Scintilation Measurments with the H-DIMM

''Twinkle Twinkle Litle Star...''

Scintillation is an important factor in measurements requiring high precision photometry (extra-solar planet detection), astrometry, and of objects with very fast intensity changes (astroseismology). Bellow are presented scintilation measurments made in mount Xolomon in Chalkidiki Greece. I present the theory of the method used. As a by-product of the scintilation mesurments an estimate of the isoplanatic angle is done for the same observing site.

The ``amount'' of scintillation can be measured by the variance $\sigma^2_i$ of the relative fluctuations in intensity $I$, $\sigma_i$ being the root-mean-square value of $(I-\left\langle I\right\rangle)=\Delta I/\left\langle I\right\rangle$ where $\left\langle \right\rangle$ denotes time average. In the literature, $\sigma^2_i$ is often called the "scintillation index" (although that expression has been used also for the rms modulation of $I$ itself). To avoid ambiguity, for $\sigma^2_i$ we will use the term `intensity variance.' The `rate' of scintillation can be measured by the width of the temporal correlation function or, equivalently, by its Fourier transform, the power spectrum. Especially in older literature, the "frequency" of scintillation expresses how often the fluctuating intensity crosses its average value.

The values for intensity variance $\sigma^2_i$ refer to the variance of the linear quantity. In some publications, the variance is instead given for the logarithm of intensity, the relation being $\sigma^2_i=[exp(\sigma^2_{ln(i)})-1]$. For small scintilation amplitudes the difference is negligible. A refractive-index undulation in the atmosphere acts as a lens, focusing the starlight. The illumination of a screen (pupil plane) at some distance from such a lens varies from place to place because alternate sections of the lens are converging and diverging. Scintillation involves a geometrical "lever-arm" effect, since the wave front wiggles must be sufficiently distant to produce brightness changes. Scintillation is normally dominated by turbulence at high altitudes (many kilometers), while seeing often has significant components originating close to the telescope.

When the turbulence causing the refractive fluctuations is at a great distance from the telescope, the irradiance becomes variable in both space and time. This intensity modulation can be observed in short-exposure images of a telescope mirror illuminated by a bright star, as a system of rapidly moving ``shadows''. With the unaided eye, such ``flying shadows'' can be glimpsed during the moments before and after a total solar eclipse, when an uneclipsed solar crescent acts as the light source. Then the `shadows' appear as elongated `bands' because of the anisotropic brightness distribution of the solar crescent.

Their motions are determined by wind components at various contributing altitudes. However, in contrast to solar eclipse phenomena, shadow patterns from stars are statistically isotropic. Scintillation may be studied either by measuring the fluctuations in image intensity, or by measuring the shadow pattern directly.The intensity of the telescopic image depends upon the sample of the shadow pattern selected by the telescope at any instant. Temporal variations occur for two main reasons. Firstly, the shadow pattern moves across the detector as the region of atmosphere producing the pattern is carried by the wind.

Most modeling indeed assumes that this pattern can be regarded as frozen in the atmosphere (Taylor's approximation), merely swept by winds across the telescope aperture. However, fluctuations also occur when the structure of the shadow pattern varies due to changes in the turbulence, or due to the relative motion of different regions of the atmosphere. Detailed studies of the spatio-temporal properties of scintillation for single and binary stars can be used to deduce quite detailed information about the often layered structure in the upper atmosphere. In order to `fully' resolve the atmospheric effects, it is necessary to limit the size of the telescope pupil, the spectral bandwidth of the detector, and the sample time of the processing equipment. Aperture averaging will reduce the vari-ance unless the telescope aperture is significantly smaller than the smallest feature size in the shadow pattern.

Thus a measure of the variance as a function of aperture size gives an estimate of these feature sizes. Different extents of the sampling aperture, and of the temporal integration, preferentially `filter' out differently distant turbulence elements. For example, naked-eye twinkling ( $\backsim 5mm$ aperture, a cutoff for frequencies above $15Hz$), arises mostly from turbulence within $1km$ of the ground.