Twinkle, Twinkle Little Star

by Robert J. Vanderbei
at Princeton University

I see stars twinkle. But, planets do not. What, EXACTLY, is the twinkle phenomenon?

Visually, when the seeing is bad to mediocre, a star under high magnification dances around, its diffraction pattern distorts, sometimes going splat in a way that reminds me of that old public service ad "this is your brain on drugs" but I have never seen a star twinkle when viewed in a telescope. That is, I have never seen the intensity fluctuate. I have taken high magnification video of stars under mediocre seeing and those frames conform to my visual experience. The star dances around from one frame to the next sometimes going splat, but the integrated intensity remains essentially fixed (there might be small, slowly changing, variations in transparency). The star never blinks off, not even for a split second. Yet, visually without a telescope, stars appear to twinkle.

So, it seems to me that twinkling must have something to do with the human eye itself. The eye's resolving power is much less than that of a telescope. But, the eye's aperture is also much smaller and so the diffraction pattern is larger. However, stars appear visually as point sources, so presumably all of the light is falling on one pixel (i.e., rod/cone). Hence, it would seem that twinkling might be explained as the light sometimes falling "between" pixels and hence getting missed by the brain. Of course, this suggests that whenever we look up at the night sky some of the stars will fall between the rods/cones while most others will not. The between-the-pixels area of the retina where light might fall but get missed by all rods/cones probably represents only a small fraction of the total area. This seems consistent with my attempts at viewing globular clusters with averted vision. When I use averted vision to view, say, M13 with my 3.5" Questar the off-axis stars seems to scintillate as I avertedly scan around M13 exactly as if the seeing were bad, even when the seeing is excellent. This explanation also seems consistent with the non-twinkling of the planets. Being (slightly) extended objects, it is possible that their light can never fall fully between the pixels and so they never appear to twinkle.

BTW, this explanation is completely different from the conventional explanation for scintillation. The wikipedia page on "scintillation (astronomy)" defines scintillation as "rapid variations in apparent brightness or color of a distant luminous object viewed through the atmosphere" and later as "variations in luminance only". The wikipedia page goes on to say...

"It is clearly established that almost all scintillation effects are caused by anomalous refraction caused by small-scale fluctuations in air density usually related to temperature gradients. Normal wind motion transporting such fluctuations across the observer's line of sight produces the irregular changes in intensity characteristic of scintillation. The primary cause of such small scale fluctuations is turbulent mixing of air with different temperatures."

At the end of the wikipedia article, the fact that one does not see intensity fluctuations when viewing through a telescope is addressed as follows:

"Scintillation effects are reduced by using a larger receiver aperture. This effect is known as aperture averaging."

This explanation sounds rather compelling but it ignores conservation of energy. I don't mind a turbulent atmosphere distorting the diffraction pattern but violating conservation of energy is a big no no if you ask me.