In both cases we want something like this:

COSMICAL MAGNETIC FIELDS THEIR ORIGIN AND THEIR ACTIVITY BY E. N. PARKER CLARENDON PRESS. OXFORD 1979 “It cannot be emphasized too strongly that the development of a solid understanding of the magnetic activity, occurring in so many forms in so many circumstances in the astronomical universe, can be achieved only by coordinated study of the various forms of activity that are accessible to quantitative observation in the solar system.” Space Weather Space Weather

Test of CISM interactive dual line of concept New product in the empirical model line Sun Corona Solar Wind Mag- Sphere Iono- Sphere CISM Physics-Based, Numerical Models Program FlaresSEPs Shock Arrival Rad. Ap, Dst Electron Profile CISM Empirical-Based, Forecast Models Program Need for better 1-to-3 day CME forecasts achieved

Chen: First analytical sun-to-earth expansion-propagation model Gopalswamy: Empirical quantification of CME deceleration Reiner: Constant drag coefficient gives wrong velocity profile Cargill: Systematic numerical modeling of drag problem Owens/Gosling: CME expansion continues to 1 AU and beyond

A CME is a bounded volume of space (i.e., it has a definite position and shape, both of which may change in time) The CME volume contains prescribed amounts of magnetic flux and mass, which remain constant in time but vary from one CME to another. The forces involved are the sum of magnetic and particle pressures acting on the surface of the CME. The volume that defines a CME expands under excess pressure inside compared to outside, and it rises under excess pressure outside below compared to above (generalized buoyancy). The life of a CME for our purpose starts as a magnetically over-pressure, prescribed initial volume (e.g., by sudden conversion of a force-free field to non-force free) Expansion, buoyancy and drag determine all subsequent dynamics

CME Propagation Expansion Sun CME

Sun/Corona Initial size ~ Initial height ~ 0.05 Rs Ambient B field = 1.6 Gauss (falls off as 1/r 2 ) Ambient density =2.5x10 9 protons/cm 3 (falls off hydrostatically with temperature 7x10 5 K) Speed range: sub-ambient to > 2000 km/s Acceleration: ~ outer corona; 200 m/s 2 typical in inner corona (up to 1000 m/s 2 ) (solar gravity = 274 m/s 2 ) Problem of “slow risers” Three phases of CME dynamics Jie Zhang data

Sun Pre-CME Growth Phase Inflationary Phase ICME r(t) Geometrical Dilation + Radial Expansion Phase

Solar Wind Speed (km/s) 1 AU Distance in Rs Ambient Medium Slow Solar Wind Hydrodynamic solar wind with Tcorona= 6x10 5 K,  =1.1, density at 1 AU=5/cc Density matched to hydrostatic value with n=3x10 8 /cc at 1.5x10 5 km height and T=7x10 6 K and constant. Densities matched at 25 Rs. Parker B field with B=5 nT at 1 AU.

Constraints on Interplanetary CME Propagation Gopalswamy et al., GRL 2000: statistical analysis of CME deceleration between ~15 Rs and 1 AU Reiner et al. Solar Wind : constraint on form of drag term in equation of motion drag  Cd ρ (V-Vsw) 2 Standard Form Observed

Constraints on ICME Parameters at 1 AU Vršnak and Gopalswamy, JGR 2002: velocity range at 1 AU << than at ~ 15 Rs Owen et al. 2004: expansion speed  ICME speed; B field uncorrelated with speed; typical size ~ 40 Rs Lepping et al, Solar Physics, 2003: Average density ~ 11/cm 2 ; average B ~ 13 nT Accelerate Decelerate Vexp = Vcme – 71.61

Equation for Expansion: Pressure Inside – Pressure Outside = (Ambient Mass Density) x (Rate of Expansion) 2 Equation for Acceleration: (Mass of CME + “Virtual Mass”) x Acceleration = Force of Gravity + Outside Magnetic Pressure on Lower Surface Area – Same on Upper Surface Area + Ditto for Outside Particle Pressure – Drag Term Input Parameters: Poloidal Magnetic Field Strength (Bo); Ratio of density inside to outside (η); Drag Coefficient (Cd); Inflation Expansion Factor (f) Equations as Expressed in Mathematica

Bo = 6 Gauss, η = 0.7, f = 10, Cd = 2 Tanh(β) Gopalswamy Template drag  Cd ρ (V-Vsw) 2 Standard Form Observed Reiner Template The Shape Fits

Baseline Case w/Magnetic Buoyancy No Magnetic Buoyancy Magnetic Buoyancy Fits ReinerTemplate Better Equations as Expressed in Mathematica

Baseline Case w/Virtual Mass No Virtual Mass Virtual Mass Fits Gopalswamy Template Better Equations as Expressed in Mathematica

Baseline Case Cd = Cd = 2 fails the Reiner Template and the Gopalswamy Template Baseline Case Cd = 2

Front-to-Back Thickness in AU Typical Value at 1 AU ~ 0.2 Field and Density at 1 AU BaselineObserved Field9.4 nT~13 nT Density13.7 cm -3 ~11 cm -3

Model-Predicted Solar Latitude Width Relative to Initial Width 10, not 3, is the desired number Expansion Velocity km/s 36 km/s at 1 AU Comp. 108 km/s by Owen’s Formula CME Acceleration m/s 2 Jie Zhang data Acceleration Agrees

Variation with Bo (in Gauss) 6 (Baseline) Reduced Speed Range As Observed Variation with Density Ratio (η) 0.7 (Baseline) Density at 1 AU = 70 cm Variation with Inflation Factor (f) 10 (Baseline) 6 3 Density at 1 AU = 45 Tradeoff between density ratio and inflation factor: N/B| 1AU = 116 η/(f Bo)

Slow Riser Solar Wind Bo = 6 Gauss as in Baseline f = 7 Density Ratio = 4 Accelerate Decelerate Cd = 1000 and Constant