Identifying Interplanetary Shock Parameters in Heliospheric MHD Simulation Results

1. Identifying Interplanetary Shock Parameters in Heliospheric MHD Simulation Results S. A. Ledvina1, D. Odstrcil2 and J. G. Luhmann1 Space Sciences Lab, University of California Berkeley CIRES, University of Colorado

2. Abstract One of the challenges of integrating SEP models into heliospheric space weather event simulations is the identification and characterization of the shock in the underlying MHD simulation results. We investigate the numerical method by which the jumps can be identified, the shock surface orientation characterized, and the upstream and downstream conditions defined. Our approach uses snapshots of observer-connected interplanetary magnetic field lines. First we determine whether a shock is on the connected field line, and record its position and the change in the MHD variables (field, density, velocity). We also examine several adjacent field lines and similarly determine the shock positions. The identification of the jumps takes into account the lack of spatial resolution at the shock front. The shock surface orientation is determined by a cross-product method. Then the shock normal angle is determined from the upstream and downstream vector fields and the normal. These calculations are relatively fast and can be embedded in a simulation run for use in overlaid SEP shock source descriptions or for analyzing the evolution of the connected

3. The CISM SEP Model • Goal: A generalized test particle code that uses the time-dependent fields and shock information from the CISM heliospheric MHD simulation for transport and (shock) source descriptions • Approach: Adapt a field-line tracer to a guiding-center particle tracer for 10-100 MeV/n ions of any mass and charge

4. Development Plans • Incorporate the CISM heliospheric B field description and shock location in the transport code, using a sequence of MHD simulation field “snapshots” • Develop an ion-kinetic hybrid model-based lookup table for the shock source description (flux, energy spectrum, pitch angle distribution) • Incorporate the above in the transport code

5. For each observer-connected field linewe need: • The shock location • The shock jump conditions in order to find the shock strength: MA,  • The shock normal angle Bn • The MHD variables • Density • Temperature • Magnetic field • Velocity

6. Some of the Issues Schematic MHD Grid Schematic Field line Trace • The process need to be fast so that it can be run at the same time as the MHD simulations. • The field-line tracer takes steps that are smaller than the MHD grid scale. • The magnetic field and plasma density can pileup in co-rotating interaction regions, interacting streams etc… that are present in the heliospheric MHD results. Must keep this in mind when looking for shocks. • The shock may be spread over 1-2 MHD grid cells. This will translate into several field-line steps.

7. The Process • Find the shock location. • Find the shock jump. • Find the shock normal angle. ICME Flux Rope Field Lines ICME Shock and Sheath

8. We have developed this procedure using the Cone Model Conceptual model: • CME as a shell-like region of enhanced density Geometrical and kinematical fitting: • Dependence of predicted CME halos on the latitude, longitude, angular width, and velocity.

9. The cone model produced a detailed picture of the evolution of the disturbance in the solar wind out to 1 AU, including all of the information needed for the SEP calculations

10. Finding the Shock by Using the Gradient Pressure The gradients in a given variable may numerically be larger in the inner heliosphere than at the shock. The first steps in the process then become: • Normalize the given variable by r2. • Calculate the gradients (with respect to r) in the normalized variable.

11. A Numerical Wrinkle The interpolation scheme used in the field-line tracing subroutine interpolates the variables continuously across the MHD grid. However, the gradients are not continuous. Instead of using a higher order interpolation scheme that would slow down the MHD calculations we filter the gradients along the field lines.

12. A Further Wrinkle • Even after applying the filter, the location of the maximum gradient (and hence the shock location) varies among the MHD variables. However, the variation is smaller than the MHD grid spacing. Normalized Gradients T v P,  B

13. Finding the Jump Conditions In order to find the jump conditions we must identify where to take the upstream and downstream values. • Upstream: Starting upstream of the shock, find where the gradients change by some value (~20%) from the background. Use this point for the upstream values. • Downstream: Starting at the shock, move downstream until the gradient equals zero. Use that location for the downstream values. • Since these values are slightly different for each variable we take the average position. • Calculate the shock jump. Shock Downstream Upstream

14. Examples Speed Density

15. The MHD parameters along the observer-connected field lines show the May 12 1997 cone model shock weakens with radial distance

16. The shock normal angle is determined by a method that uses neighboring field lines • Cross-products of vectors to neighboring shock locations define the local plane of the shock, hence theta-bn

17. Finding bn Shock locations • Construct 4 parallel (in ,  space) to the field line at + 5°. • Find the shock location along each line. • Construct a vector from the shock on the field line to the shock on each of the parallel lines. • Take the cross product between pairs of vectors. • Average the resulting vectors to get the shock normal. • Use the dot product between the normal and the magnetic field to get bn n bn B

18. Conclusions and Future Directions • We have developed a fast and easy approach to characterizing MHD shock properties in heliospheric simulations. • The method performs well on tests using the Cone Model. However there is some sub-MHD grid size variation in the locations of the shock and downstream points. • The approach will be further tested on multiple shocks in future MHD simulations. • The method will further be tested by comparing simulated CME events against observations.