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In both cases we want something like this:

COSMICAL MAGNETIC FIELDS

THEIR ORIGIN ANDTHEIR ACTIVITY

BY

E. N. PARKER

CLARENDON PRESS . OXFORD1979

“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.”

SpaceWeatherSpace

Weather

• Test of CISM interactive dual line of concept

• New product in the empirical model line

Sun CoronaSolarWind

Mag-Sphere

Iono-Sphere

CISM Physics-Based, Numerical Models Program

Flares SEPsShockArrival

Rad.Ap, Dst

ElectronProfile

CISM Empirical-Based, Forecast Models Program

Need for better1-to-3 day

CMEforecasts 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

PropagationExpansionSun

CME

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

Jie Zhang data

Sun

Pre-CMEGrowthPhase

InflationaryPhase

ICME

r(t)

Geometrical Dilation + Radial Expansion Phase

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So

lar

Win

d S

pee

d (

km/s

)

1 A

U

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.

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

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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/cm2; average B ~ 13 nT

Accelerate

Decelerate

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Vexp = 0.266 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)

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Gopalswamy Template

drag Cd ρ (V-Vsw)2 Standard Form

Observed

Reiner Template

The Shape Fits

Baseline Casew/Magnetic Buoyancy

No Magnetic Buoyancy

Magnetic Buoyancy Fits ReinerTemplate Better

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Equations as Expressed in Mathematica

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Baseline Casew/Virtual Mass

No Virtual Mass

Virtual Mass Fits Gopalswamy Template Better

Equations as Expressed in Mathematica

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Baseline Case

Cd = 2

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1

1.5

2

Cd = 2 fails the Reiner Template

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and the Gopalswamy Template

Baseline Case

Cd = 2

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0.02

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0.1

0.12

0.14

Front-to-Back Thickness in AU

Typical Value at 1 AU ~ 0.2

Field and Density at 1 AU

Baseline Observed

Field 9.4 nT ~13 nT

Density 13.7 cm-3 ~11 cm-3

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1.5

2

2.5

3

Model-Predicted Solar Latitude Width Relative to Initial Width

10, not 3, is the desired number

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Expansion Velocity km/s

36 km/s at 1 AUComp. 108 km/s by Owen’s Formula

2.5 5 7.5 10 12.5 15 17.5 20

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CME Acceleration m/s2

Jie Zhang data

Acceleration Agrees

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Variation with Bo (in Gauss)

6(Baseline)

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10

4Reduced Speed Range

As Observed

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Variation with Density Ratio (η)

0.7(Baseline)

0.4

2.0

4.0 Density at 1 AU = 70 cm-3

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Variation with Inflation Factor (f)

10(Baseline)

6

3Density at 1 AU = 45

Tradeoff between density ratio and inflation factor:N/B|1AU = 116 η/(f Bo)

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Slow RiserSolar Wind

Bo = 6 Gauss as in Baselinef = 7Density Ratio = 4

Accelerate

Decelerate

Cd = 1000 and Constant