May_12_event
The May 12 1997 event is a famous and rather simply connected active region. It is being modeled by Zoran Mikic and Rick DeVore with their respective MHD codes, and they kindly asked if we would like to compare our results with the fluxon code to theirs. It is a useful system to study, and mocking up their simulation conditions as closely as possible is a useful thing for comparing the codes' behavior.
Here is a sort of "virtual lab notebook" containing notes about our simulation.
Zoran sent the following information:
From mikicz@... Thu Nov 1 12:16:42 2007
Cc: Richard DeVore <devore@...>
From: Zoran Mikic <mikicz@...>
Subject: Fwd: Two cases
Date: Thu, 1 Nov 2007 12:15:10 -0700
To: Craig DeForest <deforest@...>
Dear Craig,
Following up on our discussions, here is an email that I had sent to
Rick DeVore last year that describes the 2 cases that are
idealizations of the May 12, 1997 magnetic field. This will
familiarize you with our thinking, and has detailed instructions on
how to generate the magnetic field. It also includes a FORTRAN
program that you can use as a detailed guide. This will be a good
way for you to start these cases.
In the next message I will also send you files of Br at r=R_sun for
the 2 cases, generated in this way, in case you want to use that
approach.
After that (and this will take a little more doing), I plan to send
you some flows that you can use to shear the magnetic field.
Please let me know if you need more information.
Best regards,
Zoran
Begin forwarded message:
> From: Zoran Mikic <mikicz@...>
> Date: November 20, 2006 12:36:00 AM PST
> To: Richard DeVore <devore@...>
> Cc: Jon Linker <Jon.A.Linker@...>
> Subject: Two cases
>
> Dear Rick,
>
> I am sending you the details for the two cases we discussed. Sorry
> for the delay. I have decided not to use the exact cases we have
> done previously, but to do two new cases that are similar, but not
> identical, to the previous cases. I will therefore have to redo
> the simulations of the eruption, but that's OK. They'll be better
> the second time around, I hope.
>
> The advantage of using two brand new cases is that the first, Case
> 1, represents an idealized model of the magnetic field on May 11,
> 1997, one day prior to the May 12 event that is a SHINE CME event.
> We have been studying this event in great detail for a while now.
> The previous cases were similar, but not a true model of the real
> field.
>
> For case 1 I used a large-scale (axisymmetric) dipole, plus a sub-
> photospheric bipole (which really is a small dipole). I chose the
> large-scale dipole to have the same flux as that in the data from
> an MDI magnetogram for May 11, 1997. The sub-surface bipole
> parameters were chosen to match the active region magnetic field,
> and again the flux was chosen to equal to that in the active region
> from the MDI data.
>
> Therefore, this represents a simple (crude) model of the active
> region that had the CME on May 12, 1997, together with a simple
> model of the overlying global field.
>
> The second case, Case 2, is identical to Case 1, but the sub-
> surface dipole has been rotated an extra 20 degrees (in the theta-
> phi plane) to make the neutral line break into two segments. This
> was done to contrast the behavior of the breakout model for a case
> without a true separatrix (Case 1) and one with a separatrix (Case 2).
>
> Below I am sending you a FORTRAN program that generates Br at
> r=R_sun for these two cases. You can run this program as is,
> except for the fact that it tries to write a 2D HDF file of Br at
> the end. You can modify this to write the file in the format that
> you desire.
>
> The magnetic field is in Gauss. Dimensions are in solar radii and
> radians.
>
> I am also attaching two files that contain the theta and phi meshes
> that I used to evaluate Br on.
>
> This is how you run the program:
>
> For case 1,
>
> dipole+bipole << EOF
tmesh.out> pmesh.out> .88,1.18599708275416326,2.42773098959991182695> .00441835195375914938,.01515262469272823430,.04692683893908539703> 2.838> br_dipole+bipole.hdf> EOF>> For case 2,>> dipole+bipole<< EOFtmesh.out> pmesh.out> .88,1.18599708275416326,2.42773098959991182695> .00441835195375914938,.03035985389240274370,.03885884094418536374> 2.838> br_dipole+bipole_two_NL.hdf> EOF>> Below are some images to help you see what these cases look like.>> Please call with any questions.>> Best regards,>> Zoran>
May12_zoran_bipole_dipole.f May12_zoran_pmesh.out May12_zoran_tmesh.out
From mikic@... Thu Nov 1 12:31:04 2007
To: Craig DeForest <deforest@...>
Cc: Richard DeVore <devore@...>
Subject: Br data files
From: Zoran Mikic <mikic@...>
Date: Thu, 1 Nov 2007 12:29:30 -0700
Dear Craig,
Attached to this message are the 2D data files (text format) of Br at
r=R_sun in spherical (theta,phi) coordinates, and a simple FORTRAN
program to read them. The data files are:
br_dipole+bipole.dat: Br for case 1 (one continuous neutral line)
br_dipole+bipole_two_NL.dat: Br for case 1 (neutral line in two segments)
These were produced by the program I sent in the previous message.
To check that you have read these files properly, I am sending the
output I get when I run the program on my machine. You might want to
use the program only as a guide and do something similar using your
favorite language.
-------------------------------------------
Case 1:
./read2d
Enter input file name: br_dipole+bipole.dat
### Reading file: br_dipole+bipole.dat
### Read in the dimensions:
NT = 221
NP = 241
### Data read successfully:
Field (min) = -21.63536
Field (max) = 28.85418
-------------------------------------------
Case 2:
./read2d
Enter input file name: br_dipole+bipole_two_NL.dat
### Reading file: br_dipole+bipole_two_NL.dat
### Read in the dimensions:
NT = 221
NP = 241
### Data read successfully:
Field (min) = -21.57562
Field (max) = 28.80972
-------------------------------------------
Best regards,
Zoran
May12_zoran_read2d.f May12_zoran_br_dipole_bipole.dat.gz May12_zoran_br_dipole_bipole_2.dat.gz
I'll port the bipole code to PDL. First, I'll use it to calculate the field strength everywhere on the photosphere, and project the photosphere onto a pixel grid with an authalic projection (I guess sin-alpha is as good as any). Then I'll Floyd-Steinberg dither a collection of fluxon footoints onto the sphere, and use the same bipole code to shoot initial field lines analytically through the field. Those field lines will become fluxons, which should relax to almost the exact same position on initial relaxation. Then we'll add rotation of the sunspots and other time-dependent effects.
I'll post a tarball of codes at the end of this page when the analysis is complete; including the source codes individually in the wiki is too tedious.
Matching Zoran's dipole calculations took a little time, because our sign and quantity conventions differ some. Here's a conversion table.
| Quantity | Zoran's name | Zoran's convention | Craig's name | Craig's convention |
| longitude | \(\phi\) (`phi`) | \(0 \rightarrow 2\pi\), 0 is central meridian | \(\theta\) (`theta`) | \(-\pi \rightarrow \pi\), 0 is central meridian |
| latitude | \(\theta\) (`theta`) | \(0 \rightarrow \pi\), 0 is north pole, \(\pi\) is south pole | \(\phi\) (`phi`) | \(-\pi/2 \rightarrow \pi/2\), 0 is equator |
| global dipole | D | \(B_{r,phot.}=cos(\theta)D\) | M_{s} | \(B_{r,phot.}=2cos(\theta)M_{s}\) |
Four-panel comparison shows that I match OK with Zoran, though I do better with a small offset (about 1/30 of a pixel). This four-panel plot is done on Zoran's irregular a priori (lon, lat) grid, which is why the axes are in arbitrary units.
I placed fluxons on a spherical Sun using Hilbert (modified Riemersma) dithering onto the lat/lon plane. Because the Plate Caree projection isn't authalic, the background field gets scaled by cos(φ) to account for the area effect.
