Create Coronal Loops via Splines
This solar active region was observed by TRACE
at 03:30UT on 12 April 2000, in the 171Å passband, characteristic
of 1-million degree gas. The TRACE (Transition Region and Coronal Explorer)
is a NASA Small Explorer mission to image the solar corona and transition
region at high angular and temporal resolution.
You can generate a Bezier spline curve to
match the large prominent loop in the image above:
Use the mouse and left click 4 times to introduce
control points over the TRACE
image:
1st
control point at foot point of a specific loop,
2nd & 3rd control points
at different points above apex of the loop, and
4th control point at the
other foot point of the loop.
Now select "Move Point" and move
the two middle points to change the curve to match the loop
BEZIER SPLINE CURVES & CORONAL LOOPS
The Bezier
spline curves are used in computer graphics to approximate
curves. The curves are manipulated by control points as the example
above illustrates. Also we have a simple movie
of the process of changing a control point which changes the shape of the
curve For a introduction to Bezier spline curves and their extension
to NURBS (non-uniform rational B-splines) see the book The NURBS Book
(by Les Piegle an Wayne Tiller, Springer, 1995). The extension
of these methods into 3D have led to a new area of solar research. It was
discovered by Allen Gary and David Alexander (Solar
Physics, 1999, 186, 123) that radial stretching
potential field lines
produced a better fit with the observed coronal
x-ray loops. A generalization of radial stretch can be accomplished by
imposing a four-dimensional polynomial Bezier volume and using their control
points to distort a volume which distorts the field lines. An example
the volume distortion shows changes in a circular loop to an elliptical
loop when the upper surfaces of the volumes are radially stretched by changing
one control point. This is a 3D extension of the method above which creates
planar curves.
PARAMETRIC TRANSFORMATION ANALYSIS
FOR DERIVING THE CORONAL MAGNETIC FIELDS
This new research program into the complex magnetic field topology
of coronal features is now being investigated by Allen Gary using Parametric
Transformation Analysis (PTA). PTA is a new and innovative method to describe
the coronal fields. PTA uses a magnetic field transformation that
parametrically transforms a field (and the associated field lines) to match
the coronal features. In this technique the field lines can be viewed as
being embedded in a plastic medium, the frozen-in-field-line concept. As
the medium is deformed the field lines are similarly deformed. However
the advantage of the PTA method is that the field line movement represents
a transformation (or mapping) of one magnetic field solution into another
magnetic field solution. This method allows the resulting magnetic field
solution to fully match the magnetic field lines with EUV/SXR coronal loops
by minimizing the differences in direction and dispersion of a collection
of PTA magnetic field lines and observed field lines (i.e., the centroids
of the coronal loops). From the new description of the magnetic field,
the coronal electric currents and magnetodynamic forces can be derived
allowing the details structure of the solar corona to be investigated.
The Java program is an adaptation of a
program by Mike Heinricks.