# The Myth Of The Starbow

Thus, with all Einstein numbers of flight [velocity as a proportion of the speed of light] greater than 0.37 a major dark spot will surround the take-off star, and a minor dark spot the target star. Between the two limiting circles of these spots, all stars visible in the sky are coloured in all the hues of the rainbow, in circles concentric to the flight direction, starting in front with violet, and continuing over blue, green, yellow and orange to red at the other end.

E. Sänger “Some Optical And Kinematical Effects In Interstellar Astronautics” Journal of the British Interplanetary Society (1962) 18(7): 273-7

Above is one of the earliest descriptions of the appearance of the sky as seen from a spacecraft travelling at close to the speed of light, written more than half a century ago. It predicts something remarkable—that the sky would be dark both ahead of and behind the spaceship, and between these two extensive discs of darkness a rainbow would appear. One of the best illustrations of this phenomenon that I’ve found appears on the cover of Frederik Pohl’s 1982 science fiction novel, Starburst, shown at the head of this post. (This is both unexpected and ironic, for reasons I’ll reveal later.)

Now, I’ve recently invested four posts in systematically piecing together the appearance of the sky from a spacecraft moving at close to the speed of light. If you’re interested, the series begins here, builds mathematical detail over the second and third posts, and draws it all together, with illustrations, in the final one. Using the equations of special relativity for aberration and Doppler shift, and applying them to black-body approximations of stellar spectra, I was able to come up with some pictures using the space simulator software Celestia.

Here’s a wide-angle view of the sky ahead seen when moving at half the speed of light:

And a tighter view at 0.95 times light speed:

And at 0.999 times light speed:

No sign of Sänger’s “minor dark spot” ahead, and no real indication of a rainbow. The stars appear hot and blue ahead, in a patch that becomes more concentrated with increasing speed, and that central area is surrounded by a scattered rim of red-shifted stars, shading off into darkness all around. At very high velocity, the blue patch begins to fade. (For a detailed step-by-step explanation of all this, see my previous posts, referenced above.)

What’s going on? Well, Sänger made an embarrassing mistake:

For simplicity’s sake we may assume that the stars in the sky, as seen from the space vehicle when at rest, are all of a medium yellow colour of perhaps λ0 = 5900Å.

He modelled all the stars in the sky as if they emitted light at a single wavelength, like a laser! Unsurprisingly, when these monochromatic stars were Doppler-shifted, they passed through all the colours of the rainbow before disappearing into ultraviolet wavelengths (ahead) or infrared (behind). Hence the dark patches fore and aft of Sänger’s speeding spacecraft, and the rainbow ring between.

But of course real stars emit light over a range of wavelengths, with peak emissions that vary according to their temperatures. As I explained in previous posts, when real stars are Doppler-shifted they change their apparent temperature, so the stars ahead of our spacecraft appear to get hotter, while those behind appear cooler. Hot stars may look white or blue, but never violet. Cool stars may be yellow or orange or red, or faded to invisibility, but there is no temperature at which they will appear green. And the fact that stars of different temperatures are scattered all across the sky means that Doppler shift can’t ever produce the concentric circles of colour that Sänger imagined. Sänger’s rainbow is a myth, based on a fatally erroneous assumption (“for simplicity’s sake”) that really should have been picked up by reviewers at the British Interplanetary Society.

Sänger’s idea would have vanished into appropriate obscurity, were it not for the fact that science fiction writer Frederik Pohl was a member of the British Interplanetary Society, and received its monthly journals. Writing about it later, Pohl mistakenly recalled reading Sänger’s article in another BIS publication, Spaceflight. (BIS members received one publication as part of their membership, and could pay to receive the other, too—it seems likely Pohl subscribed to both.) He later described his encounter with Sänger’s article like this:

Before I had even finished it I sat up in bed, crying “Eureka!” It was a great article.

“Looking For The Starbow” Destinies (1980) 2(1): 8-17

Pohl loved this image of a rainbow ring, and called it a “starbow”. He went on to feature the starbow in an award-winning novella, “The Gold At The Starbow’s End” (1972):

The first thing was that there was a sort of round black spot ahead of us where we couldn’t see anything at all […] Then we lost the Sun behind us, and a little later we saw the blackout spread to a growing circle of stars there.
[…]
Even the stars off to one side are showing relativistic colour shifts. It’s almost like a rainbow, one of those full-circle rainbows that you see on the clouds beneath you from an aeroplane sometimes. Only this circle is all around us. Nearest the black hole* in front the stars have frequency-shifted to a dull reddish colour. They go through orange and yellow and a sort of leaf green to the band nearest the black hole* in back, which are bright blue shading to purple.

If you’re on the alert, you’ll notice that Pohl got the colours the wrong way around—Sänger’s prediction placed red behind and violet ahead (not Pohl’s “purple”, which is a mixture of red and blue).

When Pohl’s novella was published as part of a collection, its striking title was used as the book title, and Pohl’s description (including the reversed colours) leaked into the cover art of one edition:Pohl was a skilled and popular writer, and he cemented the erroneous “starbow” into the consciousness of science fiction readers.

Also in 1972 the space artist Don Davis, cooperating with the  starship designer and alleged translator of Ice-Age languages (among many other things) Robert Duncan-Enzmann, produced a distinctly weird New Age image of the starbow, which you can find here. I have scant idea what that’s about.

But then, in 1979, along came John M. McKinley and Paul Doherty, of the Department of Physics at Oakland University, Michigan. They had a computer, and they were unconvinced by Sänger’s identical monochromatic stars. They instead modelled the real distribution of stars in Earth’s sky, approximating each one as a blackbody radiator of the appropriate temperature, and applying the necessary relativistic transformations:

One prediction for the appearance of the starfield from a moving reference frame has been circulated widely, despite physically objectionable features. We re-examine the physical basis for this effect. […] We conclude with a sequence of computer-generated figures to show the appearance of Earth’s starfield at various velocities. A “starbow” does not appear.

“In search of the ‘starbow’: The appearance of the starfield from a relativistic spaceship” American Journal of Physics (1979) 47(4): 309-15

The physicist (and science fiction writer) Robert L. Forward mischievously forwarded a preprint of McKinley and Doherty’s article to Pohl. And Pohl, tongue firmly in cheek, described this experience in the Destinies article I quoted above:

… “there is no starbow,” they conclude. True, they then go on to say, “we regret its demise. We have nothing so poetic to offer as its replacement, only better physics”—but what’s the good of that?

Only slightly chastened, Pohl later went on to expand the novella “The Gold At The Starbow’s End” into a frankly-not-very-good novel, Starburst, the cover of which appears at the head of this post, resplendent with a starbow. I find it difficult to imagine the confusion that might have led to that cover, given that Pohl had removed the starbow from his narrative, while managing to give McKinley and Doherty a very slight (but distinctly ungracious) kicking in the rewrite:

Right now we’re seeing more in front than I expected to and less behind. Behind, mostly just blackness. It started out like, I don’t know what you’d call it, sort of a burnt-out fuzziness, and it’s been spreading over the last few weeks. Actually in front it seems to be getting a little brighter. I don’t know if you all remember, but there was some argument about whether we’d see the starbow at all, because some old guys ran computer simulations and said it wouldn’t happen. Well, something is happening! It’s like Kneffie always says, theory is one thing, evidence is better, so there! (Ha-ha.)

As the cover of Starburst suggests, the starbow was just too good an image to die easily, and few science fiction readers (or writers) read the American Journal of Physics. Undead, the starbow continued to trudge forward—a zombie idea. In September 1988, Robert J. Sawyer had a short story published in Amazing Stories, entitled “Golden Fleece”. It scored the coveted cover illustration for that month:

It’s a slightly confusing image, illustrating a key event in the story. The vehicle in the foreground is a shuttle-craft, which is escaping from the large spacecraft in the background, a relativistic Bussard interstellar ramjet travelling from right to left. And there’s a starbow! And it’s the wrong way round again, with red at the front! I haven’t read Sawyer’s original short story, but I have read the 1990 novel of the same name, in the form of its 1999 revised edition:

The view of the starbow was magnificent. At our near-light speed, stars ahead had blue-shifted beyond normal visibility. Likewise, those behind had red-shifted into darkness. But encircling us was a thin prismatic band of glowing points, a glorious rainbow of star—violet, indigo, blue, green, yellow, orange and red.

I don’t mean to single Sawyer out, because lots of authors were still invoking the starbow in their writing, but his 1999 novel is the most recent persisting version of the starbow I’ve turned up so far, particularly notable because it recycled the Amazing Stories cover art:Twenty years after McKinley and Doherty wrote “We have nothing so poetic to offer as its replacement, only better physics”, the starbow lived on.

And you can still find it—order a starbow painting by Bill Wright on-line, here.

Note: I happened upon Stephen R. Wilk’s How The Ray Gun Got Its Zap, which I’ve previously reviewed, while searching for references to the starbow. Wilk’s chapter “The Rise And Fall And Rise Of The Starbow” overlaps with some of what I’ve written here, but also discusses starbow-like manifestations in film.

* Pohl’s “black holes” are the patches of sky devoid of visible stars ahead of and behind the narrator’s spaceship, as predicted by Sänger, not the astronomical objects of the same name.

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