Limb Magnification During Inner Eclipse Contacts
During a total eclipse of the Sun at the point of contact between the limb of the
Moon and inner limb of the Sun, irregularities in the profile of the Moon give rise
to the phenomenon of Baily's Beads. These manifest as a series of broken light arcs
and beads around the point of contact. The photograph below shows the effect during
3rd contact during the 2005 annular eclipse of the Sun as seen from Madrid, Spain.
As the amount of light passing above the lunar limb increases or decreases (as is the case
during 3rd contact) the size and intensity of the beads alters too. The height of
limb irregularities, when viewing the Moon at a relatively small magnification, is
small - certainly within a few arcseconds. As a consequence, the width and intensity of a bead
as observed, a value proportional to the amount of light streaming above the limb
at that point, provides a snapshot scan line across the lunar limb at that instant.
The diagram below shows the Sun rising rapidly behind a fictitious lunar limb profile.
The thin line under each profile depicts the light pattern that would be seen from
Processing images from the 2005-10-03 annular eclipse, it occurred to me that if you
had enough of these bead strips, they could be put to good use and could possibly reveal
detail on the profile of the lunar limb. If we take each of the strips from the
diagram above and lay them on top of one another, you can see what I'm getting at...
If the strips are laid together in chronological sequence with the oldest strip at the
bottom, a reversing effect takes place. Inverting the chronological sequence (oldest on top), is much
Applying a mild Gaussian blur to the image, brighten it slightly and bring up the
original limb profile for comparison, it should be fairly obvious that the strips treated
in this manner, do indeed reveal the original limb profile that caused them.
The beads, if they can be seen at all, only occur over a short contact arc. This means that the
technique is only good for approximately 45 degrees of selenographic latitude (a value
determined by direct measurement (see below). In addition it's important to image the
contact numerous times during the brief lifetime of the beads in order to capture
enough strips to work with. Finally, without an initial idea as to the shape of
the limb at the contact point, confirmation of the result of the process requires
generating a reasonably accurate reference profile of the limb at the time of contact.
The 2005-10-03 annular eclipse showed a particularly dramatic 3rd contact limb breakup - ideal
for testing this theory. As it happened, I was able to capture 5 images of the sequence,
covering the times: 08h59m43s, 08h59m59s, 09h00m02s, 09h00m04s and 09h00m07s.
The images are shown stacked together below together with an approximate limb profile borrowed from Fred Espenak's eclipse
prediction site. The images are stacked in inverse order - oldest to the bottom left, providing
an approximate view of the limb as described above.
The image below takes the limb stacking a stage further by closing the strip gaps.
The shape of the limb profile at the contact point is fairly evident in this image.
In order to check whether the features are indeed real, a limb profile needs to be
generated for the contact point. The program Occult was used for this purpose. Used for
accurate occultation timings, the program also has a rather effective Baily's Bead simulator.
Using the program it was possible to simulate the expected appearance of the beads
during 3rd contact of the 2005-10-03 annular eclipse as viewed from Madrid. A typical simulation
display is shown below. Using this program I was able to match specific beads from the
simulation to my own images.
The biggest benefit of the Occult program is that each bead can be identified in terms of
its Watts angle. This in turn can be used as a request for the program
to draw a Watts lunar limb profile for the portion of the limb under investigation. Using this
facility I was able to generate a fairly convincing match between a time inverted
limb stack with gaussian blurring (the technique described above). The resulting
image and matching profile are shown below. This image has been rotated for convenience.
(c) Pete Lawrence, 2005