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CISM Science Seminar Oct. 14, 2004. Fluid Dynamics of CME Expansion and Propagation. George Siscoe. 1. Statement of problem: Distinction between CME formation and CME propagation. 2. Why is this problem interesting and important?. 3. Relevance to CISM.

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## CISM Science Seminar Oct. 14, 2004

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**CISM Science Seminar**Oct. 14, 2004 Fluid Dynamics of CME Expansion and Propagation George Siscoe 1. Statement of problem: Distinction between CME formation and CME propagation 2. Why is this problem interesting and important? 3. Relevance to CISM 4. Background (Gopalswamy, Chen, Cargill, Reiner, Owens, Gosling) 5. Approach (assumptions and geometry) 6. Constraints-templates-initial conditions 7. Operative Equations, Model Variables 8. Baseline model 9. Variation with parameters 10. Problem of slow risers 11. Implications and applications**Statement of Problem**Space Physics Problem: Describe the motion and expansion of CMEs from launch in the corona to 1 AU and beyond. Space Weather Problem: Predict arrival time, speed, etc. at 1 AU of ICME from solar and coronal data**1500**1250 1000 750 500 250 50 100 150 200 In both cases we want something like this:**Distinction between CME formation and CME propagation**Emphasize key role of generalized buoyancy**Space**Weather Why is this problem interesting and important? 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.”**CISM Physics-Based, Numerical Models Program**Solar Wind Mag- Sphere Iono- Sphere Sun Corona CISM Empirical-Based, Forecast Models Program Need for better 1-to-3 day CME forecasts achieved Shock Arrival Rad. Ap, Dst Electron Profile Flares SEPs Relevance to CISM • Test of CISM interactive dual line of concept • New product in the empirical model line**Background**Chen,Gopalswamy, Reiner, Cargill, Owens, Gosling • 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**Model Assumptions**• 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**CME Propagation Sun Expansion Model Geometry**Jie Zhang data**Constraints-Templates-Ambient and Initial Conditions Sun/Corona • Initial size ~ Initial height ~ 0.05 Rs • Ambient B field = 1.6 Gauss (falls off as 1/r2) • Ambient density =2.5x109 protons/cm3 (falls off hydrostatically with temperature 7x105 K) • Speed range: sub-ambient to > 2000 km/s • Acceleration: ~ outer corona; 200 m/s2 typical in inner corona (up to 1000 m/s2) (solar gravity = 274 m/s2) • Problem of “slow risers” • Three phases of CME dynamics**Inflationary**Phase Geometrical Dilation + Radial Expansion Phase r(t) Sun ICME Pre-CME Growth Phase Three Phases of CME Expansion**350**300 250 200 Solar Wind Speed (km/s) 1 AU 150 100 50 50 100 150 200 Distance in Rs Ambient MediumSlow Solar Wind Hydrodynamic solar wind with Tcorona= 6x105 K, =1.1, density at 1 AU=5/cc Density matched to hydrostatic value with n=3x108/cc at 1.5x105 km height and T=7x106 K and constant. Densities matched at 25 Rs. Parker B field with B=5 nT at 1 AU.**1400**1200 1000 800 600 400 200 50 100 150 200 drag Cd ρ (V-Vsw)2 Standard Form Observed 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 10 2003: constraint on form of drag term in equation of motion**Accelerate**80 Vexp = 0.266 Vcme – 71.61 60 Decelerate 40 20 350 400 450 500 550 600 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/cm2; average B ~ 13 nT**Equations as Expressed in Mathematica**Operative Equations, Model Variables 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)**1000**800 600 400 200 50 100 150 200 Reiner Template 1400 drag Cd ρ (V-Vsw)2 Standard Form 1200 1000 Observed 800 600 400 200 50 100 150 200 Baseline Case Bo = 6 Gauss, η = 0.7, f = 10, Cd = 2 Tanh(β) The Shape Fits Gopalswamy Template**1400**1200 1000 800 600 Equations as Expressed in Mathematica 400 200 50 100 150 200 Need for Magnetic Buoyancy Baseline Case w/Magnetic Buoyancy No Magnetic Buoyancy Magnetic Buoyancy Fits ReinerTemplate Better**1400**1200 1000 800 600 Equations as Expressed in Mathematica 400 200 50 100 150 200 Need for Virtual Mass No Virtual Mass Baseline Case w/Virtual Mass Virtual Mass Fits Gopalswamy Template Better**2**1.5 1000 1 1400 800 1200 0.5 600 1000 800 50 100 150 200 400 600 200 400 200 50 100 150 200 50 100 150 200 Need for Variable Drag Coefficient Cd = 2 Baseline Case Baseline Case Cd = 2 Cd = 2 fails the Reiner Template and the Gopalswamy Template**0.14**Front-to-Back Thickness in AU 0.12 0.1 0.08 0.06 0.04 0.02 50 100 150 200 Other Properties of the Baseline Case Typical Value at 1 AU ~ 0.2**3**10, not 3, is the desired number 36 km/s at 1 AU Comp. 108 km/s by Owen’s Formula 100 2.5 80 Jie Zhang data 60 2 40 Expansion Velocity km/s 1.5 Model-Predicted Solar Latitude Width Relative to Initial Width 20 50 100 150 200 50 100 150 200 300 250 CME Acceleration m/s2 200 150 100 50 2.5 5 7.5 10 12.5 15 17.5 20 Inflation, Expansion, and Acceleration Acceleration Agrees**1500**1250 1000 Reduced Speed Range As Observed 750 500 Variation with Bo (in Gauss) 250 50 100 150 200 1000 1200 800 1000 800 600 600 400 400 200 200 Variation with Inflation Factor (f) Variation with Density Ratio (η) 50 100 150 200 50 100 150 200 Variation of ICME Velocity with Input Parameters 10 8 6 (Baseline) Tradeoff between density ratio and inflation factor: N/B|1AU = 116 η/(f Bo) 4 10 (Baseline) 0.4 6 0.7 (Baseline) Density at 1 AU = 45 2.0 3 4.0 Density at 1 AU = 70 cm-3**350**300 250 200 150 100 50 Accelerate 50 100 150 200 Decelerate Problem of "Slow Risers" Solar Wind Slow Riser Bo = 6 Gauss as in Baseline f = 7 Density Ratio = 4 Cd = 1000 and Constant**Some Conclusions**1. Inflation, expansion, buoyancy and drag can account qualitatively for many aspects of CME propagation. 2. Must include variable drag coefficient and virtual mass 3. Expansion too weak in present formulation 4. In consequence, inflation inconsistent with initial expansion 5. Front-to-back thickness too small 6. Expansion speed at 1 AU too small 7. Slow risers a different breed of CME 8. Opportunities here for joint investigations with numerical models

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