Magnetic Modeling of CME Progenitors

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Magnetic Modeling of CME Progenitors

• Ying Zhu1
• Advisor
• Dr. David Mckenzie2
• Collaborator
• Adria Updike2
• 1Carroll College, Helena, MT
• 2Solar Physics Group, MSU Bozeman, MT

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Introduction

• First,
• why do we care?
• Answer Space Weather Effects upon
  the Earth caused by our Sun

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Consequences
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Continue

• Second,
• whats our goal?
• Answer looking for a signature that links
  the geoeffectiveness of a given interplanetary
  cloud to the kind of source which produced it,
  so we can prepare for its future happenings

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Approach to This Study

• From the Sun
• Study the original sources of ejecta before they
  launch (CMEs)
• Reconstructing the Suns magnetic fields B
• Measuring ejection angles

• Near the Earth
• Collecting information of the given
  interplanetary clouds (ICMEs), such as cloud
  densities, temperatures, DST, magnetic fields
  intensities with directions and etc

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And Then We compare these two sets of data
(Sun and Earth) and seek a correlation between
our models.
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Reconstructing/Extrapolating The Suns Magnetic
Field

• To understand a variety of solar phenomena, we
  need the information of the strength and
  configuration of the magnetic field in the solar
  chromosphere and corona.

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A Boundary Value Problem

• To compute the magnetic field in the half space
  above the photosphere using the photospheric
  observations as boundary conditions
  (Alissandrakis)

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Assumptions

• Extrapolating the magnetic field in the upper
  layers of the solar atmosphere
• The field vanishes at infinity very far from
  the photosphere
• Electric current is parallel to the field
  (force-free magnetic field, i.e., ? is a
  constant)
• ? ? B ?B

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Mathematical Formulations

• Basic equations
• B ? ? ? ? (P IZ) ? ? (T IZ)
• T ?P
• ?2P - ?2P

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By demanding the solution to be bounded as z ? ?,
we get the general solution from the above
equations as follows

• Where k kx lx ky ly , k2 kx2 ky2,
• x x lx y ly, and kx , ky ? 0 (Nakagawa
  Raadu)

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Bk s are the Fourier coefficients of the
observed BZ (x, y, z 0), i.e., the boundary
conditions (Nakagawa Raadu)
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Thus, the components of the magnetic field become

• (Nakagawa Raadu)

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From the equations

• we can determine the topology of the magnetic
  fields, which depends on the value of ?, since
  the twist angle ? is given by (Nakagawa Raadu)
• tan ? ? / ?,
• where ? (k02 - ?2)1/2
• k0 cos ?
• The angle by which a magnetic line of force
  intersects the contour of Bz

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A larger ? Leads to A More Twisted Magnetic
Field Examples from computer simulations

• 06-Oct-1997 ? 0

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Examples

• 12-May-1997 ? -0.029

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Angle Measurement of Ejecta from The Sun

• Pre Angles in target locations with respect to
  the Suns Equator for Levels 4, 7 and 10 before
  the ejections (Level 0 is the photosphere.)
• Post Angles after launching before reaching
  the Earth, measured from the Earth with
  projection to the sky
• Axis Angles of the overall sigmoid structures
  of ejecta, i.e., the angles of sigmoid axis
• Locations where ejecta launched from the Sun

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Getting Angles One Example6-Oct-1997 ? 0
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2-D Demonstration for Pre Measurement
North
Angles for Pre
Suns Equator
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Our Data 1. Angle differences are adjusted
(assuming smaller differences)2. RS - Reversed
Sigmoid 3. All angles are in degrees
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Spearmans (rho) Rank Order Correlation
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Correlation Plots
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Interpretations and Conclusions

• Anti-correlation between the initial angles Pre
  and interplanetary angles Post
• - contradictory to what we expected
• The larger the initial angles (Pre),
• the less positive the changes of angles
• (Post-Pre) and vice versa
• We are unable to give a legitimate explanation
  for their anti-relationships, and thus cannot
  offer an approach to predict the directions of
  the ejecta to the Earth at this moment

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Other Attempts to Determine and Understand
Correlations

• Alternative One
• Difference (Pre, Post) vs. Transit time
  (explain)
• Difference (Pre, Post) vs. Latitude of CME
  (explain)
• Difference (Pre, Post) vs. Field intensity,
  cloud radius, density, DST and others

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Alternative TwoUsing rejecting
null-hypothesis to find correlationsSign of
Difference (Pre, Post) vs. Sigmoid Type
(S/RS)Rejected at the 34.238 Confidence Level
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Pre7 s North/South vs. Posts North/SouthRejecte
d at the 90.060 Confidence Level
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Pre7 s West/East vs. Posts West/EastRejected
at the 95.958 Confidence Level
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Interpretations

• Sign of difference (Pre, Post) vs. Sigmoid
  testing shows no correlation between the type of
  sigmoid (S or RS) and the sign of angle
  differences (positive or negative).
• North/South and West/East studies show no
  correlation between the initial angles direction
  and interplanetary angles direction, confirming
  the previous study done by Canfield, Leamon .
  Pevtsov.

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Alternative Three

• Assuming constant ?s throughout the magnetic
  fields space might cause some inaccuracies in
  the measurement of angles. For instance

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July the 14th, 2000

• ? -0.015

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A More Complex Modelby Assuming A Non-Uniform ?
Field (Yan et al.)
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To adjust our measuring method,

• We take the averages of Pre and Axis, and then
  correlate with Post or Difference (Pre, Post)

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Anti-correlation still exists, and we dont know
why. Post vs. Axis
Post vs. Average

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Strengths and Weaknesses of Our Model

• Superior to the potential field (? 0)
  assumption
• Assuming constant ? field lessens our computation
  efforts, since it is the only case that can be
  done numerically (FFT) from observational data
  (Alissandrakis), but this is offset by less
  accurate angle measurement compared with more
  advanced models (? ? const.)

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Continue

• Inaccuracies arise from other factors, such as
  the unobvious patterns of magnetograms, and etc

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Future Endeavors

• Using more complicated models by assuming a
  non-constant ? field
• Devising better methods for matching magnetic
  field lines with the real magnetograms
• And of course, including more events for data
  analysis

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Reference

• Alissandrakis, C.E. 1981, Astron. Astrophysics.
  100, 197.
• Canfield, R.C., Leamon R.J. and Pevtsov A.A.
  2002, J. Geophys. Res., 107, 1234.
• Nakagawa, Y. and Raadu M.A. 1972, Solar Phys.,
  25, 127.
• Yan, Y. , et al. 2001, Astrophys. J., 551, L115.