Preliminary Analysis of the Total Lunar Eclipse on May 26, 2021
This is a
preliminary analysis of the total lunar eclipse on May 26, 2021 based only on photos
and videos available on the internet.
During the event, as a sensitive global monitor of Earth`s
atmosphere, the Moon probed the northern half of the shadow cast by our planet.
Estimates of brightness and umbral enlargement are presented.
Determining the Apparent Magnitude of the Moon
In order to
estimate the brightness of the Moon, two different methods have been used:
(1) Analysis of
a wide-angle high-resolution image of totality in order to estimate the
magnitude (m) of the Moon by comparing it in brightness with neighboring stars;
(2) Inspection of photos of the Moon taken at mid-totality aiming at evaluating
the Danjon Numbers (L) of different parts of the disk based on their colors.
1.
Estimating the Magnitude of the Moon by Comparison to Nearby
Stars
A
high-resolution mid-eclipse still image obtained from a video produced at the Mauna Kea
Observatory was
enlarged and analyzed. The images of the Moon and of 21 nearby stars, most of
them from Scorpius and ranging from 2.3 to 6.4 in magnitude, were meticulously
measured on the monitor screen. Antares, not included in the analysis due to
its variability (currently at m≈+0.8±0.1), remained several times dimmer
than the Moon during totality. A least-squares fitting to a logarithm function
allowed apparent magnitudes to be significantly correlated (r2=0.94)
to image sizes, yielding m= -1.93±0.17 for the Moon (A= 291mm2) as shown
in Fig.1.
2. Estimating the Danjon
Number
The method
developed by the author has been found to yield good results. It consists in
assigning a Danjon Number (Ln) to 2, 3 or 4 parts of the Moon at midtotality according to
their colors. The mean L of the disk will be given by
multiplying each partial estimate Ln by the corresponding fraction An
(ΣnAn = 1) of the Moon`s disk and adding the results
of all parts. Further details were provided in a previous work. Three photos were analyzed.
Results are listed table 1.
Table 1 – Parameters for Estimates of Danjon Numbers
Photo |
A1 |
L1 |
A2 |
L2 |
A3 |
L3 |
L |
0.08 |
4 |
0.70 |
2.5 |
0.22 |
1.6 |
2.42 |
|
0.10 |
4 |
0.70 |
2.6 |
0.20 |
1.8 |
2.58 |
|
0.40 |
3.4 |
0.45 |
2.5 |
0.15 |
1.9 |
2.77 |
|
Mean |
<L>
= 2.59 ± 0.17 |
2.59±.17 |
Note that the
direction A1-3 represents increasing penetration into Earth`s umbral
shadow with A1 corresponding to the bright northern edge and the
lowest Danjon Numbers being assigned to A3, the southern part of the
Moon`s disk, much darker because it had reached an
inner, and consequently darker, region of the umbra.
Finally, the
magnitude of the Moon was calculated by using a correlation found by the author
between apparent magnitude (m) and the Danjon Number (L) :
m = 4.2
– 3 * L + (L / 2)2 = 4.2 – 3
* 2.59+ (2.59/2)2 = -1.89 ± 0.17
(Eq.1)
Thus both
methods gave m=-1.9±0.2 as the mean estimate of the Moon's visual magnitude at
mid-eclipse.
Explaining the Additional Darkening
Two major
factors are known to impact the brightness of the totally eclipsed Moon: (1)
how deeply it goes into Earth`s umbra and (2) the
amount of volcanic gases and aerosols present in the stratosphere. The umbral
magnitude of this eclipse, so close to 1, means that
the umbra barely covered the entire disk of the Moon at mid-eclipse. In fact,
that was the major reason why a bright band of residual light, corresponding to
the outermost part of the umbra, remained prominent during totality, capping
the northern region of the Moon`s disk.
Judging only
from its umbral magnitude, this eclipse should have been bright and rich in
colors with m=-3.3±0.2
(L=3.6±0.2), according to a correlation derived by the author for total
eclipses of umbral eclipse magnitude (U) in a “clean stratosphere” based on data gathered at 13 past eclipses
not preceded by volcanic eruptions:
m = 4.71
* U -
8.07 (13 clean eclipses r2
=0.925) (Eq.2)
And in fact
that was the mean mid-eclipse magnitude reported for the total eclipse of November
9, 2003, that had a similar umbral magnitude (U=1.02).
Thus, the
eclipse was 1.4 (=3.3-1.9) mag darker than predicted for a
clean stratosphere. In addition, its
corresponding Danjon Number being L=2.6±0.2, means that is was about a unity
lower than at a grazing total eclipse mostly illuminated by a clean
stratosphere.
The impression
that the eclipse was a bit darker than expected was shared by many observers.
Citing comments published in an article: "It was not quite the brilliant display they had
anticipated. Not quite super or blood-colored. It was not that vivid."
Up to this
point, only the
geometry of the eclipse, mainly the shallow path of the Moon across the umbra,
has been discussed. However, as previously mentioned, the darkening effect of major volcanic
eruptions should also be considered. Surprisingly though, a quick search for
stratospheric eruptions in the past couple of years failed to reveal any likely
candidates at first.
Indeed, no
major volcanic explosion capable of injecting great amounts of volcanic
aerosols into the stratosphere occurred in the past two years. However, several
smaller eruptions launched significant amounts of volcanic debris to the top of
the troposphere in 2020 and 2021, from where a fraction of that material could
have eventually reached the stratosphere. By analyzing the history of volcanic
activity during the past months with a program developed by the author, that
evaluates the darkening of the Moon at mid-totality due to any combination of
eruptions of known explosivity preceeding the eclipse, it was possible to
determine three likely culprits and their individual impacts on the apparent
magnitude of the totally eclipsed Moon.
Namely, they
were the volcanoes (eruption date, Δm): Sheveluch
(Dec. 2020, 0.6), Sinabung (Aug. 2020, 0.4) and Sabancaya (Aug. - Sep. 2020,
0.4). The volcanoes underwent series of eruptions that caused a 1.4-mag
darkening of the Moon
at mid-eclipse.
The observed
change in magnitude corresponds to a volcanic aerosol optical thickness of
0.035 (=1.4/40), considered a moderate effect on eclipse brightness. A five-point scale proposed by the author to describe the
impact (in magnitudes) of volcanic aerosols on the brightness of the totally
eclipsed Moon is: (1) minor (<0.5),
(2) small (0.5-1), (3) moderate (>1-2.5), (4) large (>2.5-4.0), (5) very
large (>4.0).
It is also possible
to say at this point that some of those aerosols, added to others launched by
more recent eruptions (San Cristóbal and Soufrière St. Vincent Volcanoes), will affect the appearance of the deep partial eclipse on
Nov. 19, 2021.
Determining the Atmospheric Enlargement of Earth`s
Umbra
With no access to limb or crater contact timings, the author
analyzed a video that showed
the entire total phase, realizing that by timing its duration it would be
possible to determine the size of the umbra. Due to the fact that the beginning
of totality would occur at a very high umbral angle (82o), even a
small change in the radius of the umbra could impact the duration of totality
significantly. Thus duration of totality became a sensitive indicator of the
atmospheric enlargement of Earth`s umbral shadow for this eclipse. For that reason, in
order to determine the atmospheric enlargement of Earth`s figure (or the Moon`s parallax (π)), which is known to vary from one
eclipse to another, a correlation between the two parameters had been
previously determined by the author as shown in Fig. 2.
However, pinpointing
the beginning and end of totality from a video proved to be a challenging task.
Thus, in order to reduce errors, five series of
timings were performed. The mean duration of totality was then approximately
determined as 14m07s+-18s. Based on the forementioned correlation, the value
was found to correspond to an enlargement of the Moon`s
parallax due to Earth`s atmosphere
of π = 1.24±0.02%, significantly
lower than its all-time mean of 1.34%, although in close agreement with
π=1.26%, used by the author to predict crater contacts for this eclipse. The value was determined based on obsevation
of recent eclipses and also on a semi-empirical approach. Contact predictions 1 and 2 were also reproduced by entering π=1.14% and 1.36%,
respectively. The observed increase in the Moon`s
parallax is equivalent to an enlargement of Earth`s umbra equal to E =
1.67±0.03%, also significantly lower than its all-time mean of 1.85%.
Totality was
never threatened for this eclipse. In fact, the unrealistic condition
π<0.75% should be satisfied for a deep partial
eclipse to happen. However, the lowest possible value of π is ≈1.1%.
Surprisingly though, some unexperienced observers referred to mid-eclipse as
“near totality”, failing to realize that the residual sliver of light that
adorned the northern edge of the Moon`disk througout
totality was in fact the outermost umbra, not the penumbra.
Table 2 summarizes the most important
parameters found .
Table 2 – Umbral Enlargement and Brightness Parameters
2021 May 26
Total Lunar Eclipse Data Table |
|||
Atmospheric Enlargement |
Moon`s Brightness |
||
Parameter |
|
Parameter |
Observed |
π (%) |
1.24±0.02 |
m |
-1.9±0.2 |
E (%) |
1.67±0.03 |
Δm |
+1.4±0.2 |
Duration of Totality (m) |
14m07s±18s |
L |
2.6±0.2 |
|
ΔL |
-1.0±0.2 |
Conclusion
The grazing total
eclipse of May 26, 2021 was moderately darkened by the presence of
stratospheric volcanic aerosols that reduced the brightness of the Moon by
about 1.4 magnitudes at mid-eclipse. In addition, the contribution of the
amosphere to Earth`s umbral shadow remained lower than
its all-time mean. Less vivid colors and a low atmospheric umbral enlargement
should also be expected for the deep partial lunar eclipse on November 19,
2021.