Scintillation - temporal properties

Main publication

  D.Dravins,  L. Lindegren,  E.Mezey  &  A.T.Young
I.  Statistical Distributions and Temporal Properties
PASP  109,  173­207  (1997)

ABSTRACT. Stellar intensity scintillation in the optical was extensively studied at the astronomical observatory on La Palma (Canary Islands). Photon-counting detectors and digital signal processors recorded temporal auto- and cross-correlation functions, power spectra, and probability distributions. This first paper of a series treats the temporal properties of scintillation, ranging from microseconds to seasons of year. Previous studies, and the mechanisms producing scintillation are reviewed. Atmospheric turbulence causes "flying shadows" on the ground, and intensity fluctuations occur both because this pattern is carried by winds, and is intrinsically changing. On very short timescales, a break in the correlation functions around 300 microseconds may be a signature of an inner scale (3 mm in the shadow pattern at windspeeds of 10 m/s). On millisecond timescales, the autocorrelation decreases for smaller telescope apertures until 5 cm, when the "flying shadows" become resolved. During any night, timescales and amplitudes evolve on scales of tens of minutes. In good summer conditions, the flying-shadow patterns are sufficiently regular and long-lived to show anti-correlation dips in autocorrelation functions, which in winter are smeared out by apparent wind shear. Recordings of intensity variance together with stellar speckle images suggest some correlation between good [angular] seeing and large scintillation. Near zenith, the temporal statistics (with up to 12:th order moments measured) is best fitted by a Beta distribution of the second kind (F-distribution), although it is well approximated by log-normal functions, evolving with time.


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 sigma2, 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 Rk = 10log{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. Rk 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, sigma2= 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 sigma2. 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 sigma2 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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