1. Characterizing Interplanetary Shocks at 1 AU
J.C. Kasper1,2, A.J. Lazarus1, S.M. Dagen1
1MIT Kavli Institute for Astrophysics and Space Research 2
Shocks: Daniel Berdichevsky, Chuck Smith, Adam Szabo, Adolfo Vinas
ACE: John Steinberg, Ruth Skoug

2. Outline Identifying shocks Analysis of shocks Timing
Methods
Selection of data
Timing
Compare methods
As a function of spacecraft separation
Validity of methods
Magnetic coplanarity
Velocity coplanarity
Radius of curvature
Compare with numerical simulation
Survey of shocks
Conclusions

3. How well can we analytically model shocks?
How well can we predict transit times of shocks?
How planar are interplanetary shocks?
How uniform are shock properties along shock surface?

4. Shock database
Catalogue all FF, SF, FR, SR, (& exotic) interplanetary shocks
Wind 300+ events online
ACE 200+ events online
IMP events (coming soon)
Voyager (ingested)
Helios, Ulysses (possibly)
Run every analysis method and save results
Each shock rated as “publishable” is online
Currently “living document” with frequent updates

5. Conservation of MHD equations

6. Rankine-Hugoniot Jump conditions

7. Prescription for RH analysis
Combine some number of the remaining conservation equations and calculate deviation of jumps from zero
A given direction determines the shock speed given density and velocity measurements
Minimum in 2 determines shock direction
Depth of minimum determines uncertainty
Mass conservation equation is fulfilled explicitly

8. Simple methods
Magnetic Coplanarity
Velocity Coplanarity (VC)

9. Shock analysis: Science VS Art
What intervals do you select upstream and downstream?
10 minutes unless there is a periodic fluctuation, than an integer number of oscillations
How many of the Rankine-Hugoniot equations should we use?
Add normal momentum flux and energy separately
What weighting to use for each equation?
Estimate measurement uncertainties
Standard deviation of equation differences
How valid are the simpler methods?
Survey as a function of shock parameters
Example – 1998 DOY 238 FF shock

10. Data selection

11. Shock orientation

12. Derived parameters

13. Shock inflow and outflow

14. Sometimes things aren’t as clear!
Small uncertainties in derived shock normals
Huge disagreement in shock direction
When are methods valid?
What’s the real uncertainty in the derived parameters?

15. Wind distant prograde orbit (DPO)
From mid 2000 to mid 2002
Wind moves to ygse +/- 300 RE
yz up to 400 RE
An excellent database for studies of transverse structure

16. 110 events seen by ACE and Wind

17. Shock timing The observed propagation time ra(ta)
spacecraft can be determined by lining up high resolution magnetic field data
16 s ACE, 3 s Wind
The propagation delay can be predicted
using the locations and the derived shock parameters
Assumptions
Shock is planar
Spacecraft motion
ra(ta)
rw(ta)
rw(tw)

18. Examples of timing delays

19. Examples of timing delays

20. Average timing error in minutes
Blue is average of the timing errors
Red is the average of the absolute values of the timing errors

21. Timing error for 110 events
S/C:
Wind
ACE
Weight
Propagation
Cadence MC
4.8
13.7
9.6 VC
3.3
9.4
3.8
9.1
MX1
3.2
8.4
3.6
10.7
MX2
2.8
7.7
8.6
MX3
7.4
8.0
RH08
2.7
7.3
7.5
RH09
3.1
8.2
3.7
9.9
RH10
9.0

22. Magnetic Coplanarity

23. Velocity Coplanarity

24. Compression ratio
Wind
ACE

25. Fast Mach numbers
Wind
ACE

26. θBn
Wind
ACE

27. Timing error and spacecraft separation
Examine timing error as a function of separation
Separation along shock surface
Minimum timing error 1 minute for small separations
Error increases with distance to 15 minutes at 250 RE
Non-planar shock or error in shock normal?

28. Radius of curvature of shock wave
To what extent is the shock surface not planar?
Calculate radius of curvature using shock normals determined at multiple locations
Could be sensitive to
Global structure
Local ripples
Error in shock normals Rc

29. Radius of curvature Record shock normal and speed at ACE
Record shock normal and speed at Wind
Calculate propagation delay between ACE and Wind
Calculate location of ACE point at Wind observation time
Determine radius of curvature

30. Radius of curvature
All bets are off if Rc is smaller than then spacecraft separation
But larger separation leads to better determination of Rc

31. Comparison of Rc calculations
Determine observed time delay
Propagate one shock to time observed at other spacecraft
Compare Rc determined using each spacecraft
Minimum values are clustered at spacecraft separation
Maximum values at ~ 1 AU

32. Distribution of Rc Different methods give different range in Rc
For MC, Rc is clustered at nominal spacecraft separation
RH has larges values of Rc on average MC VC RH
Number of events
Radius of curvature [AU]

33. Simulation of radius of curvature
Pick Rc and σθ
Place spacecraft
Calculate normals to give Rc
Draw angles from distribution and rotate
Calculate new Rc

34. Variation of Rc with separation
Error in the shock normal directions determines the rollover at small separations
Typical Rc sets asymptotic value
Consistent with typical Rc of AU
Uncertainty in direction of 10 degrees

35. Statistical indicators of geoeffectiveness
Following Jurac et al study in 2001 – 150 more events
Minimum SYMH
θBn
θBn

36. Conclusions Compared 110 shocks seen by Wind and ACE Timing analysis
In general very good agreement
Timing analysis
MX3 and RH08 perform best overall
Predict propagation to within 3 minutes
Survey methods
MC performs poorly for oblique and perpendicular shocks
VC performs poorly for low Mach number shocks
Radius of curvature consistent with 5o uncertainty in normals and Rc 0.1 AU
Results for all methods posted online