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Coronal Mass Ejection Research Project

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I am back to update where I am with my research of Coronal Mass Ejections. 

To start out, I need to go back to the very beginning. Being interested in Earth's severe weather, the Coronal Mass Ejection of June 22nd, 2015 gave a new interest in space weather and CMEs. I was looking up the parameters and tried to learn all of the basics, the solar wind, IMF, K and Kp indices, etc. There was a lack of severe weather at the time and it wasn't too long before the time of Hurricane Patricia that I began my research. I started out with Coronal Holes, but eventually I thought I might as well try to see if I can find a way to predict the time of CME arrivals. My goal for predicting a CME's arrival time was by using one satellite's Coronagraph imagery and the time of launch.

Using SOHO's LASCO C3 imagery, SDO's AIA 131 imagery and ACE and Wind solar wind data to try and find some sort of pattern. I made run after run after run of trial and error using different calculations and points in time from the imagery. I did eventually find a pattern and the image below is the final graph where I have points on paper. This begins a chain reaction to several new discoveries.


Here are the steps used per CME to put a point on the graph. 
1. Get the difference of the CME launch time to arrival time in hours. The launch time that I use is when the CME reaches 2.5Rsun from the surface of the Sun.
2. In the C3 imagery, get the point in time of when the CME first reaches the edge of the FOV and a second point in time when the opposite side of the imagery reaches the edge of the FOV. The difference between these two times in hours is the X-Axis in the graph above.
3. From step 2 get the time between the two imagery points and get the difference from the launch time. Divide the travel time from step 1 by this step's number and this is the Y-Axis on the graph.

Briefly moving forward to mid 2018 I was able to discover the exact base formula for what is seen in the image above. The formula is y=cos(pi*x)-(x/sqrt(pi/2)) and with adjustments made for the C3 image Field of View and L1 position it results to the graph below. I will say there was a huge amount of luck because a minimal amount of changes had to be made to the formula for SOHO's FOV and L1 position, compared to changes that would need to be made for the STEREO satellites.


So now we have a problem. There are multiple lines and I am now stuck because I was expecting one line. I was even marking out or skipping data points in the first graph thinking I made a mistake somewhere. It can't be due to changes of the distance from the Sun, or the pattern wouldn't exist. The Coronagraph FOV is near constant, so that is ruled out. Randomly shaped CMEs are also ruled out because again, the pattern wouldn't exist. This is where I step away from the project for a while until the CME of September 10th, 2017.

Sunspot region 2673 came and went and I am now back to my research project with a sort of cleared mind. The September 10th CME is what brought a major breakthrough. In SOHO's C3 imagery and STEREO A's C2 imagery you can see a bulge ahead of a larger trailing shock. I look around at other CMEs and I now know why there are multiple lines on the graph. A CME can have two faces, a leading and secondary shock. To say if the secondary shock was right behind the leading shock, given the distance from the sun to the secondary shock multiplied by sqrt(pi/2) gives the position of the leading shock. The 2D illusions are gone and now have the leading structure of CMEs. The lines on the graphs have a new name, Multipliers. The Multiplier is only determined by the Coronagraph imagery and not the overall CME. A very, very preliminary image from this time of the research is below to sort of show the shape.


Now looking back at both graphs at the top of the post, the first doesn't show all of the lines. It wasn't until I ran calculations on STEREO A's July 23rd, 2012 CME to find the lowest Multiplier. The old Multiplier 0, or M0, then became M2. At this current time I only know of 2 other M0 CME Coronagraph views from SOHO and STEREO B.

Like how the graph is created, the same process can be done to see what we are looking at through Coronagraph imagery by using the Multipliers. Each Multiplier's type of Coronagraph view and impacts are below.
M0 - These are still partially a mystery to me. What I currently know is that they are narrower CMEs and are closer they appear with a leading shock impact. 
M1 - These have a leading shock impact and are similar to M0 CMEs, but have a buckled outer shock as the secondary shock with a leading shock impact. 
M2 - A leading shock impact where the two view points are the leading shock. 
M3 - A leading shock impact where the two view points are a leading and secondary shock. 
M4 - A leading shock impact where the two view points are the secondary shock. 
M5 - A secondary shock impact where the two view points are a leading and secondary shock. 
M6 - A secondary shock impact where the two view points are the secondary shock.

I wanted to keep going and my next goal has changed to figure out the CME structure. I know how important it will be. Going into this I know of sqrt(pi/2) and I know where the leading and secondary shocks are. Knowing those things I did what I know best, messing around with the numbers until I found a pattern. Eventually run after run after run I was able to find the CME structure while comparing imagery and solar wind data. The result shows CMEs have 3 layers, a central core, a middle layer, and an outer layer. A direct impact through the central core will result in hitting 5 internal shocks. Going further, there is a half shock between each layer. The image below shows almost every type of impact possible and is to scale, but does not account for the correct curve.


A question would be how does the structure hold together? My guess is has something to do with the magnetic structure of CME's, but at this point it's something I can't answer. Another question would be how do the different shapes come together? My current answer would be that it is determined by the size of the central core and how explosive the CME is. If there is too much push the middle and outer layers will begin to buckle, but the chances are there are a few other factors as well. As for the internal shocks, I call them shocks for a reason. It varies, but CMEs can be shock driven at any shock. It can be almost similar to the arrival of the CME. As far as I currently know, CMEs can be shock driven all the way back to the last internal shock at minimum. 

As this is most likely new, I gave simple names to the constants and this is basically what I have used on a calculator. This is how the position of how each shock can be calculated.

A = sqrt(pi/2)       - This is used for the position of a shock
B = Second Root of A - This is used for the position of a half shock. Going past beyond the second root is uncertain and will require more research to be able to see if things become more detailed.

Examples of how I will refer to this is that the leading and secondary face of a CME is A0. The duration of the far shock is A0-A2. An impact through the edge of the central core would have impacted A0, A1, A2, A4, A5, A6, and not A3. A middle layer impact has half shock impacts at A0B1, A1B1-A4B1, A5B1.

Below are examples of the different types of impacts. Inside each graph I have lines marking each shock. Red lines are the first half shock while blue is the second half. A black line ends the CME, unless disrupted by another CME or CH. In the top left corner of each image is Coronagraph imagery. In the top right corner of each image is my best estimated line of impact through the CMEs and they do not account for the correct curve of the CME. There is a graph for the CME's IMF, Velocity, and Proton Density.

One of the best CMEs that I know of is a M0 CME that impacted STEREO B on November 8th, 2013. In the image below, the final internal shock is shown as being shock driven with the velocities at A5. All 4 previous internal shocks are seen in the IMF. The line of impact was through the far edge of the A3 shock, where the magnetic field is disrupted, making the central core visible through the IMF data.


An example of an impact through the A3 centr al core shock is a M2 CME that Wind on November 24th, 2001. A sign of this type of impact is when there is a close mirrored IMF shift near A2B1.5 to A3B0.5.


An example of an impact through the edge of the central core, missing the A3 shock, is the CME that hit STEREO A on July 23rd, 2012. This is a M0 CME. A sign of this type of impact is gradual changes of the IMF through A2-A4.


An example of a M2 CME middle layer impact is a CME that impacted ACE on May 23rd, 2002. The IMF remains near constant from A1B1-A4B1 as it runs through the middle layer.


An example of a buckled middle core impact is a M3 CME that impacted STEREO A on September 11th, 2010. This CME is closest to the T-intersections of the central core and middle layers. This may result in a sudden change of the IMF like in the image below. The IMF will also gradually change from A1-A3.


An example of a buckled outer core impact is a M3 CME that impacted ACE on April 11th, 2001. Due to the leading shock extending from A0-A2, there may be some issues with the CME being shock driven. This CME below may have had a little help from behind from another CME. It became shock driven at A3B1-A4 at the end of the buckled middle layer.


An example of a M5 secondary shock impact CME is from Wind on November 10th, 2000. The CME misses the A2 internal shock and becomes shock driven at A2B1-A3.


An example of a M5 far shock impact on DSCOVR is the CME of September 12th, 2017. There isn't much to these impacts. Once the CME passes, there may be a little wall of higher proton density from the solar wind trailing it.


This has gone well beyond where I thought this would lead to and what I have previously posted about, but this post is to close this chapter of my research. I still need to reach the goal of reliable CME arrival time forecasting using my method, so at some point in the future another chapter may begin.

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I've shared my up to date method above, but I don't think I have ever actually gone into further detail with imagery examples so I have some created now.

SOHO C3's FOV is near 32Rsun (Field of View near 32 Solar Radii) and the STEREO satellites C2 imagery has a FOV of 15Rsun. In the following images I will show the two coronagraph points in time for using my method. For the STEREO satellites the points in time are estimated to 16Rsun to make the calculations easier to work with. These first two CMEs below have one slide that shows the leading shock in green and secondary shock in red.

I will start out with a M5 CME from STEREO A that launched on August 18th, 2010.

 Launch Time: 2010/08/18 05:52Z
      C P1 Time: 07:40Z
      C P2 Time: 10:30Z
          C Range: 2:50 * 2 (STEREO is multiplied by 2 to use with the current Multiplier's graph)
 C Mean Time: 09:05Z
  Mean Range: 3:13 * 2
     Multiply By: 8.63
Estimated Arrival: 2010/08/20 13:23Z
                   Arrival: 2010/08/20 16:12Z




This CME is from SOHO's imagery on September 10th, 2014.

Launch Time: 2014/09/10 17:38Z
     C P1 Time: 22:30Z
     C P2 Time: 22:30Z
         C Range: 00:00
C Mean Time: 22:30Z
  Mean Range: 4:52
     Multiply By: 8.91
Estimated Arrival: 2014/09/12 13:00Z
                   Arrival: 2014/09/12 15:26Z




This CME from SOHO on September 13th, 2005 has secondary shocks on two sides, but the two coronagraph points are from the leading shock.

 Launch Time: 2005/09/13 20:05Z
      C P1 Time: 22:50Z
      C P2 Time: 07:00Z
         C Range: 8:10
C Mean Time: 02:55Z
  Mean Range: 6:50
     Multiply By: 5.27
Estimated Arrival: 2005/09/15 08:06Z
                   Arrival: 2005/09/15 08:28Z




M0 CMEs like the one that impacted STEREO A on July 23rd, 2012 will have the smallest arrival time offset possible compared to all Multiplies above it.

 Launch Time: 2012-07-23 02:33Z
      C P1 Time: 04:10Z
      C P2 Time: 04:54Z
         C Range: 00:44 * 2
C Mean Time: 04:32Z
  Mean Range: 1:59 * 2
     Multiply By: 4.65
Estimated Arrival: 2012/07/23 20:57Z
                   Arrival: 2012/07/23 20:36Z



These 4 examples are forecasted already knowing the Multiplier. Data sees and gave us the shapes of CMEs, we need to learn to see them too.

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Solar maximums do have the most solar activity, but on the extreme side the possibility of complex sunspot regions resulting in some powerful CMEs may be possible at almost any moment of the solar cycle. There were some CMEs from 2005 and September 2017 nearing solar minimum for examples. At 0.3AU the IMF strength is around 60nT while at 8AU the IMF is down to near 0.5nT and it will keep getting weaker. The MESSENGER satellite made a pass by Earth with with a strength of 20600nT and the Sun's magnetic field will be much stronger.

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I did mess around to create a CME model a while back to get the correct curving of the CME structure. I'm not sure that the margin of error is, but it seems fairly close.

This is the CME of September 10th, 2017. The central core is very small leading to a narrow leading shock. STEREO B's C2 imagery most likely would have been M3 or M4 if it was online. Two different preliminary curved structures are below. The orange circle would be the sun and the line intervals are in Rsun.








As well, Merry Christmas, Happy Holidays, and a Happy New Years all.

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