Limb Magnification During Inner Eclipse Contacts

The Theory...

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 Earth.

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 more interesting...

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 Practice...

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