Astronomy Principles and Practice Fourth Edition.pdf

Disturbances caused by the atmosphere 317
fluctuations is directly proportional to the brightness of the source, the constant of proportionality, κ,
depending on the quality of the site, on the telescope size and on the direction of the star (altitude and
azimuth). Thus, for bright stars with the photometric noise dominated by intensity scintillation, a single
brightness measurement would be recorded simply as B ± κ B. Without scintillation, with the noise
dominated by photon-counting statistics, a measurement of the same star would be noted as B ± √ B.
Clearly, there is a range of brightness values for which the accuracy of any photometry is dominated
by scintillation and a range dominated by photon counting statistics. The demarcation occurs when
κ B = √ B or κ = 1/ √ B. If, for example, κ ∼ 1%, over a measurement time of 1 s, the photometric
noise is dominated by scintillation if the photon count rate is greater than 10 4 s −1 .
It is well known that, to the naked eye, planets generally do not appear to twinkle. This is
because they have a greater apparent angular size than the stars. Any small component within an
extended object exhibits intensity scintillation but if the object has a sufficient angular size, then there
are sufficient elements for the overall scintillation to smooth out.
Experiments have shown that scintillation begins to be apparent when the object subtends an angle
of 10 arc seconds or less and that the magnitude of the scintillation increases as the angular size of the
object decreases, until it cannot be differentiated from stellar scintillation when the angle subtended is
about 3 arc seconds. In effect, it can be said that the apparent angular size, α, of the corrugations in
the wavefront is of the order of 3 arc seconds and their physical size, r 0 , obtained from experiments
investigating the relationship between scintillation and telescope diameter, is of the order of 100 mm.
Thus, the typical distance in the atmosphere where the deforming turbulence is taking place is given
by
r 0
α = 100 × 206 265 mm
3
≈ 7 × 10 6 mm
= 7km.
By considering the theory associated with turbulent media, Fried characterized the fluctuations
with a scale over which the parts of the corrugated wavefront can be considered as being essentially
plain. This dimension is referred to as the Fried parameter, being synonymous with the r 0 given here.
The visual behaviour of the ‘seeing’, as it affects the appearance of a star image, also depends on
the value of r 0 in relation to the telescope diameter. For a small telescope of a few centimetres diameter,
in addition to rapid fluctuations in apparent brightness, the expected diffraction pattern is likely to be
seen but with the whole structure dancing around in constant agitation. When a telescope of a few tens
of centimetres or larger is used, the image loses its sharpness and appears as an ill-defined blob without
scintillation. This image is known as the seeing disc. When a starfield is recorded on a photograph
or on a CCD frame, the images are recorded with a spread which is dominated by the seeing disc. By
making an intensity scan through any stellar image, the profile of the seeing disc may be compared
with that of the theoretical Airy diffraction pattern (see figure 19.8). The size of the disc is usually
expressed in terms of arc seconds, one definition being the angular diameter between the positions at
which the intensity has dropped by a factor of two relative to the peak intensity. The seeing disc size
and shape gives an indication of the quality of the observing site—a good site will have many nights
in the year when the seeing disc is 1 arc second or smaller. There are many observatories, however,
where such good quality seeing is not usually available.
Another important aspect to the description of the deteriorated stellar image is the way the flux
is redistributed relative to that expected in the diffraction pattern. The more the image is concentrated
into an area of a detector, the more easily a faint object might be detected; the more the concentration
of the image, the more radiation might be accepted into the narrow slit of a spectrometer. This aspect
is described by comparing the peak intensity of the seeing disc, I S , relative to that of the peak of the