The Black Drop Effect During Transits

"I had a feeling once about Mathematics that I saw it all. Depth beyond depth was revealed to me the Byss and Abyss. I saw as one might see the transit of Venus a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go." Sir Winston Leonard Spencer Churchill

Tom Van Flandern This email address is being protected from spambots. You need JavaScript enabled to view it.

2004/06/11

Abstract. Articles about the black drop effect during the 2004 June 8 transit of Venus reveal that the explanation for this previously well-understood phenomenon has been largely forgotten. The Appendix contains a table of the best transits visible from each major solar system planet.

Introduction

Innermost planet Mercury passes in front of the Sun's disk as seen from Earth (a "transit") once or twice every decade. We also observe the Galilean moons of Jupiter occasionally transiting in front of Jupiter's disk, although no outer planet can ever transit the Sun as seen from Earth. Other types of transits are rarer. One of those rarities occurred on 2004 June 8, when the planet Venus transited in front of the Sun's disk for the first time since 1882. We have to wait only eight years for the next transit of Venus, which will be at least partially visible from most of North America on 2012 June 6. However, there will then be an interval of over a century before another Venus transit occurs.[1]

Transits of Venus are more interesting to watch than transits of Mercury, and not just because they are rarer. Venus is larger and closer to Earth during transits than Mercury, so its disk is roughly six times the size of Mercury's during transit. See Figure 1.[2] But because of irradiation (see below), Venus may appear a full order of magnitude larger than Mercury. Moreover, Mercury has no significant atmosphere, whereas Venus has a very thick atmosphere. An atmosphere can concentrate background light by refraction. The result is that Venus occasionally shows an "airglow" halo of illumination around its disk. This is most easily seen near the Sun's limb, when only part of the disk of Venus is in front of the Sun's photosphere.

Historically, transits provided valuable data about the distances to these bodies and the scale of the solar system. However, modern observation techniques have made that type of usage obsolete. So transits are watched mainly because of public interest and the sense of our place in the solar system that they provide. We are privileged to be able to watch another planet pass in front of our own Sun, and to be among the first dozen generations in human history to know what these bodies are and how far they are away, and to be able to predict the local circumstances of these events to within seconds even decades in advance.

Although this transit of Venus lasted about six hours in total (for those in Europe, Africa, and Asia), only the end of the event could be seen from the Eastern U.S. The beginning and end of a transit produce an unusual phenomenon called the "black drop". In this article we will answer questions about what that means and what causes it. As with much human knowledge that hasn’t been used for a long while, many of today's astronomers, science writers, and historians seem to have forgotten about or to have never been taught the correct explanation for the black drop.

What is the black drop?

The disk of Venus is large enough that it may take 20 minutes or so to completely cross the Sun's limb so that the whole planet appears in silhouette. As Venus (or Mercury) is just moving onto the Sun's disk, some number of seconds before the circular disk of the planet separates from the limb, it begins to "drag" a black extension behind it, much like leaving a wake. This elongates and persists well after the moment when sunlight apparently should surround the entire planet disk. Then rather rapidly, this black wake disappears, and the disk looks circular.

At the end of the transit, a symmetric event occurs. The round planet disk approaches the Sun's limb. But distinctly before it gets there, a black extension rapidly appears between the disk and the limb. For both ingress and egress, the appearance of this extension is called the "black drop". See Figure 2. [3]

We can be certain that the effect is not caused by the atmosphere of Venus because Mercury shows it too, and Mercury has no sensible atmosphere. And it is not an optical illusion in the eye because photographic plates see it also. Many modern scholars refer to the effect as a mystery, and some mention that 19th century observers found it confounding because it prevented them from making accurate timings of the moment of contact. However, as recently as a generation ago, astronomers were fully aware of the cause of the black drop, and had applied that knowledge to other types of astronomical observations as well.

What causes the black drop?

When I first browsed through the photographic Palomar Sky Survey 40 years ago, I noted that bright stars were enlarged in size according to how bright they were. So I turned to the plate containing the image of Sirius, the brightest star, and noted that its photographic image was huge – so much so that it hid other stars, galaxies, quasars, and whatever background objects might lie close to the same look direction. And yet the source of this huge smudge was a point source of light. Why did the image spread so much?

Later, I learned about "seeing", an important factor to every Earthbound observer of the skies through a telescope. "Seeing" represents the apparent size of most point sources of light as their light is slightly scattered by passing through constantly moving air cells in Earth's atmosphere. These cells absorb and re-emit passing light, and refract (bend) its direction of travel. The result is that point sources on the sky have "seeing disks", enlarged by the atmosphere to a degree that depends on how calm or rough the atmospheric turbulence is at any given time. Winds at any altitude have the potential to make seeing disks larger. Moreover, the amount of the enlargement depends on the contrast between the brightness of the object and the darkness of the background, and also on the length of time that the light detector accumulates photons. The greater the brightness differential, the greater the difference between the real image size and its apparent size, always in the sense that light spreads and overlaps dark.

In the astronomers' handbooks of more than a generation ago, it was widely recognized that the apparent diameters of bright bodies were enlarged by just such a light-spreading effect known formally as "irradiation". If corrections were not applied, one would get an exaggerated estimate for the diameters of bright bodies. This apparent enlargement was especially a factor for predicting solar eclipses accurately, the times of which depend on the true diameters of the Sun and Moon rather than their apparent diameters. The corrections applied to compensate for irradiation were described in the ephemeris and almanac publications of that era.[4]

Of course, just as the bright Sun's apparent diameter was enlarged by spreading of light onto the dark background sky, the same bright photosphere also spread its light (while passing through Earth's atmosphere) onto the black disks of planets transiting the Sun. So in the case of transits, irradiation of sunlight made the apparent planet diameters smaller because the planets were the darker image. See Figure 3.<³

This difference between apparent and true planet disk diameters is of little practical importance except in critical cases such as eclipses. A simple but important consequence is that, because the amount of shrinking of the apparent diameter during transits is independent of the size of the diameter, objects one-third the apparent diameter of Mercury (a few arc seconds) would be completely overlapped by spreading solar light and display no visible disk whatever! That is undoubtedly why no asteroid or artificial satellite has ever been observed to transit the Sun, and why historic searches for inter-Mercurial planets transiting the Sun would have probably been unsuccessful even if such planets had existed.

Armed with this knowledge about irradiation, we can easily understand the black drop phenomenon. In the left half of Figure 3, the Sun's limb appears at a greater angular distance from the planet than it really is, both because the planet's disk appears smaller than it is, and because the Sun's disk appears larger than it is. Then the apparent planet disk approaching the limb remains circular until the instant when the invisible true limbs of planet and Sun make contact. At that moment, light can no longer originate from that point, so it can no longer spread and make the Sun's limb appear enlarged or the planet's limb appear shrunk. So we have the black drop, when the true planet disk and the true solar limb reveal themselves.

If the Sun's photosphere was of uniform brightness all the way to its limb and the planet had no atmosphere, the black drop would be a near-instantaneous effect. However, the real photosphere has limb darkening because of light having to be directed toward Earth at ever greater angles from the normal, and because the optical path of light from the limb has more opacity. (For the same reason, the Sun appears dimmer as it approaches Earth's horizon.) Moreover, the photosphere does not just end, but fades gradually into the much dimmer, ruby red chromosphere that normally can be seen only during total solar eclipses. [When using a hydrogen-alpha filter, the chromosphere is relatively bright, producing a "limb brightening" effect that drastically changes the appearance near this internal ("second" or "third") contact of the Sun and Venus limbs.]

So the gradual dimming of the Sun's photosphere near its limb makes the black drop effect of short-but-finite duration (a handful of seconds). And the airglow halo of refracted sunlight passing through the atmosphere of Venus creates additional ambiguity about when the exact contact has occurred. Nevertheless, contrary to the impression stated by astronomers in past transits of Venus before this effect was anticipated or understood, the black drop is the most readily timed event during the entire transit, and corresponds more precisely to the true instant of contact with the same solar limb used to compute eclipses so accurately. So now that we understand what causes the black drop, we can appreciate that it provides a timing advantage rather than a disadvantage.

Irradiation is also seen with lunar occultations

Other astronomical phenomena also show this irradiation effect – the apparent spreading of light from bright areas onto any adjacent dark areas. One of the most common, visible to amateur astronomers far more frequently than transits, is lunar occultations. When a star is bright enough to remain visible near the Moon's bright (daylight) limb, or even for fainter stars near the Moon's darker (night side) limb when that side of the crescent Moon is illuminated by Earthshine, irradiation makes the Moon's limb appear larger than it really is. As a direct result, the star appears to penetrate the Moon's limb by a short distance, as if burrowing into the surface, before the true limb cuts off its light almost instantaneously. See Figure 4.[5]

he fact that the occultation occurs with the same rapidity whether the Moon’s limb is visible or invisible to the observer confirms that the light in space is not being altered, and the illusion of irradiation must arise in Earth’s atmosphere. Photoelectric photometers can detect the actual speed at which the star disappears, which is not instantaneous because of diffraction. (Diffraction is the bending of lightwaves passing any sharp edge.) If one brings two fingers together without quite touching, a black-drop-like apparent touch can still be seen because of diffraction. But lunar image spread from diffraction is roughly three orders of magnitude smaller than that from variable refraction through moving terrestrial air cells. A typical seeing-enlarged star image would take several seconds for the Moon to cover. However, except for the rare star that has a sensible diameter or a close companion, the actual disappearance of a star at the Moon’s limb takes only a handful of milliseconds.

My thanks to Greg Hennessy <This email address is being protected from spambots. You need JavaScript enabled to view it.> for drawing my attention to an observation of the black drop effect during a 1999 November 15 Mercury transit observed from the TRACE satellite in near-Earth space. These authors point out that all ground-based observers are subject to a much larger and time-variable black-drop effect because of “seeing” effects in Earth’s atmosphere. But when that is no longer present in space, a smaller, predictable effect from diffraction remains visible from orbit.[6] Another correspondent, Peter Abrahams <This email address is being protected from spambots. You need JavaScript enabled to view it.>, mentioned two relatively recent articles by Bradley Schaefer. The first attributes the ground-based black drop simply to “terrestrial atmospheric smearing, which blurs the image.”[7] The second states: "the ideal image … will suffer smearing … that will produce a somewhat fuzzy image with contour lines (i.e., what is perceived as the edge) that are shaped like the Black Drop. The primary causes of smearing are the usual astronomical seeing (associated with small angle scattering in our Earth's atmosphere) and the usual diffraction in the telescope (the Airy pattern). Other contributing smearing mechanisms that generally do not dominate are imperfections in the telescope's optics, imperfections in the observer's eyes, the finite angular resolution of the detector, and even the physical size of the telescope's aperture."[8]

Conclusion

The black drop phenomenon seen during transits is a well-understood manifestation of irradiation, the spreading of photons by rapidly moving air cells. It provides an advantage for the accurate timing of internal (second and third) contacts for transits, not a disadvantage. Figure 5 shows one of the best photos of the actual black drop effect, taken by Uwe Schürkamp in Germany during the 2004 June 8 Venus transit.[9]

Those who missed the 2004 June 8 transit of Venus still have the 2012 June 6 event to look forward to, which will be visible from most of North America, especially the western parts. But if you miss that opportunity, you will need to book a ticket on a spacecraft to see such a transit in your lifetime, because the following transit of Venus from Earth after 2012 will be in the year 2117.

For many observers, the seconds when the black drop occurs may be the most interesting of this rare, multi-hour astronomical manifestation of Earth's place in the solar system, a transit of Venus.

Appendix

As people think about our place in the solar system, they are now starting to ask questions that would have had no foreseeable relevance to Earth residents the last time a Venus transit occurred, such as "What would an Earth transit look like if viewed from Mars?" It is interesting to contemplate that by the time of the 2117 Venus transit, people may be making plans to actually observe just such "science fiction" events.

Table I shows a few of the possibilities. (Angles are in arc seconds. Transiting planet angular diameters are also expressed as a percentage of the Sun's angular diameter.) It is interesting to note that no transits of solar system planets observed from other major planets present a larger angular diameter than transits of Venus present to Earth observers. But Earth and its Moon present the only opportunities for a 2-body transit if viewed from Mars. And transits of Jupiter observed from Saturn block the largest fraction of the arriving sunlight, roughly 5%. These events would last a day or two. During that period, sunlight reflected from Saturn and its rings would be dimmer than normal by an amount easily detected from Earth by a photometer. If views of transits of Jupiter seen from Saturn's moons were also considered, the window of opportunity for witnessing such an event would be even greater. (In fact, Jupiter's large shadow might cause temporary physical changes for asteroids and comets that enter it.) Transits of Jupiter and Saturn visible from Uranus or Neptune or their major moons should likewise have a detectable effect on the shadowed body's brightness. Our readers are challenged to be the first to predict the date and time of any such event.

Table I. The best transits visible from each major solar system planet

[1] F. Espenak (2002), "2004 and 2012 transits of Venus", http://sunearth.gsfc.nasa.gov/eclipse/transit/venus0412.html.

[2] W. Koorts (2003), "The 1882 transit of Venus: Observations from Wellington, South Africa",https://www.saao.ac.za/~wpk/tov1882/tovwell.html

[3] C. Bueter (2004), "The black drop effect",, http://www.transitofvenus.org/blackdrop.htm.

[4] H.M. Nautical Almanac Office (1961), "Explanatory supplement to the astronomical ephemeris". See index. (The later 1992 edition ceased to describe irradiation corrections.)

[5] Hands-On Universe (2004), http://hou.lbl.gov/ISE/new/moon/moongifs.html.

[6] G. Schneider, J.M. Pasachoff & L. Golub (2000), “Trace observations of the 15 November 1999 transit of Mercury”,, http://nicmosis.as.arizona.edu:8000/POSTERS/TOM1999.jpg.

[7] B. Schaefer (2000), “The Transit of Venus and the Notorious Black Drop, B.A.A.S. 32, 1383-1384.

[8] B. Schaefer (2001), “The Black Drop Effect”, J. History Astronomy 32:4, 325-336.

[9] U. Schürkamp (2004), http://www.schuerkamp.de/zope/hoover/astronomy/venus_transit_2004.