**Main publication**

**D.Dravins,
L. Lindegren,
E.Mezey
& A.T.Young**
**ATMOSPHERIC INTENSITY SCINTILLATION OF STARS.**
**I. Statistical Distributions and Temporal Properties**
*PASP *
109, 173207 (1997)

**Fig. 1. **Schematic layout of the *QVANTOS*
Mark I instrument, used for studying stellar scintillation on La Palma.
This is essentially a very fast stellar photometer, whose digital signal
processor is capable of handling large volumes of data in real time. When
required, effects of correlated detector noise can be minimized through
the use of two detectors, whose output pulse trains are cross correlated.

**Fig. 2.** A typical observed photon-count
distribution. A log-normal intensity distribution (combined with appropriate
photon noise) is fitted to the data, with the difference to the fit seen
in the bottom panel on a greatly expanded scale. The Poisson distribution
corresponding to photon noise only, with zero atmospheric intensity fluctuation,
is also shown.

**Fig. 3. **Aperture dependence of the intensity
variance *sigma*^{2}, measured at two
different times during the same night. The marked slope 7/3 corresponds
to Eq.(2), the expected behavior for large apertures. This figure illustrates
how the functional law for the aperture dependence of scintillation remains
unaffected by changes in scintillation amplitude. The data points correspond
to those in the analogous Figure 5 below for autocovariance.

**Fig. 4. **Higher-order statistical moments
(mk of order k) in atmospheric intensity scintillation,
and problems in their determination. At left are shown numerically simulated
observations: effects of increasing the number of photon count samples
N (top), and average counts per sample time <n>, keeping the autocovariance
constant = 0.14. The noise naturally decreases with an increasing number
of samples N (top left), and for fixed N it decreases with increasing <n>
(bottom left). The distribution of the moments, as obtained from many simulations,
defines the median (bold), and the 10% and 90% percentiles shaded). The
quantity plotted is R_{k} = ^{10}log{mk(actual)/mk(ideal)},
where the actual value is that obtained from either simulations or observations,
and the "ideal" is that analytically computed for a log-normal distribution
with the observed variance. R_{k} approaches
0 for long simulation series. In shorter measurement series, however, bias
phenomena appear due to the finite number of samples. At right, representative
observations are compared to simulations for relevant N and <n>, demonstrating
how the average values (but not their statistical spread) of higher-order
statistical moments are consistent with log-normal distributions.

**Fig. 5.** Aperture dependence of autocovariance
functions, measured at different times during the same night. Left (a)
shows measurements early in the evening at moderate zenith angles; Right
(b) "one hour later" shows measurements closer to midnight at small zenith
angles. The anti-correlation dips in (b) indicate a high temporal stability
in the flying shadows. Their appearance correlated with times of good seeing
in the sense of high speckle contrast and a small number of speckles.

**Fig. 6.** Stellar scintillation on very short
timescales. This plot shows the small deviations from unity of the intensity
autocorrelation function close to the origin. The apparent break in the
curve near 300 microseconds may be connected to the inner scale of atmospheric
turbulence (linear size 3 mm at windspeeds of 10 m/s). Photon noise causes
a spread of data points for the shortest delays.

**Fig. 7.** Observed autocorrelation and power
spectra of intensity scintillation, spanning four decades of timescale.
While the most characteristic timescale of scintillation in in the range
of a few milliseconds, variations are detected on all timescales examined.
The power density spectrum (center) shows the density of scintillation
power per unit frequency interval, while the power content spectrum (bottom)
shows that most power is located between 10 and 100 Hz. For these particular
data, *sigma*^{2}= 0.0044.

**Fig. 8.** The evolution of the autocovariance
of stellar intensity during a night, observed through a 60 cm telescope.
The star was Polaris, assuring a constant position in the sky. The amplitude
at the origin equals the intensity variance *sigma*^{2}.
Each curve represents a 120-second integration. The amplitude and temporal
structure of scintillation is seen to change on timescales of typically
tens of minutes.

**Fig. 9.** The evolution of the autocovariance
of stellar intensity during another night, measured through a small aperture
of 9 cm. This samples the spatially smaller scintillation patterns of higher
contrast: both the vertical and horizontal scales differ by an order of
magnitude from those in Figure 8.

**Fig 10. **Scintillation amplitudes and timescales
increase with zenith distance, here measured with a 22 cm aperture at largely
constant azimuth angle. Top: For moderate airmasses, the autocorrelation
halfwidths increase roughly as secZ, as expected from geometrical effects
(but the effect is not striking, and does not extend to the largest airmasses).
Bottom: the increase of *sigma*^{2} with
secZ, and the theoretical slopes for large (3), and small apertures (11/6).

**Fig. 11.** Representative autocovariance
functions are shown at about 10 intervals in zenith angle, measured with
a 22 cm aperture at roughly the same azimuth. There is a dramatic increase
of scintillation amplitude for larger Z.

**Fig. 12. **Intensity variance for binary
stars with equally bright components, but with the successively greater
separations of 2, 4, and 8 arcseconds, compared to single stars. The variance
is systematically smaller for binaries, showing that the scintillation
patterns are perceptibly different already some arcseconds away in the
sky.

**Fig. 13.** The correlation between intensity
variance and appearance of stellar speckle images, the latter a measure
of the angular seeing. The starlight passed a beamsplitter, and a continuous
video recording of a greatly enlarged stellar image was made simultaneously
with intensity measurements. The star was Polaris, at a constant position
in the sky. Representative stellar images are shown at different epochs
along the time axis. There appears to be a correlation, such that moments
of good angular seeing correlate with moments of high intensity variance,
while periods of poor seeing are accompanied by lower variance.

**Fig. 14.** Representative data for intensity
autocorrelation for different apertures, colors, and seasons. The parameter
causing the strongest dependence (aperture size) is shown in parallel with
that for the second strongest (wavelength). The wavelength dependence vanishes
in the largest apertures. Typical differences between excellent summer
conditions ("July") and winter weather ("November") is shown for one color.
The timescale of scintillation decreases with decreasing aperture size
until 5 cm, when the structures in the "flying shadows" on the ground become
resolved. On these small spatial scales, also differences between different
colors become visible: scintillation is slower at longer wavelengths.

**Fig. 15. **Intensity autocovariance for different
apertures, colors, and seasons. To view also the fine details near the
zero level, the quantity logarithmically plotted is the autocovariance
plus 0.001. During good summer conditions ("July") the `flying shadows'
are sufficiently regular and long-lived to generate anti-correlation dips
in the autocovariance functions for the smallest apertures. This is absent
in winter ("November"), probably because the structures are then smeared
out by wind shear. All amplitudes are scaled to Z = 45 degrees, using a
standard relation for the zenith distance dependence. In smaller apertures,
color effects become visible: scintillation amplitude is greater in the
blue, than in the red.

**Fig. 16. **Power spectral densities of intensity
scintillation for different apertures, colors, and seasons. The power increases
with decreasing aperture size until 5 cm. For larger apertures the power
decreases (especially at high frequencies, i.e. scintillation becomes"slower"),
reflecting the spatial averaging of small-scale elements in the shadow
pattern. The power spectra were obtained by directly transforming autocovariances,
producing a number of discrete data points.

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Updated JD 2,455,775