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ING Newsletter No. 6, October 2002

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A New Definition of Dark,Grey and Bright Time at ING

Ian Skillen (ING)

The legacy method used to define dark, grey and bright time at ING is based on the fraction of the night for which the Moon is below the horizon. Although this is perfectly adequate for characterising dark time, it is less so for characterising grey and bright time. As the Moon ages the focus should change to quantifying the enhanced sky surface brightness from scattered moonlight.

The optical sky surface brightness of the moonlit sky in some line-of-sight depends primarily on the Fractional Lunar Illumination, FLI, followed in significance by the angular separation between the line-of-sight and the Moon, and by the altitude of the Moon. The FLI is given to a good approximation by


where are the longitudes of the Moon and Sun respectively, and b is the latitude of the Moon. Partitioning a lunation by the fraction of each night for which the Moon is below the horizon correlates strongly with partitioning the Moon’s longitude, since |β| 5.3°, but ignores the change in longitude of the Sun by ~1° per day, and therefore does not give a consistent mapping onto FLI. As a result of this and the non-uniform motion of the Moon in its orbit, the FLI on, for example, the first and last bright nights in a given lunation can be as small as 0.45 and as large as 0.80. The difference in FLI on first and last bright nights exceeds 0.20 in ~30% of lunations, and exceeds 0.30 in ~5% of lunations. An important consequence of this is that the sky surface brightness on first and last bright nights can differ by as much as ~1.2 mag/arcsec2 with the Moon being present in the sky for the same fraction of each night. Furthermore, in such asymmetric lunations the sky brightness in the moonlit part of grey nights can be up to ~1 mag/arcsec2 brighter than in the moonlit part of the darkest bright night in the same lunation.

Inconsistent partitioning of lunations can lead to a mis-match between observing programme requirements and actual conditions. A programme allocated, for example, a specific grey-time award, based on some assumed “typical” grey-time sky background, can be scheduled in significantly brighter conditions, and vice versa, and this is detrimental to observing efficiency. These considerations prompted a reappraisal of the legacy method, and the derivation of a better alternative to it.

Sky Surface Brightness

The direct way to partition classically-scheduled time is in terms of the sky surface brightness itself, since it is this which impacts the signal-to-noise ratios for observations of a given integration time. The main contributors to the moonless sky optical surface brightness in a line-of-sight and in a specific bandpass are airglow, the zodiacal light and starlight. Benn and Ellison (1998) find the high galactic latitude, high ecliptic latitude, zenith Vsky brightness at solar minimum at the ORM to be Vsky=21.9 mag/arcsec2. The sky is brighter at low latitudes by ~0.4 mag/arcsec2, and at higher airmasses by ~0.3 mag/arcsec2 (at X~1.5), and because of variable solar activity, the airglow component is brighter by ~0.4 mag/arcsec2 at solar maximum. There is no dependence on extinction, AV, for AV<0.25 mag/airmass.

The contribution to the sky surface brightness from scattered moonlight when FLI 0.15 exceeds the spatial variations from airglow, zodiacal light and starlight, and so to partition classically-scheduled telescope time it is sufficient to partition by the illuminated fraction of the Moon’s disc, acting as a proxy for the sky surface brightness from scattered moonlight.

Two scattering mechanisms dominate the background from moonlight; Mie scattering by aerosols and Rayleigh scattering by molecules. Mie scattering is highly forward, and so Rayleigh scattering dominates for scattering angles (i.e. angular distances from the Moon) 90°. Krisciunas & Schaefer (1991) derived scattering formulae to compute the contribution of moonlight to the sky background at some airmass as a function of lunar phase, lunar zenith distance, distance from the Moon and extinction. The uncertainty in these formulae is estimated to be ~0.25 mag/arcsec2; local prevailing conditions such as enhanced levels of atmospheric dust will of course reduce their precision.  

The mean ΔVMoon from the Vsky=21.9 mag/arcsec2 dark sky is computed from these formulae for the Moon at a zenith distance of 60° (so that scattering angles of up to 120° are accommodated at airmasses ≤2), as a function of FLI in increments of 0.1, and at scattering angles ranging from 30° to 120° in increments of 5°, measured both in the azimuthal direction and in altitude (see Figure 1). The computed differences in both directions at a given scattering angle are only a few per cent. These calculations have been normalised to JKT observations of the moonlit sky, made by Chris Benn on dust-free nights in 1998. The effect of decreasing the Moon’s zenith distance on  ΔVMoon at a given angular distance from it is small, 0.1 magnitude, i.e roughly the same size as the points in Figure 1. ΔVMoon does however fall off rapidly by ~1 magnitude/arcsec2 when the Moon is low on the horizon. Therefore, Figure 1 forms a consistent basis for quantifying the effects of moonlight on the sky background at specific scattering angles from the Moon.

Figure 1
Figure 1. The brightening of the dark sky (Vsky=21.9 mag/arcsec2, corresponding to low airmass, high ecliptic and galactic latitude, and solar minimum) by scattered moonlight, calculated as a function of fractional lunar illumination and angular distance from the Moon. [ JPEG | TIFF ]

Several aspects of this Figure are noteworthy. As the scattering angle increases, the contribution of scattered moonlight to the sky surface brightness decreases up to ~90°, and then begins to increase again when Rayleigh scattering dominates. Therefore, in the presence of moonlight, a good strategy for optical observations is to observe in a broad annulus centred ~90° from the Moon whenever possible, in order to minimise the effects of scattered moonlight.

The gradient of scattered moonlight is remarkably flat at scattering angles ~90°. In fact, even at full Moon, the range in scattered moonlight within 70°–110° of the Moon is  ΔVMoon  ±0.1. Therefore, it is sensible to quantify the contribution of scattered moonlight to the sky surface brightness in terms of DVMoon computed ~90° from the Moon.

The FLI assumes greater importance in determining the sky surface brightness than angular distance from the Moon, for Moon separations 50°. The change in FLI is ~0.1 per day in the neighbourhood of quadratures,  and therefore this emphasises the importance of having consistent partitions into grey and bright categories; inconsistent partitions are in general not compensated for by the distribution of targets on the sky in relation to the Moon.

The sky brightness approaching full Moon, i.e. zero lunar phase angle, increases strongly due to the opposition effect, which arises from a combination of shadow-hiding (the shadows of lunar particles are occulted by the particles themselves) and coherent backscattering (multiple scattering   of sunlight off lunar dust grains, predominantly in the backward direction to the incident sunlight).

Dark, Grey and Bright Time

The definition of grey and bright thresholds is to some extent arbitrary. What is important is that the definition is both sensible and consistent, and that it is understood and agreed by applicants and TAC’s, and adhered to in the scheduling process. Consistency in terms of sky surface brightness is achieved by partitioning on the fractional lunar illumination, acting as a proxy for sky surface brightness 90° distant from the Moon. In terms of sensibleness, the numbers of nights in each category should not be greatly different from the legacy method, but a small increase in the number of grey nights, at the expense of bright nights, is desirable to better match demand.

Averaged over a Saros cycle (~37 semesters), the same number of dark nights (9.6), 0.7 additional grey nights (7.9) and 0.7 fewer bright nights (12.0) per lunation result from the adopted partitioning scheme:

Dark: 0.00 FLI < 0.25
Grey: 0.25 FLI < 0.65
Bright: 0.65 FLI 1.00

where the FLI is computed for 0h UT. Illuminated fraction changes by  ~0.1 per day in the region of these thresholds, and this “resolution effect” means that inconsistencies in the FLI are constrained to be   0.1 at the dark/grey and grey/bright boundaries.

For a given FLI, the fraction of the night for which the Moon is in the sky can vary by as much as ~25%, for the same reasons that the fraction of the night which is moonless does not consistently estimate the FLI. For example, at FLI=0.65 the Moon can be in the sky for between ~65% and ~90% of astronomical darkness. This could be taken into account for each night by scaling the moonlit sky surface brightness by this fraction to give a weighted background for the night, but on balance it is considered better to partition telescope time solely in terms of the worst case sky surface brightness computed ~90° from the Moon.

The predicted ranges in the zenith V sky surface brightness at high galactic and ecliptic latitudes, and solar minimum, and at an angular distance from the Moon of ~90°, are 21.2– 21.9mag/arcsec2 for dark time, and 19.9–21.2 and 18.0 – 19.9 mag/arcsec2 respectively for the moonlit parts of grey and bright time. For the mean sky, i.e. over all latitudes ~90° from the Moon, these ranges are ~0.5 mag/arcsec2 brighter because of the larger contributions of airglow, zodiacal light and starlight.  

This definition of dark, grey and bright time will be used in constructing the ING schedules from Semester 2002B onward. The exposure time calculator, SIGNAL, has been modified to offer an option specifying ‘typical’ sky surface brightnesses for dark, grey and bright time, corresponding to Vsky=21.50, 19.75 and 18.50 mag/arcsec2 respectively.

A longer version of this article is available as ING Technical Note No. 127, available at URL


It is a pleasure to acknowledge discussions with Thomas Augusteijn, Steve Bell and Rob Jeffries.


Email contact: Ian Skillen (

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