6 Sky brightness variations during the night

In the literature one can find several and discordant results about the sky brightness variations as a function of the time distance from astronomical twilight. Walker (1988b) first pointed out that the sky at zenith gets darker by $\sim$0.4 mag arcsec^-2 during the first six hours after the end of twilight. Pilachowski et al. (1989) found dramatic short time scale variations, while the steady variations were attributed to airmass effects only (see their Fig. 2). This explanation looks indeed reasonable, since the observed sky brightening is in agreement with the predictions of Garstang (1989). Krisciunas (1990, his Fig. 6) found that his data obtained in the V passband showed a decrease of $\sim$0.3 mag arcsec^-2 in the first six hours after the end of twilight, but he also remarked that this effect was not clearly seen in B. Due to the high artificial light pollution, Lockwood et al. (1990) tend to attribute the nightly sky brightness decline they observe at the Lowell Observatory, to progressive reduction of commercial activity.

Walker's findings were questioned by Leinert et al. (1995) and Mattila et al. (1996), who state that no indications for systematic every-night behaviour of a decreasing sky brightness after the end of twilight were shown by their observations. Krisciunas (1997) notes that, on average, the zenith sky brightness over Mauna Kea shows a not very convincing sky brightness change of 0.03 mag hour^-1. On the other hand he also reports cases where the darkening rate was as large as 0.24 mag hour^-1 and discusses the possibility of a reverse Walker effect taking place during a few hours before the beginning of morning twilight.

Leinert et al. (1998) touch this topic in their extensive review, pointing out that this is an often observed effect due to a decreasing release rate of the energy stored in the atmospheric layers during day time. Finally, Benn & Ellison (1998) do not find any signature of steady sky brightness variation depending on the time distance from twilights at La Palma, and suggest that the effect observed by Walker is due to the variable contribution of the zodiacal light, a hypothesis already discussed by Garstang (1997). A further revision of Walker's findings is presented here in Appendix D, where we show that the effect is significantly milder than it was thought and probably influenced by a small number of well sampled nights.

We have performed an analogous analysis on our data set, using only the measurements obtained during dark time and correcting for differential zodiacal light contribution. Since the time range covered by our observations is relatively small with respect to the solar cycle, we do not expect the solar activity to play a relevant role, and hence we reckon it is reasonable not to normalise the measured sky brightness to some reference time. This operation would be anyway very difficult, due to the vast amount of data and the lack of long time series. The results are presented in Fig. 9, where we have plotted the sky brightness vs. time from evening twilight, $\Delta t_{{\rm etwi}}$, for B, V, R and I passbands. Our data do not support the exponential drop seen by Walker (1988b) during the first 4 hours and confirm the findings by Leinert et al. (1995), Mattila et al. (1996) and Benn & Ellison (1998). This is particularly true for V and R data, while in B and especially in I one might argue that some evidence of a rough trend is visible. As a matter of fact, a blind linear least squares fit in the range 0 $\leq \Delta t_{{\rm etwi}}\leq$ 6 gives an average slope of 0.04 $\pm$ 0.01 and 0.03 $\pm$ 0.01 mag hour^-1 for the two passbands respectively. Both values are a factor of two smaller than those found by Walker (1988b) but are consistent, within the quoted errors, with the values we found revising his original data (see Appendix D). However, the fact that no average steady decline is seen in V and R casts some doubt on the statistical significance of the results one gets from B and I data. This does not mean that on some nights very strong declines can be seen, as already pointed out by Krisciunas (1997). Our data set includes several such examples, but probably the most interesting is the one which is shown in Fig. 10, where we have plotted the data collected on five consecutive nights (2000 April 3-7). As one can see, the I data (upper panel) show a clear common trend, even though segments with different slopes are present and the behaviour shown towards the end of the night during 2000 April 6 is opposite to that of 2000 April 5. This trend becomes less clear in the R passband (middle panel) and it is definitely not visible in V (lower panel), where the sky brightness remains practically constant for about 6 hours. Unfortunately, no B data are available during these nights.

Figure 9: Dark time Paranal night sky brightness, corrected for zodiacal light contribution, as a function of time distance from evening twilight. The vertical dotted lines indicate the shortest and longest night (7.4 and 10.7 hours respectively, astronomical twilight to twilight), while the dashed horizontal line is placed at the average value in each passband.

A couple of counter-examples are shown in Fig. 11: the upper and lower panels show two well sampled time series obtained on the same sky patch, which show that during those nights the sky brightness was roughly constant during the phase where the Walker effect is expected to be most efficiently at work. Instead of a steady decline, clear and smooth sinusoidal fluctuations with maximum amplitudes of $\sim$0.1 mag and time scales of the order of 0.5 hours are well visible. Finally, to show that even mixed behaviours can take place, in the central panel we have presented the R data collected on 23-02-2001, when a number of different sky patches was observed. During that night, the sky brightness had a peak-to-peak fluctuation of $\sim$0.7 mag and showed a steady increase for at least 4 hours.

To conclude, we must say that we tend to agree with Leinert et al. (1995) that the behaviour shown during single nights covers a wide variety of cases and that there is no clear average trend. We also add that mild time-dependent effects cannot be ruled out; they are probably masked by the much wider night-to-night fluctuations and possibly by the patchy nature of the night sky even during the same night.

Figure 10: Time sequences collected on April 2-7, 2000. The data have been corrected for airmass and differential zodiacal light contribution. The vertical dotted line is placed at the beginning of morning astronomical twilight.

Figure 11: Time sequences collected on 19-12-2000 (I), 23-02-2001 (R) and 16-07-2001 (I). The data have been corrected for airmass and differential zodiacal light contribution. The vertical dotted line is placed at the beginning of morning astronomical twilight.