1. IPS g-value Measurements
UCSD IPS Workshop
San Diego, December
IPS g-value Measurements
M. Tokumaru
(ISEE, Nagoya Univ.)

2. Definition of g-value
Gapper, G.R., A. Hewish, A. Purvis, and P. J. Duffett-Smith, Observing interplanetary disturbances from the ground, Nature, Vol. 296, , 1982.
: r.m.s. scintillating flux density (daily measurements)
: smoothed curve as a function of solar elongation　ε (Chebyshev polynomials used in Gapper et al., 19982)

3. Note Scintillation index: m For weak scattering,
Spherically symmetric distribution of ΔNe
g>1 (g<1) corresponds to high (low) ΔNe
Radio source
“Point P”
strong scattering
weak scattering
Sun

4. Transition Distance from Weak to Strong Scattering
Scintillation flux ΔS (index m) shows a peak at given distance, where transition from weak to strong scattering occurs.
In strong scattering, ΔS (m) decreases because intensity variation interferes or cancels to each other within the observation frequency band.
The turnover distance depends on the observing frequency.
It is roughly given by the following empirical formula.
Scintillation Index
Radial distance from the sun (Rsun)
・100 Rsun for 70 MHz
・34 Rsun for 327 MHz
・15 Rsun for 1GHz
Inner limit for g-value measurements
Rsun in solar radius、f in MHz

5. Upper Limit of g-value due to Strong Scattering
ΔSmax : maximum value at the turnover distance
(Tokumaru et al., 2005)

6. Calculation of g-value
Calculate ΔS
P(f): Power spectrum
Determine the average curve
R: Solar offset distance
Divide the daily level by the average curve

7. Calculation of ΔS Discriminate IPS from the background component
IPS comp. (Blue, P(f))
Background noise (Gray, Flat spectrum)
fN: Turnover freq., fL: Lower limit freq.
Integrate P(f) over the range between fL and fN
Correct the effect of system gain change
Take a ratio of IPS to background noise N
P(f)
fmin
fmax fN
Frequency
Power fL
Note: The change in the system gain is corrected by dividing by N.

8. Calculation of g-value
A function of aR-b is fit to IPS data for R > 0.2 AU, then data with a deviation > ±2σ are discarded. Then, the function is fit again.
Toyokawa
IPS level
Time
Radial Distance
g-value
Time
The turnover distance is assumed to be 0.2 AU for 327 MHz.

10. Radial Slopes of IPS Level Variation
IPS obs at Kiso
Year
Slope
SWIFT obs. in 2008
2008
-1.47±0.92
2007
-1.53±0.87
2006
-1.79±0.82
2005
-2.00±0.76
2004
-2.07±0.73
2003
-2.25±0.73
2002
-2.27±0.65
2001
-2.13±0.83
2000
-2.52±0.62
1999
-2.38±0.77
1998
-2.40±0.77
1997
-2.18±0.97
Average　-1.65±1.08
Low density
radio source
Sun
Flattening of radial slopes
Effect of coronal holes over the poles during the solar minimum.
Note: The slopes show here is 2 x (actual slope).

11. Spherically-Symmetric Model Fit
In the low solar activity period, we find a deficit of the scintillation level at small distances. This corresponds to the coronal hole at high latitudes.
The radial slope is fixed to b = -1.5.

12. Smoothed (Average) Curve
Two different functions are used.
Axis-symmetric model:
Spherically asymmetry model:
Period used for fitting
We fit the model to data obtained for one year, and use different average curve optimized for that year to calculate g-values.
We can use the same average curve to calculate g-values for different years, if the system is sufficiently stable.

14. Effect of Apparent Source Size
Scintillation flux ΔS (index m) depends on the apparent source size.
m decreases with increasing θ
m decreases more rapidly in the strong scattering for a larger θ
g-value is not affected by the source size effect.
log m
log R