1. Lecture 16 Simulating from the Sun to the Mud

2. Space Weather Modeling Framework – 1 [Tóth et al., 2007] The SWMF allows developers to combine models without completely rewriting them. Currently there are 9 modules in the SWMF at CCMC. Solar corona model (SC) - solar surface to 20Rs. –Cartesian -24R S <x,y,z<24R S –Magnetic field from magnetograms –Model of temperature and mass density at the Sun to give realistic results at 1AU –Line-tying at the solar surface. –Only one SC model. –Flow at the outer boundary is super fast. Eruptive event generator (EE) – used to model CMEs. –Embedded in the corona. –Represented as a boundary condition or perturbation on solar coronal model.

3. Space Weather Model Framework - 2 Inner heliosphere (IH) – Describes the heliosphere from the outer boundary of SC up to several astronomical units. –Extends from 20R S –Box -240R S <x,y,z<240R S –Uses BATS-R-US with Cartesian grid –Inner boundary from SC component. –Upstream boundary is super fast –Sets boundary conditions for magnetosphere component. Solar energetic particles (SP) – One-dimensional magnetic field lines. Transport equations describe the acceleration and spatial diffusion of particle distributions in fields obtained from SC and IH.

4. Space Weather Modeling Framework - 3 Global magnetosphere (GM) – Describes the Earth’s magnetosphere and is driven either by upstream satellite data or imbedded into the IH module of SWMF. –32R E dayside to 224R E nightside, -64R E <y,z<64R E –BATS-R-US –Inner boundary at 2.5R E. –Inner boundary conditions determined by Ionosphere Electrodynamics component (IE) which provides the electric potential at the inner boundary. – Pressure and density corrections from Inner Magnetosphere (IM) component. –Used to “nudge” the MHD solution toward more accurate inner magnetosphere values. –Provides field aligned currents to the IE component. –Provides the IM component with field line volume, average density and pressure.

5. Space Weather Modeling Framework - 4 Inner magnetosphere (IM) – Represents the inner region of the magnetosphere and is modeled by the RCM. –Solves equations describing the drift motion of keV ions and electrons. –The IM module obtains the information on closed field lines from the GM and electrostatic potential from IE –Provides pressure corrections back to GM (nudging).

6. “Nudging” (De Zeeuw et al., 2006)

7. Upper Atmosphere Upper atmosphere (UA) – Global Ionosphere- Thermosphere Model (Ridley et al., 2006). –Multi-species non-hydrostatic hydrodynamics – viscosity, thermal conduction, photochemistry, chemical reactions, ion-neutral friction, coupling of the ions to electric field, solar radiation. –Obtains gradient of potential from IE. This gradient is used to drive ion motion. –Auroral precipitation used to calculate ionization rates. –Provides Hall and Pedersen conductivities to IE – from electron density and integrated along field lines.

8. Space Weather Modeling Framework - 5 Radiation belt (RB) – The RB module is implemented using the Rice Radiation Belt Model. –Solves adiabatic transformation of phase space density on a 2D spherical grid. –Does not return information to other modules. Control and Coupling –Control module determines the overall time-stepping of the code, parallel decomposition of the models, the initiation and termination of runs and saving of restart files. –Determines when coupling should occur, how it happens, does grid interpolation, passes messages between components and synchronization.

10. Halloween Storm Simulation – The Sun Use 90 th order spherical harmonic MDI synoptic map centered around time of eruption. Use rotating coordinate system – include Coriolis and centrifugal acceleration in MHD. Highly refined grid – 3X10 -3 R S in active region. Use local time stepping to get steady state model (25000 steps) Green contours for positive B r, neutral lines dashed, active region that caused CME blue circle,

11. Initial Condition for the Heliosphere Since SC has converged to steady state only IH needs to run. Flow is superfast so steady state for IH is fast (2000 steps). During time accurate part of calculation – go to inertial frame with Earth in –XZ half plane. Cell sizes ½ to 1R S out to 60R s – largest cell 4R S. Separating IH and SC domains gives efficiency – SC lots of grids but small, IH huge but course grid.

12. Generating Eruptions Started simulation 2 days before major eruption to include effect of smaller CMEs in pre-conditioning the heliosphere. Inserted flux rope in EE component at location of eruption.

13. Switch to Time Dependent Simulation 20 minutes after insertion of flux rope CME is at 5.5R S and moving at 2100 km/s. When the CME reaches 20R s it is moving at 1500km/s as observed. Grid coarsened by factor of 4. Reached Earth at 0430 Oct. 28, 2003. Refined the active region back to 3X10 -3 R S for launch of second CME. Very time consuming so developed partial steady model with only part of simulation advancing. Temperature in simulated CME reached 10 9 K-included artificial cooling with limit of 5X10 7 K.

14. Propagation Through the Heliosphere-1 Isosurfaces where density is 3 times ambient Color coding is velocity Gray lines are IMF

15. Propagation Through the Heliosphere -2 First CME just missed the Earth Second CME –Arrived at Earth after 17.5 hours about 1.8 hours earlier than observed. –Simulation gave 1200km/s and 15nT -25nT increases. –Observations gave 2000km/s and 40nT changes. –Moved the Earth by 9 0 along its orbit so it would meet the strongest part of CME (1800km/s and 40nT). –Shifted the simulation time by 3.4 hours.

16. Comparison with Observations Data black, original simulation red, moved simulation green. Move improves fit of density and velocity. Magnetic field is bad fit.

17. Interaction of CME with the Earth Use the shifted solar wind. BATSRUS has minimum resolution of 1/4R E. IM/RCM component runs on a nonuniform latitude- longitude grid with 78X48 cells with 150 energy bins. IE/RIM grid has 1 o resolution in latitude and longitude. The UA model has 40 altitude levels between 95km and 600km. Note since there is no feedback between the heliosphere and the solar corona the SC component has only a small role – it is the most expensive part of the calculation. ACE data at L1 augmented by Geotail data were used for the control run – the Geotail data were needed because of a problem with ACE density.

18. Magnetospheric Results One hour after the shock arrives at Earth. Black solar wind flow. Colored tubes last closed field lines. Color contours are current density. Dark red is the 100nPa isosurface.

19. Large ring current – essential for driving region 2 currents. Significant differences Sun to Mud Simulation and Control Simulation

20. Observed and Simulated White Light Images Density was used as a proxy for the image. In both cases the difference before and ~one hour after eruption is plotted. At this time the positions are similar. Comparison of solar wind observations with the simulation – fluid parameters match beyond Earth but magnetic field does not.

21. (top) AMIE polar cap potential black, control simulation red, solar simulation green. (bottom) Dst- observed black. Agreement is very good in control case and solar simulation early. Ionosphere and Ground Magnetic Comparison

22. Ionospheric Density Champ satellite data black, AMIE results red and solar simulation green. Agreement is reasonable.

23. What did they Learn For the next decade the MHD models will be the primary tool for analysis of data. –Modeling frameworks will allow physics not in MHD to be included in the simulations. –There are now three framework systems available (SWMF, NCAR, CISM) Initiation of CME is major unsolved problem – I got the same impression at the CISM meeting this week. Preconditioning of heliosphere important.