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 AnnAn = 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 = 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.

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.