Estimation of Chances for Observation of Bright Limb Occultation Events

Wolfgang Rothe

Berlin, Germany

The observation of bright limb events is always a challenge for the observer and the used equipment. A pre-diction of such event starts very often again discussions whether an observation can be successful or will be hopeless even under best conditions.
A thesis, a calculation tool and technical guidelines for a successful bright limb observation are given in this contribution in order to support active observers and to avoid frustrating failures.
Working hypothesis for a successful bright limb event observation:
The focal illumination intensity of the star image must be equal (or higher) than the focal il-lumination intensity of the bright limb of the occulting celestial body.
The intensity of the star image adds to the intensity of the bright limb image when star is in the immediate vicinity of the limb immediately before the disappearance. It results in the double intensity (200%) of the con-tact spot in this case. The intensity of this spot of bright limb jumps from 200% down to the formal value 100% (or 0,75 mag) at the moment of occultation. This jump should be observable both visual and using video if the contact spot is observed with full concentration. The thesis above is valid for the faintest star component in case of stepwise occultations. Spectral class of the star will have a certain influence, it is not considered here.
May be, that a very experienced visual observer or an observer with video equipment is able to recognise smaller jumps of contact spot brightness and consequently fainter star contacts at the bright limb. On the other hand an inexperienced observer may recognise a larger jump only.
Focal illumination intensity of the star image
A star is a practical pointshaped object but its image is a little circular disk. The diameter of this disk is theo-retically estimated by diffraction of light waves at the rim of the telescope aperture. However we have to con-sider additional effects in practice which significantly enlarge the diffraction disk: mainly the atmospheric szintillation,  but also defocusing due to imperfection of  telescope and added equipment. Then the diffraction disk has to be replaced by the overall scattering disk. So we can calculate

with
 BF =  focal illumination intensity of the image
 Bx =  illumination intensity of the object with brightness x magnitudes in aperture plane
 ? = transmission efficiency of telescope
 D =  diameter of (unobstructed) telescope aperture
 f   =  equivalent  focal length of the telescope
 ds =  focal diameter of overall scattering disk (mainly influence of diffraction and seeing)
 ?s = angular diameter of overall scattering disk
The main point is here the influence of defocusing effects.

Focal illumination intensity of larger objects
Our large occulting objects as moon and the large planets up to Saturn can resolved into their real shape even by small telescopes. Then we have to modify the formula (1) into

with the new parameters
 dH = linear diameter of the large object (here is assumed as a full circular disk) in the focal plane
 ?H = angular diameter of the large object in nature (here assumed as a full circular disk)
No significant influence of defocusing effects for larger objects is given when their natural angular diameter is much larger than the overall scattering disk.
It was created a calculation tool in order to simplify the calculations above and to have a overview (Excel sheet, runs also with Lotus-1-2-3), available from the author by request. A screen shoot is shown below:

Recommendations for more successful bright limb observations
Make the star  image as sharp as possible, that means: avoid bad seeing places, plan enough time for temperature adaptation of telescope, test the use of colourfilter in case of chromatic focus differences, adjust to best focus with care. This is the most important conclusion from calculations above.
Use a large magnification (or equivalent  focal length) that allows to recognise the scattering disk of the star easily. The scattering disk should cover several elements (2x2 at least) of the light sensitive receiving device ( i.e. sensitive cells of the retina or pixels of a CCD chip) in order to reach an averaging over several elements. Individual elements may have different sensitivity or malfunction (ill or dead retina cells, hot or black pixels) which can result in an unstable star image.
Avoid any overload of video camera or eye. A saturation prevents the recognition of small differences or jumps of brightness. Use limiting aperture diaphragm (eccentric for most mirror telescopes) or neutral filters to ensure linear operation of camera or eye.
Avoid disturbing light due to internal reflexes when bright objects are in or near the field of view. Such interference can occur as small but be very bright spots at the image. Check carefully your equipment for such effects, cover critical components with black matt painting, install additional diaphragm.
 
 A good experience
The grazing lunar occultation of Regulus, mag 1,4, spec B8, on 24th April 1999, moon illumination 72%, first contacts at dark limb, later at bright limb:
This event was observed by 3 visual and 6 video observers in Germany near Berlin. One experienced visual observer in the more total region could reliably time a bright limb disappearance. Video observers recognised some bright limb events in real time at the monitor, later were recognised 20 reliable events which were com-patible to each other. This video analysis was a hard job, special adjustments for brightness and contrast of the monitor were required to identify all events surely. Some other as suspect reported bright limb events were completely incompatible, they must be excluded. It seems that Regulus gives only a small margin for video recording at the bright limb, regardless of its 1,4 mag brightness, due to the nearly blue spectrum.
Other expedition in Czechia, Germany, Poland and Slovakia observed this event with similar results.
 
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