1. Effects of Dipole Tilt Angle on Geomagnetic Activities
Motoharu Nowada (野和田 基晴)
太空科学研究所 博士後研究員
ISS/NCU
2007/12/7 : 5年50億元計画Meeting

2. Outline of this presentation
1. Motivation of this study
2. Introduction
3. Data set and the methods to correct and calculate parameters used in this study
4. Methodology of analysis
5. Results
6. Conclusions

3. Motivations of this study
1. How is the relationship between IMF clock angle , geomagnetic activity , and the dipole tilt angle? (No in-situ observation)
2. What is the cause of semi-annual variations of geomagnetic activity ? In particular, what is the cause of its seasonal dependence ?
3. What is the time scale from the energy store in the magnetotail to the release into the ionosphere.
In this study, by comparing with two time-scale cases, we can estimate roughly the time-scale of the process from storing the energy in the magnetotail to releasing the energy into the ionosphere.

4. Only MHD Simulation Study Not verified with in-situ observational data
Relationship between the geomagnetic activities, the IMF clock angle and the Earth’s dipole tilt angle
Geomagnetic activity is controlled by the scale of dayside magnetic reconnection.
A proxy of Geomagnetic Activity
Only MHD Simulation Study
Not verified with in-situ observational data
Clock angle is one of representative parameters of the solar wind condition.
[ Russell et al.,2003]

5. Corrected AL and AU indices (1978-1988)
Data Used
Solar Wind Condition
Magnetic field and solar wind velocity data obtained from IMP 8 for Eleven years
( )
Geomagnetic Activity
Corrected AL and AU indices ( )
A proxy of neutral line length, formed by dayside magnetic reconnection
AL index reflects both dayside and nightside energy input. On the other hand, AU index reflects only the energy input from the dayside region.

6. We should correct the AL and AU indices in order to remove the seasonal variations.
1. Average AL in summer solstice: 0.89 times of the average AL near winter solstice.
2. Average AU in summer solstice: 1.79 times of the average AU near winter solstice.
Both AL and AU indices show sinusoidal variations. Furthermore, it is well-known that both AL and AU indices have some offsets depending on the seasons.
Then, we should remove these offsets in order to be studied with a higher accuracy. In our database….

7. Equations to correct AL and AU
We introduce these equations to remove the offsets.
[Shue et al., 2005, 2006]

8. Dipole Tilt Angle (Φtilt) (Angle between dipole axis and GSM-Z)
Dipole tilt angles can be calculated by the summation of the annual and diurnal dipole tilt angles.
This obtained tilt angle is not different from that direct-calculated based on the sun-position and the direction of Earth’s dipole
[Shue, 1993]

9. IMF (Interplanetary Magnetic Field) Clock Angle (θ)
GSM-Z θ
IMF
Of course, we are considering the propagating time lags between former AL,AU,dipole tilt and IMF clock angle.
AL, AU and dipole tilt angle data are fixed, and the IMF clock angle data is delayed.
GSM-Y

10. Taking 60-min. and 30-min. interval averages for all parameters
60 min. duration is chosen because of a delay time of the maximum response of the geomagnetic activity to the IMF. [Arnoldy, 1971]
(b)
To compare with 60 min. averaged parameters, we took a half-interval average (30-min.) for all parameters.
These two average time scales are depending on the process from storing to releasing of the energy.

11. Putting data into 18 x 7 bins (θーΦ)

12. Relationship between |AL|, AU and θ under various Φ (60 min. average)
MHD Simulation
Observations
If we subtract the AL by the AU, the resultant values mean the energy input from the nightside due to the substorm.
From the subtraction, the nightside energy input is more dominant than the dayside energy input.

13. Relationship between |AL|, AU and θ under various Φ (30 min. average)
MHD Simulation
Observations
However, in the case of 30-min. average, the subtracted values in this case are smaller than those in 60-min. average.
From these results, 30-min. is not suitable time-scale for evaluating the process from energy store in magnetotail to the energy release into the ionosphere.

14. North-South axis (GSM-Z) IMF
Dipole Axis
Dipole Tilt Angle =5°
North-South axis (GSM-Z)
IMF
(Spring and Fall)
Sun-Earth Line (GSM-X)
Dipole Tilt Angle
Dipole Tilt Angle =10°
Reconnection region is getting narrower, associated with the increase of tilt angle.
Namely, neutral line length is getting shorter.
|AL| and AU decrease when the dipole tilt angle is getting larger.
Dipole Tilt Angle =30°
(Summer and Winter)
Magnitudes of semi-annual variation in spring and fall are larger than those in summer and fall.

15. Conclusions
1. Geomagnetic activities strongly depend on the dipole tilt angle.
2. Our results are consistent with the prediction, derived with MHD simulation.
3. Cause for magnitudes of semi-annual variation of geomagnetic activities in spring and fall larger than those in summer and winter can be explained.
4. 60-min. is better time scale than 30-min. to evaluate the energy store and its release to produce the high geomagnetic activities.

16. Poster Slides for Presentation at AGU Fall Meeting 2007

17. Effects of Dipole Tilt Angle on Geomagnetic Activities
SM43D-1621
Effects of Dipole Tilt Angle on Geomagnetic Activities
Motoharu NowadaI Jih-Hong ShueI and Christopher T. RussellII
I. Institute of Space Science, National Central University, Taiwan (R.O.C).
II. Institute of Geophysics and Planetary Physics, UCLA, U.S.A.

18. Abstract
Relationships between the clock angle of the interplanetary magnetic field (IMF) and each of the AL and AU indices are examined under various Earth's dipole tilt angles using the observational data for a period of 1978 to This study is performed by correlating the interplanetary magnetic field data obtained from the IMP 8 satellite, the AL and AU indices with the corrected seasonal variations, and the dipole tilt angle. It is found that for any value of the IMF clock angle, the values of AL and AU decrease when the dipole tilt angle becomes larger. It suggests that the geomagnetic activities strongly depend on the dipole tilt angle. Furthermore, our results are consistent with the semiannual variation of the geomagnetic activity and the predicted relationships between the geomagnetic activity, the IMF clock angle, and the dipole tilt angle, derived from the MHD simulation.

19. Motivations of this study
1. How is the relationship between IMF clock angle , geomagnetic activity , and the dipole tilt angle? (No in-situ observation)
2. What is the cause of semi-annual variations of geomagnetic activity ? In particular, what is the cause of its seasonal dependence ?
3. What is the time scale from the energy store in the magnetotail to the release into the ionosphere.
4. What is the dependence of the energy input on the IMF clock angle and dipole tilt angle ?
5. Source of energy: the energy released from the magnetotail via substorm V.S. “direct” energy input via dayside magnetic reconnection ?

20. Only MHD Simulation Study Not verified with in-situ observational data
Relationship between the geomagnetic activities, the IMF clock angle and the Earth’s dipole tilt angle
A proxy of geomagnetic activity
Only MHD Simulation Study
Not verified with in-situ observational data
[ Russell et al., 2003]

21. Corrected AL and AU indices (1978-1988)
Data Used
Solar Wind Condition
Magnetic field and solar wind velocity data obtained from IMP 8 for Eleven years
( )
Geomagnetic Activity
Corrected AL and AU indices ( )
→ A proxy of neutral line length, formed by dayside magnetic reconnection

22. We should correct the AL and AU indices in order to remove the seasonal variations.
1. Average AL in summer solstice: 0.89 times of the average AL near winter solstice.
2. Average AU in summer solstice: 1.79 times of the average AU near winter solstice.

23. Equations to correct AL and AU
[Shue et al., 2005, 2006]

24. Dipole Tilt Angle (Φtilt) (Angle between dipole axis and GSM-Z)
[Shue, 1993]

25. Taking 60-min. and 30-min. interval averages for all parameters
Clock Angle data
ALc and AUc data
60 min.
60 min.
60 min.
60 min.
60 min.
|ALc|, AU, θ, and Φ
Dipole Tilt Angle data
60 min. duration is chosen because of a delay time of the maximum response of the geomagnetic activity to the IMF. [Arnoldy, 1971]
(b)
ALc and AUc data
Dipole Tilt Angle data
Clock Angle data
・・・
30 min.
30 min.
30 min.
30 min.
30 min.
30 min.
・・・
・・・
|ALc|, AU, θ, and Φ

26. Putting data into 18 x 7 bins (θーΦ)

27. Relationship between |AL|, AU and θ under various Φ (60 min. average)
MHD Simulation
Observations

28. Relationship between |AL|, AU and θ under various Φ (30 min. average)
MHD Simulation
Observations

29. The region where the open field lines is getting narrower.
The lengeth of neutral line, shown by a solid curve is getting shorter.
|AL| and AU decrease when the dipole tilt angle is getting larger.
Θ = 150°
Θ = 135°
Spring and Fall
Spring and Fall
Latitude
Latitude
Magnitudes of semi-annual variation in spring and fall are larger than those in summer and fall.
Summer and Winter
Summer and Winter
[ Russell et al., 2003]
Longitude
Longitude
Larger Φ

30. Relationship between SW energy input and |AL| and AU
Poyinting Flux

31. Relationship between S and |AL| and AU

32. Relationship between S and |AL| and AU

33. Relationship between θ and S under various Φ

34. Conclusions
1. Geomagnetic activities strongly depend on the dipole tilt angle.
2. Our results are consistent with the prediction, derived with MHD simulation.
3. Cause for magnitudes of semi-annual variation of geomagnetic activities in spring and fall larger than those in summer and winter can be explained.
4. 60-min. is better time scale than 30-min. to evaluate the energy store and its release to produce the high geomagnetic activities.

35. Conclusions
5. The input of solar wind energy is proportional to the geomagnetic activity under large IMF clock angle.
6. Amount of the energy input from the nightside via substorm is larger than that via dayside magnetic reconnection.
7. In the case that the dipole tilt angle is small (particularly, Φ=5°) and the IMF clock angle is large (more than 90°), the solar wind energy is easy to penetrate into the magnetosphere.
⇒ Effect of the dipole tilt angle exists for the input of solar wind energy.

36. Extra Figures

37. IMF (Interplanetary Magnetic Field) Clock Angle (θ)
GSM-Z θ
IMF
GSM-Y

38. Calculating Time Delay (Tprop) between Solar Wind Conditions and Geomagnetic Activities　
Tsolarwind : Propagation time (satellite – bow shock)
Tmagnetosheath : Propagation time (bow shock – magnetopause) Fixed 4 min.
Tfieldline : Propagation time (magnetopause – center of Earth) Fixed 2min.
Xsatellite ,Ysatellite : X,Y location of the satellite
X0: 15, Y0: 0 (the average position of the subsolar bow shock) Fixed.
T0 : Mean solar rotation period
Vsolarwind : Average SW speed
a : Mean radial distance from Sun to Earth
[Hsu and McPherron., 2003]

39. Taking 60 min. and 30 min. interval averages for all parameters
Clock Angle data
ALc and AUc data
60 min.
60 min.
60 min.
60 min.
60 min.
|ALc|, AU, θ, and Φ
Dipole Tilt Angle data
(b)
ALc and AUc data
Dipole Tilt Angle data
Clock Angle data
60 min. duration is chosen because of a delay time of the maximum response of the geomagnetic activity to the IMF. [Arnoldy, 1971]
30 min.
・・・
|ALc|, AU, θ, and Φ

40. North-South axis (GSM-Z) IMF
Dipole Axis
Dipole Tilt Angle =5°
North-South axis (GSM-Z)
IMF
(Spring and Fall)
Sun-Earth Line (GSM-X)
Dipole Tilt Angle
Dipole Tilt Angle =10°
Reconnection region is getting narrower, associated with the increase of tilt angle.
Namely, neutral line length is getting shorter.
|AL| and AU decrease when the dipole tilt angle is getting larger.
Dipole Tilt Angle =30°
(Summer and Winter)
Magnitudes of semi-annual variation in spring and fall are larger than those in summer and fall.

41. Relationship between |AL|, AU and θ under various Φ (60 min. average)
MHD Simulation
Observations

42. Relationship between |AL|, AU and θ under various Φ (30 min. average)
MHD Simulation
Observations

43. Relationship between θ and S under various Φ