1. Munetoshi Tokumaru （ISEE, Nagoya University）
Analysis of Solar Wind Density Turbulence using Interplanetary Scintillation Measurements
Preliminary Results
Munetoshi Tokumaru
（ISEE, Nagoya University）

2. Introduction
Spatial spectrum of the solar wind density turbulence is reflected in the high frequency portion of temporal spectrum of interplanetary scintillation (IPS).
Flattening by Fresnel filter occurs at the low frequency portion of IPS.
Solar wind density fluctuations
Frequency
Fresnel filter
Power

3. This Study
Determine solar wind turbulence parameters by fitting a model to IPS spectra observed at Toyokawa.
Observations
2 strong IPS sources: 3C273, 3C48
Period: 2012, 2013（solar maximum）
Solar elongation： 0.2 AU < R <1 AU（weak scattering regime for 327 MHz）
Model
Spatial spectrum of solar wind turbulence：defined by power-law index (α), axial ratio (AR) of anisotropy, level (CN)
Use of solar wind speeds V derived from 3-station measurements as a fixed parameter.
Usually, V is one of free parameters in the fitting analysis.
Investigate the relation between α, AR, and speeds.

4. Model Weak scattering & thin screen at the point P Free parameters:
CN, α, AR
Fixed parameter:
Solar Wind Speed: V (kF=2πfF/V)
Source size θ (kc=1/Zθ)
3C273: 60 mas, 3C48 : 100 mas
point-P-Earth distance: Z, wavelength: λ
Fresnel frequency
Fresnel Filter
Finite Source Size Effect

5. Spectral Fitting Analysis
White noise component
V=459 km/s, AR=1.07, α= 3.8
Least Squares Fitting: Marquardt Method
Fitting in Log-Log Space
Weighting Function: 1/N

6. Correlation between V1 and V3
V1: 4 Free para (Cn, fF(V), AR, α)
CC =
Open: 3C273
Solid: 3C48
N=105, p = 0%
V1(km/s)= / / E-01*V3 (km/s)
(Err= km/s)
V3(km/s)= / / E-01*V1(km/s)
(Err= km/s)

7. Histograms of AR and α determined from spectral fitting analysis (Fixed V)
In the fitting analysis, V is given from three-station measurements V3.
Free parameters are Cn, AR, α.
N=105
AR = /
α = /
Kolmogorov (11/3)

8. Relation between α and speed V (Fixed V)
Open: 3C273
Solid: 3C48
CC =
N= 105, p=6.6 %
α= / E-02+/ E-03*V
(Err= )
V = / / *α
(Err= )
No correlation or weak positive dependence on V (its significance is poor).

9. IPS Observations at Ooty and STEL (Manoharan et al., 1994)
Power-law index α ← Spectral fitting analysis using Ooty IPS obs.
Speed V　← STEL IPS obs.
sol. min.
sol. max.
Three-component model of solar wind density turbulence
low freq.：Kolmogorov, intermediate freq：flattening, high freq.：inner scale cutoff
The dependence of α on V is ascribed to the selection effect of the frequency range in the spectrum.

10. Relation between AR and Speed V (Fixed V)
Open: 3C273
Solid: 3C48
CC =
N= 105, p= 5%
AR = / E-03+/ E-03*V
(Err= )
V = / / *AR
(Err= )
Weak positive dependence on V, but Its significance is rather poor.

11. Radial Variation of AR (left) and α (right)

12. Radial Dependence of AR (left) and α (right)
Microwave IPS measurements in 1994 (Yamauchi et al., 1998)
Solid circles: Slow wind, Open triangles: Fast wind
Fast wind is associated with larger α for R> 40 Rs (0.2 AU)
No difference in AR between fast and slow winds

13. Relation between AR and α (Fixed V)
CC=
N=105, p = 0%
α = / / *AR
(Err= )
AR = / / E-01*α
(Err= )
Open: 3C273
Solid: 3C48
Significant negative correlation between α and AR
This might suggests that AR is strongly coupled with α in the model.

14. Spectral Fitting Analysis of Kashima IPS Observations at 2,8, and 22 GHz in 1991
Speed
Spectral indices α become smaller, and axial ratios AR increase in the near-Sun region, where the solar wind speeds decrease.
What is the physical meaning?
Axial ratio
Spectral index
Tokumaru et al., 1992

15. Comparison between c/a and AR (Fixed V)
x’ (radial) y’
The parameter c/a, which represents anisotropy of turbulence, is determined from three-station IPS measurements.
Weak positive correlation between AR derived from spectral fit analysis and c/a derived from 3-station measurements? But, its significance is very poor.
isotropic: c/a=0
anisotropic: c/a≠0
CC =
N= 105, p = 5 %
AR= / E / *(c/a)
(Err= )
(c/a) = / E / E-01*AR
(Err= )
Open: 3C273
Solid: 3C48

16. Summary
We determine solar wind turbulence parameters; α and AR, by fitting a model to IPS spectra observed at Toyokawa
Solar wind speeds derived from 3-station measurements are used for this analysis.
solar maximum, data for 1AU>R>0.2AU
AR ~ 1.0 (isotropic), α~4 (slightly steeper than Kolmogorov=11/3)
α, AR: weak dependence on speed? (further study is needed)
Negative correlation between AR and α
Weak positive correlation between AR and c/a? (further study is needed).