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Optical Sky Background
The optical sky background depends on a number of parameters including the target - moon angular separation, lunar phase, ecliptic latitude, zenith angle, and phase of the solar cycle (e.g. Krisciunas 1997, PASP, 209, 1181; Krisciunas and Schaefer 1991, PASP, 103, 1033; Benn and Ellison 1998, La Palma Technical Note 115). A model was constructed following the prescription of Krisciunas (1997) and Krisciunas and Schaefer (1991).
The graph below shows the cumulative probability distributions of V-band sky brightness at an arbitrary phase in the solar cycle for three model observation scenarios. In the first model the target is always at the zenith. The second and third models are more realistic Monte Carlo realisations of likely queue and classical programs. In the second model targets were chosen with a gaussian distribution in Hour Angle with sigma=1 hour, and with a distribution in Declination between -20 and +90 degrees based on the surface area of the celestial sphere. The third model is the same as the second, but with the further constraint that the target must be at least 30 degrees from the moon. It may seem surprising that the results of these 3 models differ so little. This is due to the fact that the primary dependence of night sky brightness is on lunar phase, and secondarily on moon - target distance.
The results of these calculations indicate that the sky at Mauna Kea is fainter than 20.78 mag/arcsec2 for 50% of the time and fainter than 21.37 mag/arcsec2 for 20% of the time for any random target. (For an unbiased distribution of queue-mode nights the moon is below the horizon for about half the time, of course).
The values presented in the observing constraints table are modified slightly each year or so to account for the nominal solar cycle variation.
The colour of the sky changes with lunar phase. Adopted values are shown in the table below (taken from ESO, by scaling V for inferred equivalent lunar phase, and from Walker, NOAO Newsletter No. 10). The conversion between the sky background category and the number of nights from new moon indicates the constraints that are applied to schedule classical observations and do not necessarily correspond to conventional definitions of dark, grey and bright time.
|Sky Background Category||Approx Nights From New Moon (+/-)||Sky Brightness (mag/arcsec2)|
|=< 3||21.3||V + 0.0||V + 0.8||V - 0.9|
|=< 7||20.7||V - 1.5||V + 0.2||V - 0.8|
|=< 11||19.5||V - 2.2||V - 0.0||V - 0.4|
|=< 14||18.0||V - 3.0||V - 0.5||V - 0.1|
Note that the V-band sky is brighter at low ecliptic latitude by ~0.4 mag (Benn and Ellison 1998. La Palma Technical Note 115).
Data from HM Nautical Almanac Office, showing sun and moon rising and setting times and lunar phases for Mauna Kea and Cerro Pachon/Tololo/La Silla can be found here.
The broad-band sky brightnesses given in the table above have been used to scaled a model optical sky spectrum . These spectra are used in the Integration Time Calculators. The sky spectrum is patched to the near-IR sky spectrum at a wavelength of 920nm. An example is shown below (for 50%, 'dark' conditions) and the data file is available.