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 jck@mit.edu Shocks: Daniel Berdichevsky, Chuck Smith, Adam Szabo, Adolfo Vinas ACE: John Steinberg, Ruth Skoug

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

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?

Shock database Catalogue all FF, SF, FR, SR, (& exotic) interplanetary shocks Wind 300+ events online ACE 200+ events online IMP-8 300+ events (coming soon) Voyager (ingested) Helios, Ulysses (possibly) Run every analysis method and save results Each shock rated as “publishable” is online http://space.mit.edu/~jck/shockdb.shockdb.html Currently “living document” with frequent updates

Conservation of MHD equations

Rankine-Hugoniot Jump conditions

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

Simple methods Magnetic Coplanarity Velocity Coplanarity (VC)

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

Data selection

Shock orientation

Derived parameters

Shock inflow and outflow

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?

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

110 events seen by ACE and Wind

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)

Examples of timing delays

Examples of timing delays

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

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

Magnetic Coplanarity

Velocity Coplanarity

Compression ratio Wind ACE

Fast Mach numbers Wind ACE

θBn Wind ACE

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?

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

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

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

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

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]

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

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 0.07-0.1 AU Uncertainty in direction of 10 degrees

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

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 http://space.mit.edu/~jck/shockdb/shockdb.html