A 60 kHz SID “Radio Telescope” Observation of the 2017-08-21 Solar Eclipse

An amateur-built solar flare detector at Cotter Arkansas monitors the ionosphere-refracted signal from the WWVB 60 kHz time standard transmitter near Ft. Collins, Colorado. The refraction region of the skywave propagation path, which is sensitive to the extent of ionosphere ionization and thus the level of incoming ionizing radiation from the Sun, is over central Kansas. During the August 21, 2017 total solar eclipse, the maximum shadow at the refraction spot was ~96.5% of totality, and the instrument recorded a strong eclipse signal. The plot of signal strength versus time was linear beginning about half-way between first contact and maximum, agreeing with a mathematical model for the area of overlap of circles, which should vary virtually linearly between half-overlap and maximum but not before half-overlap. The inverted V plot was also linear beyond maximum but sloped downward more steeply, losing linearity at about the same signal strength where linearity was attained during the first half of the eclipse; thus, the inverted V is asymmetric. These results raise several questions: Is the observed linearity actually due to a time-ordered linear decrease of luminous area between mid-eclipse and maximum, or is it due to some quirk of the receiving system? Is it possible that the observed asymmetry is related to the ?

My instrument in Cotter Arkansas is a radio telescope only in the sense that it uses low frequency radio to sound the ionosphere; it monitors the skywave’s signal strength arriving from National Bureau of Standards and Technology radio station WWVB, located near Ft. Collins Colorado. The presumed county-sized volume of ionosphere above Kansas, where the 60 kHz waves refract back toward the ground around Cotter, is sensitive to changes in its degree of ionzation, which shows up in the strength of the received radio waves; so it is actually a detector of incoming ionizing radiation ranging between short wavelength UV, through x-rays, to gamma radiation. Solar flares in the range X, M and C produce enough x-rays and short wavelength UV to show up in the time-ordered recordings from instruments like mine (however, most flare detectors of this type operate in the VLF frequency range below 30 kHz). The flare-related events are called Sudden Ionization Disturbances (SID). These instruments might also detect the stronger Gamma Ray Burst (GRB) phenomena, and they are sensitive to Solar eclipses, for the same reason that ionospheric propagation of radio waves is enhanced beginning around sunset and increasing into the night.

I did not make any special preparations for the August 2017 Solar eclipse, as seen from Cotter; I just let my receiver record as usual while my wife and I were in Missouri at a small town called Leslie, very near the eclipse centerline. Normally, my recordings run about a week before I download data, and I wondered what might show up in my information, because the sensitive spot above Kansas would be about 96.5% eclipsed. As it turned out, I received a strong eclipse signal.

My SID system’s major components are: an 8-ft, preamplified loop antenna oriented (permanently) roughly NW/SE to maximize the 60 kHz LF signal from WWVB (Ft. Collins, CO); a Ralph Burhans heterodyne up-converter for relocating the signal to 4060 kHz (a shortwave frequency); a Kenwood R-2000 communications receiver for amplifying the 4060 kHz signal; a type of “third detector” circuit for averaging the receiver’s audio frequency signal strength; and a computer with DC analog to digital capability for logging signal strength as a function of time. . The instrument operates at a fixed gain setting, which involves some front end (preamp) attenuation (also kept constant); my very minimal experience with only three strong X-flares (ever!) is that even with front-end attenuation, receiver saturation becomes evident above a scale value of 300. In comparison, the solar eclipse described in this paper produced a signal that did not quite reach a scale value of 250.

The operating program that I wrote in QBASIC stores one-minute averages of signal strength along with a time stamp from a real-time clock, with the data in text format. The start times of the one minute averaging intervals are accurate to the second. The best time to begin a recording is pre-dawn, when the WWVB signal is usually strongest, and I start the operating program with visual reference to a WWVB synchronized Westclox “atomic” clock, which is always checked for validity against the audio clock and voice signals from WWV HF. Doing this manually, the time error of pressing “ENTER” is ~0.2 seconds. The clock cost ~$12.

The coordinates of Cotter Observatory are North 36 deg 16’ 9.4”, West 92 deg 32’ 9.6”, EPE ~ 11 ft, elevation 560 ft MSL.

The upward deflection of the mid-day eclipse signal was about like that of a strong M-flare or perhaps even a weak X-flare, but its profile near the peak was very different from that of a solar flare. Figure 1 shows the SID receiver’s data for most of August 21, 2017, and Figure 2 is an expanded scatter plot of just the upper part of the eclipse peak, where each data point is the outcome of the one minute signal averaging increments of the instrument (see experimental details). The innermost data preceding and following maximum eclipse were surprisingly linear, with linearity beginning ~40 minutes before the eclipse and ending ~27 minutes afterward. In other words, the preceding and following slopes of the “inverted V” plot of Figure 2 were distinctly different. Also, in both cases the linearlty ended on going below about 70 on the signal amplitude scale.

Does the observed asymmetry fit a corresponding asymmetry of the moon’s shadow? Eclipse information for Jefferson City, MO:

(https://www.timeanddate.com/eclipse/solar/2017-august-21)

shows that first contact with the penumbral shadow began 88 minutes before mid eclipse and last contact was 87 minutes afterward, nearly symmetrical and probably fairly similar to the point along the eclipse centerline where my ionosphere spot was nearest to the centerline. An 88/87 dis-symmetry of the Sun’s illumination does not seem consistent with the observed +4.5/-7.6 dis-symmetry of slopes in Figure 2!

I consulted the mathematical literature for a possible explanation of the linearity seen in Figure

2.The loss of illumination should be fairly proportional to the moon/sun overlap area, and because the moon and Sun have similar angular diameters, the problem can be modeled, as a first approximation, as the area of overlap (A) between two circles and how A varies as a function of the distance (d) between the centers of those circles. A good treatment of this problem and the derivation of A = F(d,r), where r is the radius of the circles, can be found here:

http://jwilson.coe.uga.edu/EMAT6680Su12/Carreras/EMAT6690/Essay2/essay2.html

Wilson’s derived equation for A as a function of d (r is assumed to be 1), along with a plot of A vs. d is shown in Figure 3:

(https://www.timeanddate.com/eclipse/solar/2017-august-21)

shows that first contact with the penumbral shadow began 88 minutes before mid eclipse and last contact was 87 minutes afterward, nearly symmetrical and probably fairly similar to the point along the eclipse centerline where my ionosphere spot was nearest to the centerline. An 88/87 dis-symmetry of the Sun’s illumination does not seem consistent with the observed +4.5/-7.6 dis-symmetry of slopes in Figure 2!

I consulted the mathematical literature for a possible explanation of the linearity seen in Figure

2.The loss of illumination should be fairly proportional to the moon/sun overlap area, and because the moon and Sun have similar angular diameters, the problem can be modeled, as a first approximation, as the area of overlap (A) between two circles and how A varies as a function of the distance (d) between the centers of those circles. A good treatment of this problem and the derivation of A = F(d,r), where r is the radius of the circles, can be found here:

http://jwilson.coe.uga.edu/EMAT6680Su12/Carreras/EMAT6690/Essay2/essay2.html

Wilson’s derived equation for A as a function of d (r is assumed to be 1), along with a plot of A vs. d is shown in Figure 3:

The upper left-hand end of this plot corresponds to total eclipse, and as it turns out, the function is quasi-linear all the way down to A/2. This is interesting because linearity of the shadow curve should end at the mid-point of a penumbral eclipse. Applying that to the first penumbral contact time of the eclipse at Jefferson City, MO, linearity should set in at 88 minutes/2, or 44 minutes before mid-eclipse, which is close to the observed departure from linearity at about 40 minutes in Figure 2. This makes the dis-symmetry of the second half of the eclipse seem all the more perplexing! If the Sun is near the zenith during an eclipse (and it was on 2017-08-21), we should be able to rotate this plot around the A axis and see what the other half of the eclipse looks like - a fairly symmetrical inverted V - at least at visible light wavelengths. But again, these are only first order approximations, and we are not observing at visible wavelengths. For one thing, the two radii are not equal, and because of limb darkening and possible sunspots, luminosity is not exactly proportional to the uneclipsed area even at visible wavelengths:

Or what is much more relevant, the illumination at ionizing wavelengths is also not constant across the solar disk:

Keeping these limitations in mind, the quasi-linear portion of the shadow function can be represented by an empirical equation

A ~ -0.0114d +1, where the intercept, b, is scaled as π/π = 1.1

My next question was this: “How far away from totality can the observer (or ionosphere sensitive spot) be and record a fairly linear-looking inverted V, like the scatter plot of Figure 2?

That moved me to work out an approximate empirical equation that corrects for an observing position at some distance away from the centerline. To keep it as simple as posible, the region of totality is virtually a point, like what happens in eclipses that are at the dividing line between annular and total.* Thus, the center line of Figure 6 is just a line and not a broad shadow path.

A ~ -0.0114d +1, where the intercept, b, is scaled as π/π = 1.1

My next question was this: “How far away from totality can the observer (or ionosphere sensitive spot) be and record a fairly linear-looking inverted V, like the scatter plot of Figure 2?

That moved me to work out an approximate empirical equation that corrects for an observing position at some distance away from the centerline. To keep it as simple as posible, the region of totality is virtually a point, like what happens in eclipses that are at the dividing line between annular and total.* Thus, the center line of Figure 6 is just a line and not a broad shadow path.

It is given that A = 1 (totally eclipsed) on the center line of Figure 6, and the observer will be illuminated to a degree depending on his/her distance from the centerline, so the total illumination when the shadow is closest to the observer will be proportional to:

A(O) = A - A’ 2

Where A’ is the fraction of the Sun’s image that is not eclipsed, and when the moon’s shadow is nearest to the observer, A’ = 1 - f, where f is the fraction of total eclipse at the observer’s position. At d = 0, angle theta is 0 and Cos(0) = 1, but beyond that point the value of A’ will decrease as theta increases; the decrease is proportional to Cos(theta), where theta is, in turn, a function of d:

A’ ~ (1 - f)Cos[F(d)] 3

It is not hard to see, by inspection, that F(d) is the arctangent of d/d(0), thus:

A’ ~ (1 - f)Cos{Tan?[d/d(O)]} 4

The area component A’ will diminish to near zero as theta trends toward 90 degrees, and even

when d is only 4 (Figure 6) the length of the hypotenuse is becoming comparable to the length

of d; so “light curves” for the center line and offset observing positions will become virtually the

same (i.e., differ by less than the experimental error). I wrote a program in QBASIC that

combines equations 1 and 4 according to equation 2. The program generates tables of ordered

pairs of A and d, where d is varied for any desired offset distance, including zero. Then I used

the PLOTLY APP** ( https://plot.ly/ ) and my tabulations (in text format) to generate the following

hypothetical recordings. Figure 7 compares the centerline (a straight line) with the

model-predicted response for observation at the 96.5% observing position.

A(O) = A - A’ 2

Where A’ is the fraction of the Sun’s image that is not eclipsed, and when the moon’s shadow is nearest to the observer, A’ = 1 - f, where f is the fraction of total eclipse at the observer’s position. At d = 0, angle theta is 0 and Cos(0) = 1, but beyond that point the value of A’ will decrease as theta increases; the decrease is proportional to Cos(theta), where theta is, in turn, a function of d:

A’ ~ (1 - f)Cos[F(d)] 3

It is not hard to see, by inspection, that F(d) is the arctangent of d/d(0), thus:

A’ ~ (1 - f)Cos{Tan?[d/d(O)]} 4

The area component A’ will diminish to near zero as theta trends toward 90 degrees, and even

when d is only 4 (Figure 6) the length of the hypotenuse is becoming comparable to the length

of d; so “light curves” for the center line and offset observing positions will become virtually the

same (i.e., differ by less than the experimental error). I wrote a program in QBASIC that

combines equations 1 and 4 according to equation 2. The program generates tables of ordered

pairs of A and d, where d is varied for any desired offset distance, including zero. Then I used

the PLOTLY APP** ( https://plot.ly/ ) and my tabulations (in text format) to generate the following

hypothetical recordings. Figure 7 compares the centerline (a straight line) with the

model-predicted response for observation at the 96.5% observing position.

Considering the scatter in the observational data of Figure 2, the plot of Figure 7 is virtually linear beyond 6 minutes, and that significantly downward-curved region less than six minutes from mid-eclipse blends into the flattened and curved apex of Figure 2. The model is not exact, especially for the August 21, 2017 solar eclipse, but it certainly seems to allow for the linearity of Figure 2.

Figure 8 compares a broader range of eclipses, but it doesn’t plot 96.5% to avoid crowding. Even at 95% the linearity is beginning to disappear. If I had known about the possibilities of a SID receiver during solar eclipses I would have made my system portable and taken it with me to Leslie, MO! That would have put my ionosphere refractive spot much closer to the eclipse centerline.

I am a chemist, thus too far out of my element to draw any reliable conclusions about the

meaning of my data. I do wonder if the asymmetry of slopes in Figure 2 has anything to do with

the supersonic shadow’s*bow wave phenomenon, a compression effect *, which was finally

documented during this eclipse by Shun-Rong Zhang’s group at MIT. See their complete

*Geophysical Research Letter *here:

http://onlinelibrary.wiley.com/doi/10.1002/2017GL076054/full . The steeper slope after the

vertex might be related to the stern wave and its wake of*expansion *. My instrument *is *sensing

the ionosphere, so the possibility that it is detecting bow and stern wave effects does not seem

remote. Based on my time data, which I believe are accurate, the*apparent position *of the

ionosphere refractive spot was not mid-way between Ft. Collins and Cotter but about three

minutes of time southeastward (roughly 75 miles).

Figure 8 compares a broader range of eclipses, but it doesn’t plot 96.5% to avoid crowding. Even at 95% the linearity is beginning to disappear. If I had known about the possibilities of a SID receiver during solar eclipses I would have made my system portable and taken it with me to Leslie, MO! That would have put my ionosphere refractive spot much closer to the eclipse centerline.

I am a chemist, thus too far out of my element to draw any reliable conclusions about the

meaning of my data. I do wonder if the asymmetry of slopes in Figure 2 has anything to do with

the supersonic shadow’s

documented during this eclipse by Shun-Rong Zhang’s group at MIT. See their complete

http://onlinelibrary.wiley.com/doi/10.1002/2017GL076054/full . The steeper slope after the

vertex might be related to the stern wave and its wake of

the ionosphere, so the possibility that it is detecting bow and stern wave effects does not seem

remote. Based on my time data, which I believe are accurate, the

ionosphere refractive spot was not mid-way between Ft. Collins and Cotter but about three

minutes of time southeastward (roughly 75 miles).

Finally, I see low amplitude ripples in the up-slope of Figure 2, and the published animations of the bow wave effect shows distinct ripples:

(https://www.youtube.com/watch?v=8vivMEVBwys&feature=youtu.be).

Figures 9 and 10 snapshots the ripples referred to. They are more evident on the sternward (northwest) side, similar to what you see in the wake of a boat or a ship.

(https://www.youtube.com/watch?v=8vivMEVBwys&feature=youtu.be).

Figures 9 and 10 snapshots the ripples referred to. They are more evident on the sternward (northwest) side, similar to what you see in the wake of a boat or a ship.

*This assumes a very brief totality. The light curve along the center line of the August 21, 2017 Solar eclipse would have been an inverted V with a flattened apex- flattened for about 2.7 minutes. But there is a species of eclipses, one with a sharp apex, and I actually witnessed one of those near a place called “LaPlace” in southern Louisiana: a very thin annular eclipse. The sudden plunge of light gets to a lot of people in the path of totality, especially if it’s their first one. There was indeed an illumination plunge during that eclipse, enough to photograph prominences and scare novices, but it reversed very rapidly. Some present likened it to a strobe of darkness. I said it “...seemed to me like something bounced.”

See:http://www.nytimes.com/1984/05/31/us/millions-in-south-treated-to-rare-view-of-solar-eclipse.html

**I give PLOTLY a really first class rating, but they want to make money and no longer even allow screen captures of their entry page (although that screen still permits basic plotting activity for potential customers), so PLOTLY, Inc., is no longer accommodating the poor, retired folks like me. I had to photograph my result with a Kodak electronic camera! My apologies.

Submitted by John R. Wright, February 14, 2018

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Link to PDF file

by John Wright in Cotter, AR, email cotterobservatory403@gmail.com