Transcript In both cases we want something like this: COSMICAL MAGNETIC FIELDS THEIR ORIGIN AND THEIR ACTIVITY BY E.

In both cases we want something like this:
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COSMICAL
MAGNETIC FIELDS
THEIR ORIGIN AND
THEIR ACTIVITY
BY
E. N. PARKER
CLARENDON PRESS . OXFORD
1979
Space
Weather
“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
Sun
Corona
• Test of CISM
interactive dual line
of concept
• New product in the
empirical model line
Solar
Wind
MagSphere
IonoSphere
Need for better
1-to-3 day
CME
forecasts achieved
Flares
SEPs
Shock
Arrival
Rad.
Ap, Dst
Electron
Profile
CISM Empirical-Based, Forecast Models Program
• 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
CME
Sun
Expansion
Propagation
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•
•
•
•
•
•
Sun/Corona
Zhang data
Initial size ~ InitialJieheight
~ 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
Sun
Geometrical Dilation +
Radial Expansion Phase
r(t)
ICME
Pre-CME
Growth
Phase
350
300
250
200
1 AU
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.
Solar Wind Speed (km/s)
Ambient Medium
Slow Solar Wind
150
100
50
50
100
Distance in Rs
150
200
Constraints on Interplanetary CME
Propagation
1400
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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1000
800
600
400
200
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100
150
200
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
80
Accelerate
Vexp = 0.266 Vcme – 71.61
60
40
Decelerate
20
350
400
450
500
550
600
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)
1000
800
600
The Shape Fits
400
200
Gopalswamy
Template
50
100
150
200
Reiner
Template
1400
1200
1000
drag  Cd ρ (V-Vsw)2 Standard Form
800
Observed
600
400
200
50
100
150
200
Equations as Expressed in Mathematica
1400
1200
1000
800
600
400
200
Baseline Case
w/Magnetic Buoyancy
No Magnetic Buoyancy
Magnetic Buoyancy Fits ReinerTemplate Better
50
100
150
200
Equations as Expressed in Mathematica
1400
1200
No Virtual Mass
1000
800
600
Baseline Case
w/Virtual Mass
400
200
Virtual Mass Fits Gopalswamy Template Better
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100
150
200
2
Cd = 2
1.5
1
Baseline Case
0.5
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100
150
200
1000
1400
Baseline Case
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800
1000
600
800
Cd = 2
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400
400
200
200
Cd = 2 fails the Reiner Template
and the Gopalswamy Template
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50
100
100
150
150
200
200
0.14
0.12
Front-to-Back Thickness in AU
0.1
0.08
Typical Value at 1 AU ~ 0.2
0.06
0.04
0.02
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100
150
200
Field and Density at 1 AU
Baseline
Observed
Field
9.4 nT
~13 nT
Density
13.7 cm-3
~11 cm-3
3
10, not 3, is the desired number
100
2.5
36 km/s at 1 AU
Comp. 108 km/s by Owen’s Formula
80
60
2
40
1.5
Model-Predicted Solar Latitude Width
Relative to Initial Width
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100
150
20
Expansion Velocity km/s
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200
100
300
Jie Zhang data
250
CME Acceleration
m/s2
200
150
Acceleration Agrees
100
50
2.5
5
7.5
10
12.5
15
17.5
20
150
200
1500
10
1250
8
1000
6
Tradeoff
Reduced Speed
Range between
density ratio and
As Observed
inflation factor:
N/B|1AU = 116 η/(f Bo)
(Baseline)
750
4
500
250
Variation with Bo (in Gauss)
50
1200
1000
800
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150
200
1000
0.4
10
(Baseline)
800
0.7
6
(Baseline)
Density at 1 AU = 45
600
2.0
3
600
400
400
200
4.0
Density at 1 AU = 70
cm-3
200
Variation with Inflation Factor (f)
Variation with Density Ratio (η)
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150
200
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150
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300
Accelerate
Solar Wind
Slow Riser
250
200
150
Decelerate
100
50
50
Bo = 6 Gauss as in Baseline
f=7
Density Ratio = 4
Cd = 1000 and Constant
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150
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