7 Testing the moon brightness model

As we have mentioned in Sect. 4.2, some data have been collected when the moon contribution to the sky brightness is conspicuous and this offers us the possibility of directly measuring its effect and comparing it with the model by Krisciunas & Schaefer (1991) which, to our knowledge, is the only one available in the literature.

To estimate the fraction of sky brightness generated by scattered moon light, we have subtracted to the observed fluxes the average values reported in Table 4 for each passband. The results are presented in the lower panel of Fig. 12, where we have plotted only those data for which the observed value was larger than the dark time one. As expected, the largest deviations are seen in B, where the sky brightness can increase by about 3 mag at 10 days after new moon, while in I, at roughly the same moon age, this deviation just reaches $\sim$1.2 mag. It is interesting to note that most exposure time calculators for modern instruments make use of the function published by Walker (1987) to compute the expected sky brightness as a function of moon age. As already noticed by Krisciunas (1990), this gives rather optimistic estimates, real data being most of the time noticeably brighter. This is clearly visible in Fig. 12, where we have overplotted Walker's function for the V passband to our data: already at 6 days past new moon the observed V data (open squares) show maximum deviations of the order of 1 mag. These results are fully compatible with those presented by Krisciunas (1990) in his Fig. 8.

Figure 12: Lower panel: observed sky brightness variation as a function of moon age for B, V, R and I. The solid line traces the data published by Walker (1987) for the V passband while the upper scale shows the fractional lunar illumination. Upper panel: comparison between the observed and predicted moon contribution (Krisciunas & Schaefer 1991). Plotted are only those data points for which the global brightness is larger than the typical dark time brightness.

Another weak point of Walker's function is that it has one input parameter only, namely the moon phase, and this is clearly not enough to predict with sufficient accuracy the sky brightness. This, in fact, depends on a number of parameters, some of which, of course, are known only when the time the target is going to be observed is known. In this respect, the model by Krisciunas & Schaefer (1991) is much more promising, since it takes into account all relevant astronomical circumstances. The model accuracy was tested by the authors themselves, who reported rms deviations as large as 23% in a brightness range which spans over 20 times the typical value observed during dark time.

Figure 13: Lower panel: nightly average sky brightness in the R passband vs. solar density flux. The filled circles represent data taken at MJD > 52114, while the solid line indicates a linear least squares fit to all data. Upper panel: Penticton-Ottawa solar flux at 2800 MHz during the time interval discussed in this paper. The open circles indicate the values which correspond to the data presented in the lower panel and the dotted line is placed at the median value for the solar density flux.

In the upper panel of Fig. 12 we have compared our results with the model predictions, including B,V,R and I data. We emphasise that we have used average values for the extinction coefficients and dark time sky brightness and this certainly has some impact on the computed values. On the other hand, this is the typical configuration under which the procedure would be implemented in an exposure time calculator, and hence it gives a realistic evaluation of the model practical accuracy. Figure 12 shows that, even if deviations as large as 0.4 mag are detected, the model gives a reasonable reproduction of the data in the brightness range covered by our observations. This is actually less than half with respect to the one encompassed by the data shown in Fig. 3 of Krisciunas & Schaefer (1991), which reach $\sim$8300 sbu in the V band.

 

 

Table 5: Dark time zenith night sky brightness measured at various observatories (adapted from Benn & Ellison 1998). $S_{10.7~{\rm cm}}$ is the Penticton-Ottawa solar density flux at 2800 MHz (Covington 1969).

Site	Year	$S_{10.7~{\rm cm}}$	U	B	V	R	I	Reference
		MJy	mag arcsec-2
La Silla	1978	1.5	-	22.8	21.7	20.8	19.5	Mattila et al. (1996)
Kitt Peak	1987	0.9	-	22.9	21.9	-	-	Pilachowski et al. (1989)
Cerro Tololo	1987-8	0.9	22.0	22.7	21.8	20.9	19.9	Walker (1987, 1988a)
Calar Alto	1990	2.0	22.2	22.6	21.5	20.6	18.7	Leinert et al. (1995)
La Palma	1994-6	0.8	22.0	22.7	21.9	21.0	20.0	Benn & Ellison (1998)
Mauna Kea	1995-6	0.8	-	22.8	21.9	-	-	Krisciunas (1997)
Paranal	2000-1	1.8	22.3	22.6	21.6	20.9	19.7	this work