1 AU allows to locate the break
[Bruno & Telloni, 2017]
f -1 observed for f<10-4 Hz, about 1 decade lower than in fast wind.
assuming the same radial dependence for fast and slow wind but considering different advection time  break location should be at higher frequency
longer transit time unable to explain break location
Slow wind appears to be older than it should be
predicted location
fast wind location
break location
PSP and Solar Orbiter should record a different radial dependence for this break wrt fast wind

15. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Large scales: Origin of f -1
1) first interpretation for the IMF observations (Matthaeus and Goldstein, 1986):
A superposition, within the Alfvénic radius, of uncorrelated samples of turbulence, whose correlation lengths are log-normally distributed, would produce S(f)~1/f [Montroll and Shlesinger, 1982]
Ulysses
1 day
1 hour
Matthaeus et al., ApJ, 2007
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

16. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Large scales: Origin of f -1
1) first interpretation for the IMF observations (Matthaeus and Goldstein, 1986):
A superposition, within the Alfvénic radius, of uncorrelated samples of turbulence, whose correlation lengths are log-normally distributed, would produce S(f)~1/f [Montroll and Shlesinger, 1982]
2) Alfvén waves reflection (Velli et al., 1989; Verdini et al., 2012; Perez and Chandran, 2013; Tenerani and Velli, 2017):
outward modes reflected by large-scale gradients interact non-linearly to produce a turbulent cascade with a spectrum scaling 1/f already within the sub-Alfvénic solar wind
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

17. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Large scales: Origin of f -1
1) first interpretation for the IMF observations (Matthaeus and Goldstein, 1986):
A superposition, within the Alfvénic radius, of uncorrelated samples of turbulence, whose correlation lengths are log-normally distributed, would produce S(f)~1/f [Montroll and Shlesinger, 1982]
2) Alfvén waves reflection (Velli et al., 1989; Verdini et al., 2012; Perez and Chandran, 2013; Tenerani and Velli, 2017):
outward modes reflected by large-scale gradients interact non-linearly to produce a turbulent cascade with a spectrum scaling 1/f already within the sub-Alfvénic solar wind
3) Numerical modeling (Dmitruk et al., ):
Upward traveling low frequency waves at coronal base are capable of self-generating 1/f spectrum in density and B
1/f not present in similar hydrodynamics simulations (role of magnetic field)
Compensated spectrum by Dmitruk et al.,
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

18. Large scales: Origin of f -1
1) first interpretation for the IMF observations (Matthaeus and Goldstein, 1986):
A superposition, within the Alfvénic radius, of uncorrelated samples of turbulence, whose correlation lengths are log-normally distributed, would produce S(f)~1/f [Montroll and Shlesinger, 1982]
2) Alfvén waves reflection (Velli et al., 1989; Verdini et al., 2012; Perez and Chandran, 2013; Tenerani and Velli, 2017):
outward modes reflected by large-scale gradients interact non-linearly to produce a turbulent cascade with a spectrum scaling 1/f already within the sub-Alfvénic solar wind
3) Numerical modeling (Dmitruk et al., ):
Upward traveling low frequency waves at coronal base are capable of self-generating 1/f spectrum in density and B
1/f not present in similar hydrodynamics simulations (role of magnetic field)
4) Full disk magnetograms (Nakagawa & Levine, 1974):
1/k spectral region was found in photospheric observations
Possible link between the structured surface of the sun and 1/f scaling in IMF ?
hypotheses could be tested by PSP and RS&IS obs. of Solar Orbiter could verify hypothesys 4
normalized magnetic energy spectrum
~25d
~10h
Nakagawa and Levine, 1974

19. Fluid scales: Origin of f -5/3 (Kolmogorov spectrum)
𝑓 −1
𝑓 −5/3
𝑓 𝑏
Z+: outward mode
Z-: inward mode
𝑓 −3
 0

20. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Z+ and Z- in the inner heliosphere
[Z- locally generated]
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

21. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Z+ and Z- in the inner heliosphere
[Z- locally generated] RA
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

22. Z+ and Z- in the inner heliosphere [Z- locally generated]
AEB Accelerating Expanding Box model
Inward modes at diff. times RA
[Tenerani & Velli, 2017]
reflected inward modes (t+t)
inward modes
at time t
anomalous component due to inhomogeneities (t+t)
(for predicted spectra see presentation by S. Cranmer tomorrow)

23. Z+ and Z- in the inner heliosphere [Z- locally generated]
2D and Slab crosshelicity smooth radial behavior across the critical point (Zank et al., 2017)
(see presentation by P. Hunana tomorrow)

24. Further open questions about Alfvénic turbulence:
Helios plasma resolution does not allow to build Elsasser variables throughout the inertial range
[frequency break radial dependence from Bruno and Trenchi, 2014] fb

25. PSP and Solar Orbiter will provide plasma sampling up to kinetic scales for the first time in the inner heliosphere fb
and beyond

26. During the wind expansion the high frequency break shifts to lower frequencies
high frequency break R-1.1 (Bruno and Trenchi 2014)
break location at 20Rs
Around the Alfvén radius (~20Rs):
high frequency break ~4 Hz
power density level (R-4.2) (Bavassano et al., 1982) about 2 decades higher than at 0.3AU
The estimated effective Reynolds number
PSP will verify this estimate
break location at 20Rs

27. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
The location of the high-freq break well predicted by the wavenumber 𝑘 𝑟 associated to the resonant condition for // propagating Alfvén modes
[Bruno and Trenchi, 2014]
Surprising result since turbulence develops via k rather than k//
(Shebalin et al., 1983)
This result is waiting to be confirmed by high resolution field and plasma observations within the inner heliosphere
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

28. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Transition region beyond the break
[Bruno et al., 2014]
Spectral index ‘’q’’ becomes flatter moving from faster to slower wind
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

29. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Transition region beyond the break
q = (-4.40.5)+(2.5  0.5)w/w0(-0.3  0.1)
[Bruno et al., 2014]
Spectral index ‘’q’’ becomes flatter moving from faster to slower wind
q= -4.4 0.5 asymptotic limit
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

30. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Proton temperature anisotropy : radial evolution
Fast wind
[empirical relation by Marsch et al., 2004]
[Matteini et al., 2007]
Ion cyclotron (solid), mirror (dotted), parallel (dashed),
and the oblique (dash-dotted) fire hose instabilities.
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

31. Proton temperature anisotropy : radial evolution
Fast wind
[Telloni and Bruno, 2016]
Moving to shorter heliocentric distances, ICWs population should assume a more relevant role within fast wind
[Matteini et al., 2007]
Ion cyclotron (solid), mirror (dotted), parallel (dashed),
and the oblique (dash-dotted) fire hose instabilities.
[empirical relation by Marsch et al., 2004]

32. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA
Final comments:
Most of the results/predictions about the inner heliosphere rely on turbulence observed within one single corotating stream detected at 3 different heliocentric distances (stationarity of source region assumed).
Future observations, especially those combined between PSP and Orbiter, will allow to remove the stationarity assumption, observing the same plasma parcels at different distances. Particularly important will be the observations across the critical radius.
A better determination of source conditions and radial gradients are at the basis for a correct modelling of turbulence transport in the solar wind.
Thank you.
Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA

33. Roberto Bruno, PSP-SO Joint Meeting, October 2-6, Laurel, MD, USA