50100150200 250 500 750 1000 1250 1500 in both cases we want something like this:
Post on 21-Dec-2015
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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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0.5
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
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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
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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