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                                   JACQUES M. BECKERS
                                   Scottsdale, AZ 85255 USA

    The scintillation of point-like objects is primarily caused by thermal fluctuations in the
    upper atmosphere. For it the scintillation index (σI2) is proportional to the height integral
    of Cn2(h) weighted by a height dependent function F(h) = h α where α = +5/3. For
    extended objects like the Sun or the Moon the height contribution to the (much smaller)
    scintillation is quite different. Because of their size the effects of the optical turbulence is
    averaged over an ever increasing area as the distance to the detector increases. Assuming
    vertical viewing, the area diameter increases like h*Ω where Ω is the angular diameter of
    the Sun or Moon. For Kolmogorov turbulence the function F(h) then still has the same
    shape, but with α = -1/3 so that the lower layers contribute more to scintillation. This
    makes it a good tool for the probing of the lower atmospheric layers. Unlike the σI2 for
    stellar scintillation, the σI2 for the Sun and the Moon is wavelength independent. Using
    an array of scintillometers one can probe the Cn2(h) distribution of those lower layers in a
    technique called SHABAR. SHABARs have been used in site testing for lower
    atmosphere probing for solar and nighttime telescopes. The aim is to establish the height
    to place telescopes, like the Advanced Technology Solar Telescope (ATST), to minimize
    boundary layer seeing effects. SHABAR site tests using the Moon are planned both for
    Arctic sites (Hickson„s contribution to this meeting) and Antarctic sites (Storey‟s
    contribution to this meeting) where boundary layer heights are very site dependant
    reaching sometimes very small values. In my contribution I described some of the solar
    results related to the ATST site testing. The scintillation of planets have an F(h) function
    different in shape from that of the Sun or Moon. For low heights, where their beams still
    are narrow, F(h) has an α of +5/3 (as for stars); for large heights it is -1/3 (as for the Sun
    & Moon). For Mars the height contributions F(h) for seeing and scintillation are similar.


In a paper in 1993 E. Seykora1 describes how he measured the scintillation of
integrated sunlight at the National Solar Observatory, Sacramento Peak site and
found it to be exceedingly well correlated with the atmospheric seeing. The
amount of scintillation is much smaller than that of stars (0.1% - 0.01% vs.
about 10%) but clearly detectable and separated from atmospheric transparency

changes. Beckers2 showed how the solar scintillation index σI2 relates to the
atmospheric refractive index structure Cn2(h) as proportional to h-1/3∙Cn2(h)dh,
quite different from that for stars where the weighting function is h +5/3. The solar
scintillation is therefore dominated by ground/boundary layer turbulence. The
good correlation between it and atmospheric seeing is the result of the fact that
in daytime ground layer seeing dominates at Sacramento Peak.
     Beckers3 used the properties of solar scintillation to develop a device to
sense the height profile of Cn2(h) in the ground layer by using an array of solar
scintillometers called the SHABAR (= SHAdow BAnd Ranger). It was used for
the site testing for the 4-meter Advanced Technology Solar Telescope (ATST) 4.
The inversion of the scintillometer array signals to Cn2(h) has been described by
Socas-Navarro5. The full report of the ATST site testing effort can be found on
the web site of the National Solar Observatory6.
     The figure below is taken from Beckers3 and shows the amount of
scintillation resulting from 1 arcsec seeing layers located at different altitudes
for a variety of extended objects.

     Because of its approximately equal size the lunar and solar scintillation
indices are approximately equal. For the planets the cone size at low elevations
is small, so the index follows the h+5/6 of stars. At higher elevations the cone size
becomes large enough to follow the Sun/Moon h-1/3 rule.

     The figure also indicates the effect of the finite outer scale of turbulence on
the scintillation index. It is only of interest for scintillation arising at high


1.   E.J. Seykora, “Solar scintillation and the monitoring of solar seeing”, Solar Physics 145, 389
2.   J.M. Beckers, “On the Relation between Scintillation and Seeing Observations of Extended
     Objects”, Solar Physics 145, 399 (1993)
3.   J.M. Beckers, “Seeing Monitor for Solar and other Extended Object Observations”,
     Experimental Astronomy 12, 1 (2001)
4.   F. Hill, J. Beckers and co-authors, “Solar site testing for the Advanced Technology Solar
     Telescope”, Proceedings SPIE 5489, 122 (2004)
5.   H. Socas-Navarro, J.M. Beckers and co-authors, “Solar Site Survey for the Advanced
     Technology Solar Telescope. I. Analysis of the Seeing Data”, Pub. Astron. Soc. Pacific 117,
     1296 (2005)
6.   “ATST Site Survey Working Group Final Report”, http://atst.nso edu/site/finalreport, (2008)

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