Solar wind turbulence from radio occultation data

1. Solar wind turbulence from radio occultation data Chashei, I.V. Lebedev Physical Institute, Moscow, Russia Efimov, A.I., Institute of Radio Engineering & Electronics, Moscow, Russia Bird, M.K. Radio Astronomical Institute, Univ. Bonn, Bonn, Germany

2. TURBULENCE • Turbulence is a permanent property of the solar wind. • Fluctuations spectra of B, N, V… cover many decades in wavenumbers / frequencies. • Formed flow R > 20 RS , in situ + radiooccultation data. • Acceleration region: R < 10 RS, no in situ data. • Below we concentrate mainly on Galileo and Ulysses spacecraft data.

3. GEOMETRY OF CORONAL RADIO OCCULTATION EXPERIMENT

4. OBSERVATIONAL DATA • SPACECRAFT GALILEO (1994-2002) ANDULYSSES (1991-1997) • HIGH STABILITY RADIO SIGNALS AT S-BAND (2295 МHz) • GROUND BASED NASA-DSN TRACKING STATIONS: • GOLDSTONE(DSS 14) • CANBERRA (DSS 43) • MADRID (DSS 63) • MEASUREMENTS OF FREQUENCY FLUCTUATIONS • SAMPLING RATE: 1 Hz • RECORDS AT INDIVIDUAL STATIONS → • TEMPORAL POWER SPECTRA OF FREQUENCY FLUCTUATIONS • CROSS CORRELATION OF OVERLAPPING RECORDS → – VELOCITY OF THE DENSITY IRREGULARITIES • SOLAR OFFSET R: 7 R < R < 80 R

5. EXAMPLE (ULYSSES) OF FREQUENCY FLUCTUATION RECORD

6. TEMPORAL POWER SPECTRA OF THE FREQUENCY FLUCTUATIONS • Typical temporal spectra are power law • Power law interval is bounded by the frequency of the turbulence outer scale at low frequencies and the noise level at high frequencies • Power law spectral index of the temporal frequency fluctuation spectrum is related to the power law index of the 3D spatial turbulence spectrum р by the equation = р-3

7. FREQUENCY FLUCTUATION POWER SPECTRA: SOME EXAMPLES

8. CROSS-CORRELATION FUNCTION:FREQUENCY FLUCTUATIONS

9. RADIAL EVOLUTION OF THE SPECTRAL INDEX (LOW HELIOLATITUDES)

10. RADIAL EVOLUTION OF THE SPECTRAL INDEX (HIGH HELIOLATITUDES,R = 22-30 R)

11. FRACTIONAL LEVEL OF DENSITY VARIANCE ( SLOW SOLAR WIND,GALILEO)

12. DENSITY TURBULENCE OUTER SCALE

13. DENSITY TURBULENCE OUTER SCALE Radial dependence approximation L0( R ) = A ( R / RS )m with A = 0.24 RS and m = 0.8 , very close to linear.

14. RESULTS • A change of the turbulence regime occurs at the transition from the acceleration region to the region of the developed solar wind. (Also, Woo & Armstrong, 1979) • FR fluctuations measurements in the acceleration regions shows that flat flicker type spectra with p=3 are also typical for magnetic field fluctuations (Chashei, Efimov, Bird et al., 2000). Recently (Chashei, Shishov & Altyntsev) the evidences were found from the analysis of angular structure of the sources of microwave subsecond pulses for such spectra in the lower corona. • The heliocentric distance of this change of turbulence regime is greater for the fast solar wind than for the slow solar wind during the period of low solar activity.

15. RESULTS • The fractional density fluctuations tend to increase slowly with increasing heliocentric distance. • Turbulence outer scale increases approximately linear with increase of heliocentric distance in the range 10RS < R < 80 RS . • Galileo data (1994-2002): no changes of slow wind turbulence during the solar activity cycle.

16. TURBULENCE MODEL(acceleration region) • The source of turbulence is a spectrum of Alfvén waves (magnetic field fluctuations), propagating away from the Sun. • Slow and fast magnetosonic waves are generated locally via nonlinear interactions with Alfvén waves. Density fluctuations are dominated by slow magnetosonic waves. • Turbulence is weak in the solar wind acceleration region (R < 20 R). • The fractional level of turbulent energy increases with increasing heliocentric distance. • Temporal power spectra are flat ( = 0, р = 3.0). No cascading of turbulence energy from the turbulence outer scale to smaller scales.

17. TURBULENCE MODEL(change in turbulence regime) • The turbulence power spectrum of the developed solar wind in the inertial spectral range is defined by nonlinear cascading processes. Source of turbulence energy – l.f. (outer scale) Alfven waves. Nonlinear generation of magnetosonic waves (density fluctuations) (Spangler &Spitler, Ph. Pl., 2004). Spectra: • Kolmogorov (p=11/3) or • Iroshnikov-Kraichnan (p=7/2) spectra. • The change in turbulence regime is caused by the increase of fractional turbulence level (and increase of fractional level of fast magnetosonic waves compared with slow magnetosonic waves). • The more distant transition for the fast solar wind may be explained by the lower value of the plasma parameter  = 4P/B2 , i.е. by stronger ambient magnetic fields above the coronal holes.

18. TURBULENCE MODEL (outer scale) • Data are related to the region of formed solar wind flow. • Model : Wk=C1k-nat k<k0 , Wk=C2 k-mat k>k0 ; linear (WKB) propagation of Alfven waves at k<k0 ; nonlinear cascading at k>k0 (Kolmogorov, Kraichnan, 4-waves interactions); equal linear and nonlinear increments at k=k0; k0 (R, n, m). LF spectrum can be assumed as flicker spectrum with n=1 (Helios =>Denscat, Beinroth & Neubauer, 1983; Ulysses => Hourbury & Balogh, 2001). • Comparison of the models with observational data: best agreement at n=1 is found for the Kraichnan turbulence.

19. CONCLUSIONS • Turbulence regimes in the acceleration region and in the formed solar wind are strongly different. • Sufficiently good agreement between the observational data and the model.