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According to "Why do stars flicker?", the twinkling of stars (stellar scintillation) is caused by the thick layers of turbulent air in the Earth's atmosphere. While the explanation is convincing, it would be better to have some quantitative justification.

Since the twinkling of stars is easily observed, it is reasonable to estimate the twinkling rate as ~ $1\textrm{s}^{-1}$. How can one obtain a similar estimate from the underlying theory?

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The underlying theory would be atmospheric turbulence with the size of turbulent elements ranging from several hundred meters to millimeters. Therefore, the twinkling rate will not be a single frequency but a continuous spectrum of frequencies ranging from 0.001 Hz to 1000 Hz. Of course, the amplitude of the lower frequencies will depend on the turbulent state of the atmosphere. The higher frequencies however, belong to the inertial subrange of atmospheric turbulence in which energy is transfered from larger to smaller eddies. This range is independent of any large scale motion.

To answer the question, the visible twinkling rate is the superposition of all larger motions in the atmosphere between the star and the observer.

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  • $\begingroup$ How do you calculate the frequency from the size of turbulent elements? $\endgroup$
    – leongz
    Jul 9 '13 at 16:02
  • $\begingroup$ If you divide a velocity by a length you get a frequency, so when a turbulent eddy of 1 m size is passing by your anemometer at 10 m/s you will get a contribution in the energy spectrum at 10 Hz. Stellar scintillation is mainly influenced by turbulence in the upper atmosphere. There is no scintillation frequency, but noise (a spectrum of frequencies). This paper shows how stellar scintillation affects telescopes at different sites: arxiv.org/pdf/1208.3824v1.pdf. $\endgroup$
    – Aziraphale
    Jul 10 '13 at 6:35

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