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Visibility of stars, halos, and rainbows
during solar eclipses
Gunther P. Können1,* and Claudia Hinz2
1Sophialaan 4, NL-3761DK Soest, The Netherlands
2Deutscher Wetterdienst, Bergwetterwarte Wendelstein, D-83735 Bayrischzell, Germany
*Corresponding author konnen@planet.nl
Received 27 February 2008; revised 22 May 2008; accepted 22 May 2008;
posted 22 May 2008 (Doc. ID 93011); published 13 June 2008
The visibility of stars, planets, diffraction coronas, halos, and rainbows during the partial and total
phases of a solar eclipse is studied. The limiting magnitude during various stages of the partial phase
is presented. The sky radiance during totality with respect to noneclipse conditionsis revisited and found
to be typically 1=4000. The corresponding limiting magnitude is þ3:5. At totality, the signal-to-back-
ground ratio of diffraction coronas, halos, and rainbows has dropped by a factor of 250. It is found that
diffraction coronas around the totally eclipsed Sun may nevertheless occur. Analyses of lunar halo ob-
servations during twilight indicate that bright halo displays may also persist during totality. Rainbows
during totality seem impossible. © 2008 Optical Society of America
OCIS codes: 010.2940, 010.1290, 350.1260.
1. Introduction
We discuss the visibility of stars and planets during
partial and total solar eclipses and the occurrence of
rainbows, halos and diffraction coronas during
eclipses. The discussion brings together studies of
sky brightness during eclipses, studies of limiting
magnitudes under various conditions, and visibility
studies in meteorological optics. In all of these fields
there exists a vast amount of literature, but to our
knowledge these areas are rarely combined. With re-
spect to sky brightness data during totality, the basic
sources are the overview articles from the 1970s by
Sharp et al. [1], Silverman and Mullen [2], as well as
the summarizing work by Dandekar [3], Shaw [4],
and others. Extensive studies of limiting magni-
tudes—the stellar magnitude of the faintest point
source that can be seen against a luminous back-
ground—in the laboratory, during twilight, and dur-
ing daytime, were performed during the 1940 and
1950s, most notably by Blackwell [5], Lamar et al.
[6], Hecht [7], Tousey and Hulburt [8,9], Weaver
[10], Koomen et al. [11], and Tousey and Koomen
[12]. The gained knowledge of limiting magnitudes
has been only meagerly applied to eclipses. Silver-
man and Mullen [2], in discussing star sightings dur-
ing totality, remark that the limiting magnitude is
about þ3and add to this that, indeed, on a few occa-
sions third magnitude stars have been observed, but
that these observations are the result of chance
rather than of deliberate attempts at star observa-
tions. Despite his call for systematic pursuits of stars
during totality, little progress has been made since.
The appearance of phenomena from meteorologi-
cal optics—diffraction coronas, halos, and rainbows
—during eclipses, and their capability to persist dur-
ing totality has received even less attention. The un-
predictability of their appearances obviously hinders
the planning of systematic observation campaigns
for these phenomena. In some recent cases, however,
the required cirrus or altocumulus clouds have been
present during totality together with keen observers
on the ground. By virtue of these observations and
the existence of long observational records of ordin-
ary halos, it is now possible to assess their capability
to remain visible during eclipses.
0003-6935/08/340H14-11$15.00/0
© 2008 Optical Society of America
H14 APPLIED OPTICS / Vol. 47, No. 34 / 1 December 2008
A crucial parameter in this study is Itot=I0%, which
is the sky brightness during totality with respect to
the brightness under noneclipse conditions. Based on
the authority of the two overview articles [1,2], one
usually takes for this a value of 10−3. Part of the pre-
sent study is devoted to revisiting the literature on
which the traditional value is based, which leads
us to conclude that this value is about half an order
of magnitude too high.
We split the paper into two parts. The first describes
effects during the partial phase; the second during to-
tality. Apart from sightings of stars, diffraction coro-
nas, halos, and rainbows, some other real or
psychophysical effects will be touched on in this paper.
2. Partial Phase
A. Eclipse Timeline
The time span between the first contact of the Moon
and the start of totality (second contact) is typically
70–90 min. A central value is 80 min; this value is
used in this paper to define the eclipse timeline.
During this partial phase the magnitude of the
eclipse, being the fraction of the solar diameter that
is obscured by the Moon, increases about linearly
with time. The obscuration of the Sun, which is
the fraction of the surface area of the solar disc that
is hidden by the Moon (and hence governs the at-
tenuation of the light of the Sun), lags a bit behind
in the beginning of the partial phase: after a half
hour from the first contact the magnitude of the
eclipse is already 0.4, but the obscuration only
29%. After this it accelerates: in the remaining
50 min to totality the obscuration increases almost
linearly with the eclipse magnitude and hence with
time [13]. See Table 1, in which the Sun’s photo-
metric brightness is calculated as a function of
eclipse magnitude for a typical eclipse (ratio lu-
nar/solar disk diameter 1.04). Limb darkening [14]
is taken into account in Table 1, but its effect be-
comes apparent only for deep partial eclipses: for
eclipse magnitudes of 0.8, 0.90, and 0.95 it causes
an additional weakening of the Sun’s radiance by
15%, 25%, and 35% respectively, amounting to about
50% just before totality. We note that the wave-
length dependency of the limb darkening has little
effect on the Sun’s brightness, as it affects these
weakening factors by less than 10% in the
500–600 nm range.
B. Human Perception of Attenuation
The reduction in illumination remains initially un-
noticed by the human eye for three reasons. First,
according to Fechner’s law [15], the eye responds
logarithmically to stimuli; second, the decrease in
radiance of the blue sky and our surroundings is
the same as that of the primary light source, so that
contrasts remain unaffected; and third, just like a
good camcorder, the eye adapts effectively to
changes in the overall illumination. Rather than
the light looking dimmer, one perceives that fixed
light sources—like the planet Venus or a remote
street light—seem to gain in brightness. Only when
the eclipse magnitude exceeds 0.9, hence about
10 min before totality, does the continuous decrease
of the light intensity start to become noticeable [16].
This happens when the rate of decrease in the light
level has risen to 15%=min, which is comparable
with the rate during ordinary [3,11,17–19] civil twi-
light. At that point, the absolute level of the illumi-
nation is already a factor of 10 less than at the
beginning of the eclipse.
Via other human senses, the decrease in radiation
is apparent much earlier. Almost everyone (see, e.g.,
[20]) experiences a chilling feeling at eclipse magni-
tude 0.6 (about a half hour before totality). Measure-
ments show that the air temperature has dropped
by less than 2°C at that stage [21], which is not suf-
ficient to explain this cold sensation. The explana-
tion of this is that our temperature sensation is
determined mainly by the Sun’s radiation and
hardly by the real temperature [22]: a decrease in
direct Sun radiation from 100% to 75% creates
(during still weather and temperatures around
15°C–25°C) a sensation similar to a temperature
drop of no less than 5°C. Everyone knows indeed
how strong the effect can be of a small cloud blocking
the Sun: apparently our sense for cold is a much bet-
ter detector for absolute radiation than our adapt-
ing eyes.
When the eclipse magnitude exceeds 0.9, obser-
vers start to perceive a bluish hue in the sky and
landscape. Reports of it date back to the 19th cen-
Table 1. Obscuration and Brightness of the Partially Eclipsed Sun
for Wavelength 550 nm and Moon=Sun Diameter Ratio 1.04
Eclipse
Magnitudea
Time
till
Totality Obscurationb
Brightness
Sunc
Stellar
Magnitude
Sund
080 mine0 100% −26:70
0.1 72 min 4% 97% −26:67
0.2 64 min 11% 91% −26:60
0.3 56 min 19% 82% −26:49
0.4 48 min 29% 72% −26:34
0.5 40 min 40% 60% −26:14
0.6 32 min 51% 47% −25:88
0.7 24 min 63% 34% −25:52
0.8 16 min 76% 21% −24:99
0.85 12 min 82% 15% −24:60
0.9 8min 88% 9% −24:04
0.95 4min 94.6% 3.5% −23:05
0.975 2min 97.6% 1.3% −22:02
0.985 75 s 98.7% 0.7% −21:30
0.995 24 s 99.7%f0.13%f−19:48
0.998 10 s 99.93%f0.03%f−18:00
aPart of the solar diameter obscured by the Moon.
bPart of the solar surface area obscured by the Moon.
cLimb darkening factors [14] for 550 nm applied.
dFor solar elevation 40°.
eValue varies somewhat between different eclipses.
fFrom obscuration of 99.7% the decrease in sky radiance stag-
nates with respect to that of the Sun [18,27].
1 December 2008 / Vol. 47, No. 34 / APPLIED OPTICS H15
tury [23] and continue till the present [20,24,25].
The effect is unexplained and is likely to be a phy-
siological and psychological response to the low and
decreasing light levels, perhaps in combination with
the sensation of cold. The bluish tinge sensation is
strong enough to be noticed by many [26].
Even for eclipse magnitudes exceeding 0.99 the
eclipse phenomenology can be interpreted in terms
of attenuated, but otherwise unchanged, sunlight
[1]. Only if an obscuration of 99.7% is reached, that
is less than 30 s before totality, the decrease in sky-
light radiance starts to stagnate with respect to that
of the Sun [1,4,27].
C. Appearance of Planets and Stars
The sky radiance follows that of the primary source,
the Sun. With the decreasing sky radiance, the limit-
ing magnitude, being the stellar magnitude of the
faintest star that can be seen, goes up. At full day,
sea level, and clear air conditions, the limiting mag-
nitude is typically −3:5in the regions of the sky that
are farther than ∼40° from the horizon [8,10,12].
This value is in concordance with the observational
experience of G. P. Können that Venus can be quite
easily spotted with the unaided eye during full day
even when its brightness is less than −4:0magnitude
and the Sun is as high as 60° in the sky.
With the decrease in sky light during the course of
the partial phase, the visibility of Venus improves.
For point sources, however [5,9], the increase in lim-
iting magnitude progresses slower than the decrease
in sky brightness implies: a diminishing of the sky
brightness by 5 magnitudes results in an increase
of only 4 points in limiting magnitude [12]. Table 2
shows that Jupiter and Sirius appear no sooner than
about 10 min before totality; about 2:5 min before to-
tality the limiting magnitude crosses the zero level.
Theory fits well with the observations, as in 2006
Mercury (þ1:0magnitude, elongation 25°) was re-
ported to be visually observed during the last minute
before totality [16,20].
Figure 1summarizes the sky brightness and limit-
ing magnitude data during the last 2 min before to-
tality. The representation is that developed by Sharp
[1], who expresses the sky brightness Irelative to
that at obscuration 98.7%. At that point, the bright-
ness of Sun and sky has decreased with respect to
noneclipse conditions by a factor of 144 (for wave-
length 550 nm and Moon/Sun radius 1.04), but the
Sun’s role as primary light source remains un-
changed. The right axis shows the sky brightness
with respect to noneclipse conditions I=I0%, where
the factor 144 is used to derive their values from
the I=I98:7%values. Bars indicate the sensitivity of
the factor 144 to variations in wavelength (8%)
and eclipse magnitude (3%). The limiting magni-
tudes and the moments of appearance of the nine
brightest stars that are closer than 25° to the ecliptic
are added to the right-hand axis. The solid line repre-
sents the attenuation of sunlight; the dashed line in-
dicates the decrease in brightness of the sky, which
starts to deviate from that of the Sun [1,4,27] for an
obscuration of 99.7%.
D. Diffraction Coronas, Halos, and Rainbows during the
Partial Phase
Contrary to the situation for point sources, the vis-
ibility of light sources with sizes exceeding ∼0:3° de-
pends, for sky radiances down to civil twilight, only
on the signal-to-background ratio [5,6,9]. Because up
to an obscuration of 99.7% the intensities of sunlight
and sky light are attenuated in the same way, the
signal-to-background ratio of diffraction coronas,
halos, and rainbows generated by the light of the
partially eclipsed Sun remains constant. This im-
plies that up to that point the visibility of these
objects remains unchanged. In the last 30 s before
totality the signal-to-background ratio starts to
worsen as the attenuation of the sky retards, but till
the very last stage of partiality the Sun keeps its po-
sition as the prominent light source in the sky. As
long as the scattering particles are directly lit, dif-
fraction coronas, halos, and such can persist without
significant loss in visibility. This is illustrated in
Fig. 2, taken 9s before totality [28], where a pollen
corona is formed around the last unobscured piece
of Sun.
Table 2. Limiting Magnitudes during the Partial and Total Phases of an Eclipse
Eclipse
Magnitude Obscuration
Time till
Totality
Limiting
MagnitudeaPlanets/Stars Visible
00%80 min −3:5Venus
0.72 66% 23 min −2:5
0.888 86.8% 9min −1:5Jupiter, Sirius
0.954 95.3% 3:7min −0:5Canopus, Mercury
0.980 98.2% 97 sþ0:5αCen, Arcturus, Vega, Rigel, Capella, Procyon, Saturn
0.986 98.9% 65 sþ1:0Achenar, βCen, Altair, Aldebaran, αCrucis, Antares, Betelgeuse
0.991 99.4% 44 sþ1:5Spica, Pollux, Fomalhaut, Deneb, βCrucis, Regulus
Mid-totalityb100% —þ3:5E.g., Alcyone in Pleiades cluster
aAt clear sky and sea level.
bLimiting magnitude as derived in this work.
H16 APPLIED OPTICS / Vol. 47, No. 34 / 1 December 2008
3. Totality
A. Transition to Totality
In a transition phase of about 30 s, the scene changes
from directly sunlit to total eclipse conditions. In that
time span the direct sunlight disappears, 10 s before
still being of magnitude −18, to be replaced by the
corona, of magnitude −12:0[29–31]. The decrease
in illumination continues after second contact is
reached, as in the initial stage of totality part of
the sky is still directly lit by the Sun (Fig. 3)and
hence is relatively bright. The end of the transition
phase occurs when the sunlit part of the sky has dis-
appeared behind the horizon.
Fig. 1. Sky radiance Irelative to that at 98.7% solar obscuration
I98:7%as a function of percent of obscuration. The solid line shows
the brightness of the Sun relative to that at 98.7% solar obscura-
tion for Moon/Sun radius 1.04 and wavelength 550 nm. The dots
with the standard deviations are observed sky radiances, and
the dashed line is a fit through these points as reported by Sharp
[1]. The right-hand vertical axis represents the radiance relative to
that at zero solar obscuration, I=I0%. The two solid bars show the
respective variation of the 10−2point of that axis for Moon/Sun ra-
dius (M/S) values ranging from 1.01 to 1.06 and for wavelengths
from 500 to 600 nm. The limiting magnitudes (ml) and the magni-
tudes of the nine stars that are closer than 25° to the ecliptic and
brighter than magnitude 1.5 are added to that axis. Capella, the
brightest among them, would fall on a I=I98:7%value of 2.25.
Fig. 2. (Color online) Pollen corona around the deeply eclipsed
Sun, 9s before totality. The solar obscuration is 99.92%. Even
at this very last stage of partiality, the light of the Sun completely
outshines that of the solar corona and determines the formation of
the pollen corona (photo by Emma Herranen; Belek, south Turkey,
29 March 2006; see also [28]).
Fig. 3. (Color online) Left, the sky at mid-totality. Right, on the edge of totality, 10 s before third contact. The boundary between direct
sunlit and the indirectly lit air mass has approached the Sun to 30°. This boundary line is sharply visible because we are looking almost
parallel to the lunar umbra. Fisheye lens, horizontal field of view 135° (photos G.P. Können, at 3:7km NW of the center line of totality; Side/
Colakli, south Turkey, 29 March 2006).
1 December 2008 / Vol. 47, No. 34 / APPLIED OPTICS H17
Visually, the transition phase represents a strong
sensation of light dimming, which extends well into
the initial stage of totality. This sensation is even
stronger under an overcast sky, as G. P. Können
knows from his experience during the 1999 Luxem-
burg and 2006 Turkey eclipses. The reason is that
the time needed for the lunar umbra to cross the
sky is shorter if the effective scattering height is low-
er, which is the case under a cloud deck. The visual
transition phase during the overcast eclipse in Lux-
emburg of 1999 lasted only 10 s, in agreement with
the data of a fixed-diaphragm video by Rob van Dor-
land [32]; the visual transition phase during the 2006
Turkey eclipse was three times longer.
At second and third contacts the boundary be-
tween directly and indirectly lit air masses passes
straight through the Sun. Because we are looking
parallel to the lunar umbra, it is instantly visible
as a sharply defined line in the sky. In Fig. 3(right),
taken 10 s before third contact, there is a gradient in
sky radiance of a factor of 4 in a 20° interval across
the boundary. In the regions of the sky where the
boundary is clearly defined, the drop in radiance dur-
ing the transition to totality may be much steeper
than radiance measurements of the zenith sky
[3,18,27,33,34] suggest.
Figure 3also illustrates that the brightness varia-
tion of the zenith sky need not coincide with that of
the Sun: in this particular case, the former lagged be-
hind. This effect may partly explain the observed
asymmetries with respect to the time of mid-totality
in instrumentally recorded light curves of the zenith
sky [1,4,35–37].
The factor of 4 sky radiance difference across the
lunar shadow implies that light on the sunlit site
of it consists of 75% primary scattered light and
25% multiply scattered light. This quantifies the loss
in the signal-to-background ratio of halos and diffrac-
tion coronas and such during the very last stage be-
fore totality. As the radiance of halos or diffraction
coronas from sunlit particles is proportional to that
of the primary scattered component of sky light, this
indicates that the signal-to-background ratio of these
near-Sun phenomena has dropped by no more than
25% with respect to noneclipse conditions. In accor-
dance with Fig. 2and the Hennig halo discussed
below, this implies that the visibility of these phe-
nomena remains remarkable stable till the moment
that the umbra reaches them.
When the sunlit part of the sky has disappeared
and totality is stabilized, the brightness of the sky
is comparable with twilight, or solar depression an-
gle 5°–7°([1,3,18,19,27,33,35,38]; see also [4]), hence
like at the end of ordinary civil twilight. This means
that the light level remains high enough to keep the
human eye in the region of photoptic (cone) vision.
The light distribution in the sky is remarkably
smooth [4]. For zenith distances zless than 70°, its
main features can be well understood from second-
order scattering modeling [39–41], in which the de-
pendence of the light distribution turns out [39]to
be basically proportional to the path length factor
1=cosðzÞ. For understanding the region closer to
the horizon, single scattering has to be invoked
[42]. The two eclipse overview articles [1,2] indicate
the loss in sky radiance with respect to noneclipse
conditions to be 3 orders of magnitude. Other sources
[3,4,18,33,34] as well as theoretical modeling [39,41]
indicate that this value is on the conservative side.
The most prominent light source in the sky is the
solar corona. With a brightness of −12:0magnitude it
stands out against the sky like the Moon at phase
0.93 (elongation 150°) against a twilight sky at solar
depression angle 5°–7°. In that situation, the contri-
bution to the irradiance by the corona light is negli-
gible with respect to that of the sky [41]. Hence the
corona, like the Moon during civil twilight, casts no
shadows.
B. Appearance of Stars and of the Eclipsing Moon
Figure 4summarizes sky brightness observations
during totality. Again the sky radiance is expressed
relative to that at obscuration 98.7%. The figure con-
tains 16 data points of eclipse observations from
ground level (less than 500 m above sea level) with
solar elevation higher than 20°. These include six
data points from Fig. 2 of [1]. Details are given in Ta-
ble 3. The observations refer often, but not always, to
the zenith. The right axis of Fig. 4shows the sky
brightness with respect to noneclipse conditions
Itot=I0%, where the above-mentioned factor 144 is
used to derive their values from the Itot=I98:7%values.
The limiting magnitudes corresponding to the right-
hand axis, as derived from Fig. 1 of [12], are indi-
cated. They can be considered to be representative
for regions in the sky that are higher than ∼40° from
the horizon.
The data in Fig. 4indicate a typical value of
Itot=I98:7%of about 0.035. This indicates a central es-
timate for Itot=I0%of 1=4000, which fits the data
points within a factor of 2. This implies that the loss
in sky radiance with respect to noneclipse conditions
is half an order of magnitude higher than the value
recommended by Sharp et al. [1,2]. The 1=4000 value
is in accordance with the values directly reported by
the various observers in Table 3, as well as with the
value calculated by the radiative transfer model [41].
It is also consistent with the radiance loss [8,11]of
the sky from full day till solar depression angle 6°,
and hence with the twilight equivalence of the sky
at totality.
The factor 1=4000 implies a limiting magnitude of
about þ3:5. The gradient in radiance of a factor of 4
in an interval of 20° across the lunar shadow in Fig. 3
implies that the increase in limiting magnitude from
þ2:5till its final value of þ3:5may progress almost
stepwise.
Accepting that the value of þ3:5is not too far from
the truth, a perfect object for future testing of the
limiting magnitude during totality is the Pleiades
cluster. The magnitudes 2.9, 3.6, 3.7, and 3.9 of its
H18 APPLIED OPTICS / Vol. 47, No. 34 / 1 December 2008
four brightest stars cover well the uncertainty range
of the limiting magnitude during totality.
Next to the solar corona and the planet Venus, the
brightest object in the sky is the eclipsing Moon. The
earthshine on the new Moon makes it an object of
magnitude −3:0, as can easily be calculated from
the brightness of the full Earth as seen from the
Moon (−16:9) and the value (30%) of the Moon’s op-
position effect [45–47]. The factor 1=4000 implies
that the signal-to-background ratio is the same as
that for the easily observable gibbous Moon at full
day. Nonetheless, the human eye perceives an ink-
black disk instead. The cause is the contrast with
the bright corona. The black disk illusion (Fig. 5)
is among the strongest optical illusions that
exists [48].
C. Diffraction Coronas, Halos, and Rainbows during
Totality
1. General
As the radiance of the solar corona is 106times weak-
er than the uneclipsed Sun, whereas the sky radi-
Fig. 4. Sky radiance Itot during totality relative to that at 98.7% solar obscuration I98:7%as a function of wavelength. The dots are narrow-
band observations; the crosses, put at wavelength 550 nm, indicate broadband observations in the visible range (see Table 3). The right-
hand vertical axis represents the radiance relative to that at zero solar obscuration, Itot=I0%. The solid bar shows the variation of the 10−4
point of that axis for wavelengths from 450 till 600 nm. The limiting magnitudes (ml) corresponding to the sky radiances is added to that
axis. The solid line is a rough fit through the data.
Table 3. Sky Brightness at Totality
Year (Eclipse
Magnitude [43])
Solar
Elevation Wavelength Itot=I98:7%Itot=I0%Reported Observer, Remarks
1937 (1.075) 30° visible 0.024aRichtmyer [31]
1947 (1.056) 40° visible 0.035a1=4000 Richardson and Hulburt [37]
1952 (1.037) 61° visible 0.042aBatchelder et al. [36]
1963 (1.022) 24°560 nm 0.023aSharp et al. [18]
520 nm 0.033a1=3500
600 nm 0.010a
1966 (1.023) 68°540 nm 0.040 1=2500 Lloyd and Silverman [34]
1970 (1.041) 37°430 nm 0.032 Hall [44]
510 nm 0.028
590 nm 0.010
1970 (1.041) 46°420 nm 0.031 1=7300 Dandekar and Turtle [33]
560 nm 0.024 1=6400
630 nm 0.019 1=5800
1973 (1.072) 37°400 nm 0.034 Shaw [4], solar vertical, 90° from the Sun
midvisible 0.022b
600 nm 0.028 1=7500
aValues derived by Sharp [2].
bValue reported by Shaw [4].
1 December 2008 / Vol. 47, No. 34 / APPLIED OPTICS H19
ance during totality has dropped only by a factor of
4000, the signal-to-background ratio of diffraction
coronas, halos, and rainbows generated by the light
of the corona is 250 times less than during noneclipse
or pretotality conditions. It is not clear beforehand to
what degree solar-corona generated phenomena of
this type can stand out against the background light
of the sky during totality.
2. Diffraction Coronas during Totality
Despite the poor signal-to-background conditions,
the diffraction corona, being the brightest among
these three phenomena, has indeed regularly been
observed around the totally eclipsed Sun, and in
1999 even photographed. The first person who man-
aged to obtain an unequivocal picture of a diffraction
corona around the totally eclipsed Sun seems to be
the Dutch observer Monique van Boxtel; her picture
is reproduced as Fig. 6. Inspection of videos taken by
others during totality reveals that in some of them
diffraction coronas can also be discerned, like for in-
stance in the video taken by Anton van der Salm [49]
during the 1991 Mexican eclipse. These videotaped
diffraction coronas are usually much more difficult
to recognize than the one in Fig. 6. A main reason
for this is that eclipse photographers usually apply
big telephoto lenses that tend to overmagnify a dif-
fraction corona.
In the course of the 20th century, a few other
eclipse watchers have reported the sighting of a dif-
fraction corona around the totally eclipsed Sun [50],
but we never saw pictures of them published. Per-
haps the disappointment about the spoiling presence
of the diffraction-corona-generating clouds during to-
tality is sometimes too great to appreciate the effect.
In some cases the diffraction corona has been ob-
served but not recognized as such, like in 1998 when
it was mistakenly identified as a possible (bluish) ex-
tension of the solar corona at 3:5° of the Sun [48].
3. Halos during Totality
Halos are weaker than diffraction coronas. It is not
immediately clear whether the visibility of halos
can withstand the dramatic loss in the signal-to-
background ratio that occurs at totality. Reports
about eclipse halos are lacking, although the German
halo observer Udo Hennig saw and photographed a
22° halo that remained visible till 3s before the to-
tality of the 2006 eclipse (Fig. 7). After the beginning
of totality this halo submerged in the background
light of the sky, as could be testified by Hennig’s
two pictures that were taken during totality. The re-
turn of the halo could not be verified, as no posttotal-
ity pictures were taken. Hennig’s series of pictures
started 5min before totality (at obscuration 92%),
and his eight pictures taken during the increasing
deeper partiality confirm our conclusion in Subsec-
tion 3.A that the signal-to-background ratio of a halo
generated by a partially eclipsed Sun remains vir-
tually constant till the very last moments before to-
tality. However, Hennig’s observation gives no
indication as to how far the visibility of halos can sur-
vive the transition to totality, as this particular halo,
which G. P. Können happened to see at about 300 m
from Hennig’s spot, was only of mediocre brightness.
To test whether brighter displays may persist dur-
ing totality, we analyzed the lunar halo observations
during twilight in the 21-year database of the Ger-
man Halo Network (AKM, Arbeitskreis Meteore
[51]). The introduction of lunar halos as an analogy
of solar-corona-induced halos is justified by the fact
that the smearing of a halo by the ∼1°-wide solar cor-
ona is still small with respect to a halo’s typical width
and diffraction broadening [52]. At elongation 150°
(phase 0.94), hence 30° from full, the brightness of
the Moon equals that of the solar corona, while the
sky radiance during totality roughly approximates
twilight conditions for a solar depression angle of
about 5°–7° (or 6°1°). Using the brightness data
of the Moon [53] as a function of elongation and
Fig. 5. (Color online) Black disk illusion. The eclipsing Moon
shows up to the human eye as black. Pasting a copy of its image
against the sky shows its actual brightness with respect to the sky
(magnification of a photo from C. Brinkerink; Side, south Turkey,
29 March 2006).
Fig. 6. (Color online) Diffraction corona around the totally
eclipsed Sun. The light of the solar corona turns out to be suffi-
ciently strong to produce a diffraction corona, which stays visible
against the twilightlike background of the sky during totality
(photo by Monique van Boxtel; Gmunden, Austria, 11 August 1999).
H20 APPLIED OPTICS / Vol. 47, No. 34 / 1 December 2008
the radiance of the twilight sky as a function of solar
depression and the Moon’s position in the sky [11,12],
we determined, for values of lunar elongation other
than 150°, the solar depression angle at which the
Moon/sky radiance ratio equals that of the Moon
at elongation 150° (phase 0.94) and solar depression
angle 6°. For instance, for the Moon in first quarter,
where its radiance is a factor of 5 less than at elonga-
tion 150°, this happens when the solar depression is
7:6° (Fig. 8), which occurs in the mid-latitudes about
45 min after sunset. Hence a halo that appears
around the Moon in first quarter while the Sun is
7:6° below the horizon would have the same sig-
nal-to-background ratio as if that halo had appeared
around the Moon at elongation 150° and solar de-
pression angle 6° as well as if it had appeared around
the totally eclipsed Sun under nominal eclipse condi-
tions. Then we plotted the lunar phase and the solar
depression of the evening lunar 22° halos in the AKM
database that are observed before the end of nautical
twilight (solar depression less than 12°) as well as
the band of conditions equivalent to elongation
150° and depression angle 6° with a 1° range around
it. This was done after a rigorous data selection (Ap-
pendix A). The resulting plot is shown as Fig. 8.
It turns out that 14 out of the 168 data points in
Fig. 8are in the band or on the left-hand side of
it, whereas the left-hand boundary of the remaining
154 dots roughly follows the shape of the right-hand
side of the band. In the case of these 14 points, their
position in the plot indicates that the observed halo
would have had an equal or better signal-to-back-
ground ratio if it had appeared around the eclipsed
Sun instead of around the Moon. These 14 points are
from the data of 5 of the 9 observers responsible for
the dots in Fig. 8. They all refer to situations in which
the Moon stood well above the horizon: only in one
case was the lunar height below 34°, while averaged
over all 14 observations the lunar elevation turns out
to be 47°. Coding errors in date and/or time may have
caused dots to shift from the point cloud toward the
left, but it seems unlikely that such an effect applies
to all of these 14 outlying dots. So at least some of
them seem real.
Our conclusion from Fig. 8is that halos that are
generated by the light of the solar corona are not al-
ways doomed to disappear in background light of the
sky during totality, but may in some cases stay visible.
This conclusion is based not only on the existence of
the 14 outlying points, but also on the proximity of the
edge of the point cloud of the remaining 154 dots to the
band, in combination with the conservative nature of
the graph when used as diagnostic for the appearance
Fig. 7. (Color online) Left, 22° halo of mediocre brightness around the deeply eclipsed Sun, about 3s before totality. The lunar shadow,
approaching from the right bottom (see Fig. 3) has not yet reached the halo. At totality, the halo disappeared in the background illumina-
tion (photo by Udo Hennig; Side/Colakli, south Turkey, 29 March 2006, 10∶54∶52 UT). Right, 22° halo around the uneclipsed Sun. Owing to
its extreme brightness this halo attracted wide attention. If the Hennig halo had been as bright as this one, it might have stayed visible
during the total phase of the eclipse (photo by Dorothé Trompert; Alice Springs, Australia, 15 November 2005 13∶17 LT).
Fig. 8. Lunar 22° halo recordings during evening twilight as func-
tion of solar depression angle and lunar elongation (90° is first
quarter; 180° is full Moon). The dashed curve indicates the situa-
tion in which the signal-to-background ratio is the same as that for
a solar-corona-generated halo during totality for a nominal eclipse;
the band around it indicates the range. Dots in the band or on the
left side of it indicate observations for which the halo/sky radiance
ratios were lower than when that halo would have been present
during the totality of a typical solar eclipse. The presence of dots
in that region indicates that halos could persist during the totality.
The observations are by the Halo Network of the Arbeitskreis Me-
teore e.V, Germany, 1986–2006 (see Appendix A).
1 December 2008 / Vol. 47, No. 34 / APPLIED OPTICS H21
of halos during totality (see Appendix A). Future ob-
servations during the transition from the partial
phase to totality are needed to experimentally find
out to what extent bright halos can survive the 2–3
order of magnitude loss in signal-to-background ratio
and to confirm their persistency during totality.
4. Rainbows during Totality
Rainbows are much weaker than halos. Given the
just-mentioned analogy to the light conditions dur-
ing twilight, it seems almost impossible that rain-
bows that are created by the light of the corona
could ever be bright enough to rise over the sky back-
ground. Nonetheless, in 1970 a quite far-reaching
claim about the visibility of eclipse rainbows ap-
peared in the British journal Weather [50]. How
far this claim can be taken seriously is questionable.
The motivation to write this article was apparently a
Letter to the Editor by the British Princess Margaret
to the magazine Country Life about a lunar rainbow,
and this fact may have prompted the author of the
Weather article to make a somewhat stronger state-
ment than the facts justify. Critical inspection of the
eclipse report that forms the basis of this claim (from
1901, by Maunder [54]), shows that the bow was not
observed by the author, but by a group 20 km away.
Hence the information is only second hand, and the
report contains no explicit indication that the bow
persisted during the totality. The observed pink color
in the bow, which Maunder suggests it may be caused
by the hydrogen emission lines of the prominences,
can be easily explained by the presence of a supernu-
merary bow. Probably this “eclipse rainbow”is ob-
served only during the partial phase. A rainbow
during totality seems impossible.
4. Conclusions
Our analysis leads us to the following conclusions:
•For partial eclipses greater than 0.9, stars can
become visible in the sky.
•The signal-to-background ratio of halos and dif-
fraction coronas generated by a partially eclipsed
Sun remains virtually constant throughout the en-
tire partial phase.
•The radiance of the sky during totality is typi-
cally a factor 4000 lower than at noneclipse con-
ditions.
•This central estimate is half an order of mag-
nitude higher than the classical value.
•During totality, the signal-to-background ratio
of solar-corona-induced diffraction coronas, halos,
and rainbows is a factor 250 times smaller than dur-
ing nontotality.
•The limiting magnitude during totality is
about þ3:5.
•The Pleiades represent a very suitable object to
observationally test the limiting magnitude during
totality.
•Diffraction coronas are bright enough to stay
visible during totality.
•Intrinsically bright halos also seem to be cap-
able of remaining visible during totality.
•Rainbows during totality seem impossible. An
opposing report probably refers to a rainbow during
the partial phase.
Appendix A: Selection and Data Handling of Twilight
Halos
The observational data that forms the basis of Fig. 8
are from the Halo Section of the Arbeitskreis Me-
teore e.V (Working Group Meteors, abbreviated
AKM [51]), which is the organization that coordi-
nates and documents the halo observations in Cen-
tral Europe. This group, based in Germany, on 1
January 1979 introduced a systematic coding system
(developed by Andre Knöfel and Gerhard Stemmler)
for halo observations [55,56]. This system is of a
structure similar to the coding used in the worldwide
exchange of synoptic weather observations. The
coded elements include the identification number
of the observer, the date, the place of observation
(home, work, or elsewhere), the halo-generating light
source, the day of observation, the halo form, its
brightness and a number of other halo-related de-
tails [57]. Two time indicators are coded: the moment
that the halo was first seen, and the duration of the
halo. The time of first appearance is always coded in
Central European Time (CET, GMT þ1), regardless
whether daylight saving time is effective, and re-
gardless of the time zone where the observer hap-
pens to stay. In most cases, the time of first
appearance is rounded to the nearest 5min; the
duration is given in units of 10 min. For twilight ha-
los, these truncations can cause an error in solar ele-
vation of maximally 0:4° at the first appearance but
of 1:3° at the last appearance.
By the end of 2006, all observations from 1 Janu-
ary 1986 onward were put into the computer. At that
point, the database contained over 65,000 observa-
tions. The number of observers per year grew from
a dozen in the 1980s to more than 30 now. The com-
ing and going of observers resulted in changes of ob-
serving points in the course of the years. In total, 78
observers contributed to the 1986–2006 database.
Most of them live in Germany. The data selection pro-
ceeded in several steps.
First, AKM member Udo Hennig selected the 42
observers with more than 40 observations of lunar
halos in their files and calculated the solar depres-
sion angles at the start, middle, and end of their ob-
servations. From these 42 files we deleted all
observations that were done at places other than
the observer’s home, as well as all observation other
than paraselenae and 22° halos around the Moon. As
it turned out that lunar halo observations referred
four times more often to the 22° halo than to parase-
lenae, we took the analysis further with 22° halo ob-
servations only, that being the only halo whose
appearance is independent of lunar elevation angle.
From this rarefied dataset we selected the files with
at least 20 observations of lunar 22° halos during
H22 APPLIED OPTICS / Vol. 47, No. 34 / 1 December 2008
nautical or civil twilight (solar depression angle 12°
or less). This reduced the number of observers to 9,
all of them living in Germany. These remaining ob-
servers and locations are Richard Löwenherz (town
Klettwitz, identification number 01), Hartmut
Bretschneider (Schneeberg, 04), Gerald Berthold
(Chemnitz, 09), Jürgen Rendtel (Potsdam, 10), Udo
Hennig (Radeberg, 15), Holger Lau (Pirna, 29), Wolf-
gang Hinz (Brannenburg, 38), Claudia Hinz (Bran-
nenburg, 51), and the Weather Station Laage-
Kronskamp (59). The geographical latitudes of these
observers are typically between 51° and 53°N.
From this data set, we decided to use only the eve-
ning observations in the analysis. There are two rea-
sons for that: first, the uncertainty in solar depression
angle due to the truncations in time (see above) is low-
er; second, coding errors related to daylight saving
time would result in underpopulation of events dur-
ing evening twilight, but overpopulation of events
during morning twilight. After this final selection
and the deletion of double observations in the series
of the couple Hinz (10 in total), there remained 168
observations at a solar depression angle of 12° or less;
83 of them are taken at a solar depression angle of 10°
or less, 26 of them are taken at a solar depression an-
gle of 8° or less, and 4 of them are taken during civil
twilight (solar depression 6° or less).
It should be noted that the picture that arises from
Fig. 8about the visibility of eclipse halos—that is,
where the solar corona has taken over the role of pri-
mary light source—is a conservative one. First, it is
plausible that during evening twilight the very first
appearance of a lunar halo is easily missed, which
causes a systematic shift in the solar depression angle
of the dots of Fig. 8toward the right. For halos during
eclipses such an effect does not occur, as the persis-
tence of a halo at the transition to from pretotality
to totality is easily verified. Second, a halo like the
parhelion is usually more light intensive than the
22° halo and therefore has an even better chance to
persist during totality. A parhelion is easy to monitor
during the transition to totality, but because of its
small size is difficult to find during twilight.
U. Hennig is acknowledged for preprocessing the
halo data of the AKM.
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