# Presentation: 494710

## Interpreting STEREO observations of 3D CMEs

**Sarah Gibson, Joan Burkepile, and Giuliana de Toma**
- HAO/NCAR

- Sarah Gibson

- STEREO conference, Paris, March 19, 2002

- Paul Charbonneau

**Notes:**
STOP BEFORE EACH NEW VG - explain what it shows. 

Some connection to Black holes?

I will use CMEs to refer to Coronal Mass Ejection throughout 

This  picture shows ONE VIEW of CME, with twisted structure

Describe the picture - white light scattered off of coronal electrons, 
density indicator: comment that our observations are limited by the fact 
we only see projections. 

Motivation: This twistedness a key to dynamic evolution of CME - helps us 
Potentially with both when erupt, and why!   - MODELS 

Our model captures the two basic features (3-d and twisted! ) of the CME  in 
a physically self-consistent manner 

## Outline and motivation

**STEREO will provide multiple simultaneous views**

**The CME is a 3D beast**

**Data analysis tools for STEREO analysis need to be developed**

**Conclusions**

**Our approach: forward modeling**

**3D density models of CME**

**Simple “ice cream cone” model **
**Variation on full 3d MHD model (*****Gibson and Low, 1996*****)**

**Requires an efficient means of searching model space**

**Genetic algorithms**

**Notes:**
First of all I will show observations that will show 
       different views of CME, different observables (density/temperature)
       different lines of sight (limb/disk) --> demonstrate 3-d 

       twisted structures and their relation to CMEs (including sigmoids, or S-shapes) 
      (help for prediction of earth effects, geomagnetic storms?) 

Next I will describe magnetic field modeling - why the magnetic field? 

       explain flux freezing.  nearly perfectly conducting plasma --> 
       plasma can only move along magnetic field lines.  If magnetic field 
       is dominant, then this means that the field is fixed and plasma moves 
       along them like in Pooh toy 

Corona is like this (closed field structures show up as bright structures 
(streamers, active regions) material is trapped) 

 If plasma forces (gas/dynamic) dominate, then field is pulled along/around
 with/by the plasma (can't demonstrate without  breaking the toy).  Photosphere 
gas pressure dominates (field elements moved around).  Further out the wind 
takes over and (essentially pulls the magnetic field lines out radially.) 

In a CME or related structures, it means that the plasma morphology is 
giving us important clues about the magnetic field structure, i.e. that it is 
twisted.  Important because we can't directly measure the field
But since plasma observations are so complicated(varying with density,
 temperature, l.o.s.) we really need field models to get a handle on 
interpreting plasma data. 

Next I will talk about basic models of magnetic field in CMEs 

       slinky (show it!) and the spheromak (spherical version of slinky commonly encountered in fusion research) 

       the latter we will compare to 3-d observations and then make conclusions regarding its usefulness and future directions for modeling 

Finally I will conclude by commenting on the big picture of why we should care about twisted fields anyway 

## Coronal Mass Ejections 

- Episodic expulsions of plasma  >~ 1015 grams each

**Notes:**
White light limb most standard view

White light density sensitive only

dramatic eruptions - significant fraction of solar wind (few percent) 

 CME movie  - comment on size compared to sun, energetic particles hitting spacecraft  (mention last week's biggies), and so essentially earth (L1 most of the way to earth).  One of the space-weather effects  - radio and Xrays arrive in 8 minutes,  and maybe 2-3 times a cycle this can overload cell phones - also X-rays mess with ionosphere, cause short-wave fadeouts and drag on  satellites) Then energetic particles (accelerated by flare) travelling at reasonable fraction of speed of light (arrive 20 mins -- continue for days).  For these (solar protons) we have basically no warning (although this is what sigmoids are all about mention) - luckily the closed part of earth's magnetosphere shields us from the worst effect of these (all those spacecraft electronics and astronauts on EVA might be at risk - and cumulative radiation could be bad).  But get out of the earth's magnetosphere, say far side of moon,  or mission to mars -possible serious effects.  Also solar protons hit the poles, shortwave disturbance, wide-spread blackout of   communmications (polar cap absorption event).   NOTE because high energy particles travel along field lines, most effective if come from West limb. 

## White light CMEs

- 3-Part structure

**Notes:**
Characteristic 3 part structure- especially for CMEs seen near the limb

first show how the CMEs are 3-d.  Mention that movie was of coronagraph -easiest 
way to observe CME, at the limb.  But  even there the CME structures vary, e.g.
 3-part (streamer precursor days, CME hours)(most important) and U shape.   
(dont identify Ushape with core premanturely) But what about the ones that hit 
us? Show halo movie. 

## White light CMEs

- U-shape

**Notes:**
Also see U shapes- some think these are disconnected structures, but we will present alternative interpretation

## White light CMEs

- Halo

**Notes:**
CMEs coming right at us, or away from us - from this can’t distinguish

## CMEs (and associated phenomena) in emission

- “Cold” emission ~ 104 K -- H-alpha): prominence eruption

**Notes:**
limb - white light density sensitive only and occulted disk, can't see source
emission - temperature and density
Prominence = white light core = filaments on the disk
H-alpha=5-10000K  (Halpha=first Balmer line of Hydrogen, velocity not 
important in Halpha limb - 10 angstrom wide line)

## CMEs (and associated phenomena) in emission

- Hot emission (~ 106 K -- FeXII): Dimmings

**Notes:**
Long, but shows several things

Dimmings during eruptions - multiple times!
 Region is one with S-shape or sigmoid structure, will discuss in a minute
Density not temperature, observed in multiple temperaturs
 We will later interpret this dimming as the expansion of the cavity as seen in white light

## CMEs have a complex, 3D density and temperature structure.

- 3D complexity is well illustrated by twisted structures associated with CMES

**Notes:**
S was an indication, here’s the smoking gun - Granddaddy prominence

## Apparent twist in white light CME core

**Notes:**
The last vg showed twist in erupting prominence, now core- same thing

## Apparent braided type structure seen in filament (projected on solar disk)

**Notes:**
All the same thing! Filament - not erupting - this is important, because some people say that twist is only present during eruption.  Admittedly projection is tricky, but toggle back to the previous two slides, and compare 

## The many faces of the CME

**Notes:**
So to review- observations show CME is 3D and twisted

## STEREO mission

- The STEREO mission setup:  two identical spacecraft with identical instrument complements will move in opposite directions away from the Sun-Earth line.  Thus, the instruments will provide 2 of 3 observing angles, with the third being covered by instruments viewing along the Sun-Earth line.  The SECCHI component of the STEREO mission will include a suite of remote sensing instruments including two white light coronagraphs (COR1 and COR2) and an EUV imager (EUV1), known collectively as the Sun Centered Imaging Package (SCIP), as well as a Heliospheric Imager (HI).

**Notes:**
Only way to test this is multiple simultaneous observations of CMEs along different lines of sight

## Why use a model?

- Technique: Genetic Algorithm Based Forward Method

**How can models be related to observables?**

**For the dynamic CME, tomographic methods are of limited use**
** **
**Parameterized model allows 3-d fit to observations (assuming a good model)**

**We will consider density models <---> white light coronagraph observations**

**pB(r,********e****(r,********)**
**pB = polarized brightness**
**N****e**** = electron number density**
******) = Thomson scattering**

## Inverse method:

- Technique: Genetic Algorithm Based Forward Method

**Forward method:**

- Given a parametrized CME density model, the (matrix) integral equation can be inverted with respect to Brightness (B) or polarized Brightness (pB) observations to yield the best model parameters (if, as is usual, the model is nonlinear in its parameters, this requires for example iterative stepping in the direction of *steepest descent*).

- Density is specified from a CME model, and integrated along the line of sight to yield B or pB intensity.  This is directly compared to observations to determine a goodness of fit.  If parameter space is sufficiently searched, the best fit solution(s) can be determined.

**pB(r,********e****(r,********)**

## Technique: Genetic Algorithm Based Forward Method

**Why use a forward method?**

- 3-D coronal inverse problem fundamentally ill-posed: **observational nonuniqueness** and **model degeneracy**

**Error amplification** is intrinsic to nonlinear inversion of integral equations

- A forward technique that thoroughly searches parameter space allows **observational nonuniqueness** and **model parameter degeneracy** to be mapped out and **quantified as global error bars**
**Additional observational information**, such as white light observations along the three STEREO lines of sight or on-disk observations pinpointing the CME location and/or angular extent, **can easily be incorporated**

**Error amplification is avoided** by using the forward method

**Notes:**

Error amplification: 
Observational nonuniqueness: (multiple density solutions yielding identical B/pB projections in the plane of the sky - see e.g. Figure 6).
The problem is generally nonlinear in the model parameters leading to model degeneracy (multiple parameter sets yielding identical density solutions).

## Technique: Genetic Algorithm Based Forward Method

**Why use genetic algorithms?**

- Need a **global optimizer** to span parameter space
- Grid search or Monte Carlo method: number of evaluations ~ Nresnpar
- Example: to randomly generate METHINKS IT IS A WEASEL  ~ **10****33  ****iterations**
- Introduce **natural selection** (that is, choose a“population” of 10 random choices of 23 letters,  select the one that best matches target sentence, make new population of 10 duplicates each with one letter randomly toggled, continue):  **1240 iterations**

- Like the above example, genetic algorithms contain elements of **inheritance** (which makes search more **efficient**) and **mutation** (which helps **avoid local minima**)
- Moreover, G.A. parameter sets (the members of the population)are coded into chromosome-inspired strings: pairs of these are spliced together via a **crossover** operation, allowing some of the next population (“children”) the possibility of possessing the best of both “parents”.  This both **increases efficiency** and allows a **broader exploration of parameter space**.

- See Paul Charbonneau’s “pikaia” page for more information and a public domain genetic algorithm routine: http://www.hao.ucar.edu/public/research/si/pikaia/pikaia.html

**Notes:**

Error amplification: 
Observational nonuniqueness: (multiple density solutions yielding identical B/pB projections in the plane of the sky - see e.g. Figure 6).
The problem is generally nonlinear in the model parameters leading to model degeneracy (multiple parameter sets yielding identical density solutions).

## Technique: Genetic Algorithm Based Forward Method

**How are genetic algorithms implemented?**

- Assuming a problem where a set of model parameters determines an observable property, start with a randomly generated “population” of parameter sets
- Evaluate the goodness of fit (``fitness'') of each member of the current population (through a chi square measure with the data, for example).
- Select pairs of solutions (``parents'') from the current population, with the probability of a given solution being selected made proportional to that solution's fitness.
- Breed the two solutions selected in (2) and produce two new solutions (``offspring''), introducing elements of “crossover” and “mutation”.
- Repeat steps (2)-(3) until the number of offspring produced equals the number of individuals in the current population.
- Use the new population of offspring to replace the old population.
- Repeat steps (1) through (5) until some termination criterion is satisfied (e.g., the best solution of the current population reaches a goodness of fit exceeding some preset value).

**Notes:**

Error amplification: 
Observational nonuniqueness: (multiple density solutions yielding identical B/pB projections in the plane of the sky - see e.g. Figure 6).
The problem is generally nonlinear in the model parameters leading to model degeneracy (multiple parameter sets yielding identical density solutions).

## Density models: 1) “Ice cream cone”

- When projected in 2-D, the basic 3-D “ice cream cone” model captures the commonly observed white-light loop-cavity morphology.

**Notes:**
Coronal mass ejections (CMEs), when observed in white light, appear as two-dimensional projections of three-dimensional structures.
The most common CME morphology observed in 2-D white light coronal images is the 3-part structure of loop-cavity-core.
Coronal mass ejection “Ice cream cone” density model geometry.  The striped lines indicate the section of the cone revealed by a vertical cut through the cone.  The coronal density is enhanced in a shell bounded by two concentric spherical surfaces with radii o and I, joined to the origin by two cones with half angles o and I, such that 

i = Rc x sini

o = Rc x sino

where Rc is the distance from the origin to the center of the concentric spheres along the z  coordinate.  The interior of the cone can have a density below the ambient coronal background density to simulate a cavity .

## White light coronal observations

- March 14, 2002 white light coronagraph images, MLSO/Mark 4 (left) and LASCO/C2 (right).

**Notes:**
Coronal mass ejections (CMEs), when observed in white light, appear as two-dimensional projections of three-dimensional structures.
The most common CME morphology observed in 2-D white light coronal images is the 3-part structure of loop-cavity-core.
Coronal mass ejection “Ice cream cone” density model geometry.  The striped lines indicate the section of the cone revealed by a vertical cut through the cone.  The coronal density is enhanced in a shell bounded by two concentric spherical surfaces with radii o and I, joined to the origin by two cones with half angles o and I, such that 

i = Rc x sini

o = Rc x sino

where Rc is the distance from the origin to the center of the concentric spheres along the z  coordinate.  The interior of the cone can have a density below the ambient coronal background density to simulate a cavity .

## LASCO/C2 observed brightness

- “Ice cream cone” **model** brightness

- LASCO/C2 **observed **brightness

- Density models: 1) “Ice cream cone”

## Density models: 1) “Ice cream cone”

- Case 1: CME centered at west limb (90o), i=30o,  o=35o, Rc=4 Rsun

- Case 2: CME centered at 45o, shell density double Case 1,  i=50o,  o=55o, Rc=2.7 Rsun

**-50****o**

**Earth’s view**

**50****o**

**-50****o**

**50****o**

**Earth’s view**

**Notes:**
Two “ice cream cone” model CMEs with similar appearances from the Earth’s line-of-sight (center images), but very different views from the STEREO eyes (left/right images, +/- 50o). Case 1:  i=30o,  o=35o, Rc=4 Rsun; Case 2: i=50o,  o=55o, Rc=2.7 Rsun.  Case 1 is centered at the West limb (90o) for the Earth’s line-of-sight, and Case 2 is positioned at 45o (where 0o is the central meridian).  Case 2 shell density is a factor of two times greater than the Case 1 shell density.  Images go out to 8 Rsun

## Density models: 2) Modified MHD model

- Another way of obtaining a 3-part loop-cavity-core structure is by using a 3-D MHD model of the CME (*Gibson and Low, 1998*).  In this case, the 3-part morphology of the density distribution is physically defined by the magnetic field topology.

**Notes:**
Figure 4.   (a) white light observation of a three-part CME (August 18, 1980) from the SMM white-light coronagraph  (Illing and Hundhausen, 1986).  (b) model (Gibson and Low, 1998) reproduction of white light (pB) and (c) underlying model magnetic field lines, viewed along the CME axial flux rope.  Red and green field lines show the external field pointing in and out of the poles respectively, and blue and yellow lines are examples of twisted magnetic field within the CME.

## Theoretical description of CMEs

- Need to solve ideal magnetohydrodynamic (MHD) equations in order to
- self-consistently describe the magnetic field and its interaction with the
- coronal plasma.

- Model complexity must be sufficient to reproduce the essential
- observational complexities.

**Notes:**
Conservation of momentum
Conservation of mass (continuity equation)
Induction equation

We close the system with polytropic relation between pressure and density, 
which combined with the ideal gas law takes the place of an energy equation.

Must solve MHD- relate field, density, velocity, pressure, temperature...
 momenturm eq. , induction (E=VXB in there FAraday law), mass
continuity, and energy equation represented by ASSUMPTION of
 polytropic relation between density and pressure. 

 Non-trivial - can't throw out too much.  3-d, time dependent, gravity. 
 Model complexity must match observation complexity. 

And specifically answer dynamic CME question - how do you hurl 10^15 g of 
material out and escape sun's gravity?  - a twisted magnetic configuration 
provides the expelling energy.  Note we are not going to dwell on the question
 - our model answers it.  Rather dwell on how well the magnetic configuration 
we've chosen matches plasma observations. 

## What are spheromaks?

- Spherical, closed magnetic system containing comparable toroidal and poloidal magnetic fields generated by currents within the structure

- Images from Cantarella, et al., 1999

**Notes:**
No children’s toy of speromak!
 really deformed slinky wrapped on self and filling a spherical volume - 
topologically the same

Slinky closed on itself (show with slinky)
 expand to fill a sphere
 stretch point in middle into line (axis is important!)

comment that it is Woltjer's model of crab nebula)

2 flux ropes:  slinky - poloidal field lines wrapping around toroidal circle (see in 3 
in the cut - orange slices)

Second is less obvious - its topological source (topology hasn’t changed in 1-3!)
arose from closing slinky on itself - thus one toroidal loop encircling poloidal 
winds - in 3 by stretching out the center point into a line, this second loop now 
loops more than one time around that central axis

## MHD Model:  Gibson and Low (1998)

**Notes:**
Second view identical to gluck 
First view shows slinky looking down on it - but the axis or hole  also has 
windings around that axis

Stretch and tether it - put in photosphere (hold slinky over screen - NEW flux rope, 
not the slinky, but the toroidal windings, suspended in the atmosphere -this is 
where our prominence sits  fascinating aspect of spheromak topology!

Point out that the spheromak field, stretched and tethered, is in an otherwise open
 magnetic field, this is the basis of our MHD model

## Spheromaks

- Why do we use them to model CMEs?
- Circular cross-section: CME observations don't support linear-type structure *(Fisher&Munro, 1984; Webb, 1988; Thompson et al, 1999)** *
- Vector magnetogram observations of emerging field orientation and rotation well captured by spheromak model *(Lites et al, 1995)*
- Spheromak model solution yields plasma distributions satisfying a range of observed prominence structures and always yields a bubble-type cavity

- Spheromaks represent the spheroidal nature of CMEs better than a linear slinky.

**Notes:**
Why spheromaks rather than flux ropes? linear limited, and how do we make it
 ball-like and relate to surroundings - spheromak - I will show captures CME 
observations very well indeed.

       flux ropes are linear structure intrinsically.  CMEs aspect ratio spherical 
(filaments oriented N/S vs E/W - Webb 88 - if linear, there should  be narrower 
CMEs at limb when neutral line/filament is parallel to equator - but no.

       as we'll see gives wider range of CME types, spherical cavity

       matches emerging flux observations

## MHD Model Results

- Lites and Low, 1996

**Notes:**
NOT a CARTOON
relate field to density physically and self-consistently

"Two-flux" system - "axial flux rope" (twisted)  and "simple bipole loops"  =
 equivalent to slinky and new rope, or poloidal and toroidal - presence of 
photosphere affects how much twist is in the atmosphere

Illustrates why we are harping on our new flux rope, it’s the important one, it’s the 
one that can have winds suspended in the atmosphere, that’s where the mass sits

S shaped neutral lline

Full MHD - quantitative density --> pB, 3 part, arises from the topology - core is
 prominence sitting in the bottoms of the winds of the new flux rope, cavity is 
where mass drains out, front is interface with exterior fields (current sheet, 
density drop)

## MHD Model predictions at the limb (white light)

- SMM CME observed Aug 18, 1980, Gibson & Low model CME, viewed along CME toroidal axis

## MHD Model predictions at the limb (white light)

- SMM CME observed March 15, 1980, Gibson & Low model CME, viewed perpendicular CME toroidal axis

## MHD Model predictions at the limb (white light)

**Notes:**
ONE MODEL DID ALL THESE KINDS OF WL CMEs
 IMPORTANCE OF PROJECTION EFFECTS

## On-disk behavior - comparison to emission observations (Gibson et al., 1999; Gibson and Low, 2000)  

**Observations**

**Model (at coronal base)**

- Density

- X-ray emission

- Magnetic field

**Notes:**
DESIGNED FOR LIMB, BUT WHAT ABOUT DISK???

Dense core overlies S-shaped neutral line intrinsic to spheromak cross-section, 
cavity reproduced as axisymmetrically skewed twin dimmings, Xray intensity r
eproduced, but “blobby” because heating is polytropic and large-scale

physical quantities from SXT matchup - Field = .263- .44 G, temperature is 
1.6 - 2.9 e6, density 1.5 e8 - 3.7 e7, we do get denser and cooler material at the
 core (although blobby by nature), and beta is 3-6ish.

## Deconstructing 3D CME observations

- Three views of MHD model CME

- Axis along l.o.s

- Axis perpendicular to l.o.s

- Off-limb, and axis at an angle to l.o.s

**Notes:**
All three have observational counterpoints (we’ve seen)
Question - range in CMEs from range in structures, or just different views of one type of structure?

## Density models: 2) Modified MHD model

- For the purpose of fitting to a range of white light CME observations, we retain the 3-part morphology defined by the Gibson and Low model, but modify the MHD solution to allow for variation of the density profiles within the three region.

**50****o**

**-50****o**

**Earth’s view**

## Summary and Future Work

- Our technique incorporates the following:
-  CME density models (ice-cream cone, modified MHD)
-  forward method (avoids error amplification, maps out degeneracy)
-  genetic algorithm global optimization (efficient and comprehensive)
- We plan to develop the technique in anticipation of its application to STEREO observations, and also to immediately use it to investigate existing observations of CMEs. Specifically, we will:
- Apply our technique to existing data to test and further develop models
-  Set up the code to incorporate STEREO datasets (run sample cases)
-  Include more realistic coronal background models (e.g. *Gibson et al, 1996*)

**Notes:**
Observations of CME plasma, and by inference field, show us that they are 
3-d and twisted, and we can model it rather nicely and match  observations.

We have a nifty model: Strengths of our model - 3-d self-consistent- point by point
 - not cartoon solution!!!  and it was made as a limb  model- anyone can get an S,
 groovy that we could - emphasize one model - many possible manifestations.

This has been a great problem to work on - recent DATA stimulates supports it, 
MODEL - 3-d + time-dependent, you'd think we'd need  to do numerical, but in fact
 numerical not there yet, we did it analytically!!!  powerful tool!  INTERPRETATION
 - new unrivalled  insight relate observations of plasma to field, limb to disk.   
CONCLUSION - twist can do it.

Note that our model has limitations (S the wrong way, big loopy tops)which are 
probably caused by the boundary condition - FUTURE so are working on numerical 
extensions that can smooth that out, and other analytic models without that 
problem.  But note these retain the spherical nature which is essential to get 
3-d  WE LEARN FROM LIMITATIIONS = where to go next?

Feedback loop 
		Observations of plasma structure --> motivate and constrain/test  models of 
	magnetic structure 
      		 magnetic field models --> 3d density model --> forward problem --> 
	deconstruct plasma observations

BUT the 3d model is still important - not only does it match 3D density structures, 
but it gives physical insight into WHY the density is the way it is.  It links the p
hotosphere to the corona and ultimately has implications even more far-reaching