Besides being the first systematic campaign of night sky brightness measurements at Cerro Paranal, the survey we have presented here has many properties that make it rather unique. First of all, the fact that it is completely automatic ensures that each single frame which passes through the quality checks contributes to build a continously growing sample. Furthermore, since the data are produced by a very large telescope, the measurements accuracy is quite high when compared to that generally achieved in this kind of study, which most of the time make use of small telescopes. Another important fact, related to both the large collecting area and the use of a CCD detector, is that the usual problem of faint unresolved stars is practically absent. In fact, with small telescopes, it is very difficult to avoid the inclusion of stars fainter than V= 13 in the beam of the photoelectric photometer (see for example Walker 1988b). The contribution of such stars is 39.1 S₁₀(V) (Roach & Gordon 1973, Table 2-I) which corresponds to about 13% of the global sky brightness. Now, with the standard configuration and a seeing of 1 $^{\prime \prime }$ , during dark time FORS1 can reach a 5 $\sigma$ peak limiting magnitude $V\simeq$ 23.3 in a 60 s exposure for unresolved objects. As the simulations show (see Patat 2003), the algorithm we have adopted to estimate the sky background is practically undisturbed by the presence of such stars, unless their number is very large, a case which would be rejected anyway by the $\Delta$ -test (Patat 2003). Now, since the typical contribution of stars with $V\geq$ 20 is 3.2 S₁₀(V)(Roach & Gordon 1973), we can conclude that the effect of faint unresolved stars on our measurements is less than 1%.

Another distinguishing feature is the time coverage. As reported by Benn & Ellison (1998), the large majority of published sky brightness measurements were carried out during a limited number of nights (see their Table 1). The only remarkable exception is represented by their own work, which made use of 427 CCD images collected on 63 nights in ten years. Nevertheless, this has to be compared with our survey which produced about 3900 measurements during the first 18 months of steady operation. This high time frequency allows one to carry out a detailed analysis of time dependent effects, as we have shown in Sect. 6 and to get statistically robust estimates of the typical dark time zenith sky brightness.

The values we have obtained for Paranal are compared to those of other dark astronomical sites in Table 5. The first thing one notices is that the values for Cerro Paranal are very similar to those reported for La Silla, which were also obtained during a maximum of solar activity. They are also not very different from those of Calar Alto, obtained in a similar solar cycle phase, even though Paranal and La Silla are clearly darker in R and definitely in I. All other sites presented in Table 5 have data which were obtained during solar minima and are therefore expected to show systematically lower sky brightness values. This is indeed the case. For example, the V values measured at Paranal are about 0.3 mag brighter then those obtained at other sites at minimum solar activity (Kitt Peak, Cerro Tololo, La Palma and Mauna Kea). The same behaviour, even though somewhat less pronounced, is seen in B and I, while it is much less obvious in R. Finally, the U data show an inverse trend, in the sense that at those wavelengths the sky appears to be brighter at solar minima. Interestingly, a plot similar to that of Fig. 13 also gives a negative slope, which turns into a variation $\Delta U=-$ 0.7 $\pm$ 0.5 mag arcsec^-2 during a full solar cycle. Due to the rather large error and the small number of nights (11), we think that no firm conclusion can be drawn about a possible systematic effect, but we notice that a similar behaviour is found by Leinert et al. (1995) for the u passband (see their Fig. 6). Since the airglow in U is dominated by the O₂ Herzberg bands $A^3\Sigma-X^3\Sigma$ (Broadfoot & Kendall 1968), the fact that their intensity seems to decrease with an increasing ionising solar flux could probably give some information on the physical state of the emitting layers, where molecular oxygen is confined.

At any rate, the BVRI Paranal sky brightness will probably decrease in the next 5-6 years, to reach its natural minimum around 2007. The expected darkening is of the order of 0.4-0.5 mag arcsec^-2 (Walker 1988b), but the direct measurements will give the exact values for this particular site. In the next years this survey will provide an unprecedented mapping of the dependency from solar activity. So far, in fact, this correlation has been investigated with sparse data, affected by a rather high spread due to the night-to-night variations of the airglow (see for instance Fig. 4 by Krisciunas 1990), which tend to mask any other effect and make any conclusion rather uncertain.

As already pointed out by several authors, the night sky can vary significantly over different time scales, following physical processes that are not completely understood. As we have shown in the previous section, even the daily variations in the solar ionising radiation are not sufficient to account for the observed night-to-night fluctuations. Moreover, the observed scatter in the dark time sky brightness (see Sect. 5) is certainly not produced by the measurement accuracy and can be as large as 0.25 mag (rms) in the I passband; since the observed distribution is practically Gaussian (see Fig. 7), this means that the I sky brightness can range over $\sim$ 1.4 mag, even after removing the effects of airmass and zodiacal light contribution. This unpredictable variation has the unpleasant effect of causing maximum signal-to-noise changes of about a factor of 2.

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{MS3223f14.eps} \end{figure}$

Figure 14: V, R and I (from top to bottom) dark time sky brightness measured at Paranal from April 2000 to September 2001. For each passband the average value (dashed line) and the $\pm$ 1 $\sigma$ interval (dotted lines) are plotted. The large solid dots are placed at the seasonal average values computed within the time interval indicated by the horizontal error bars, while the vertical error bars represent the corresponding rms sky brightness dispersion. The labels on the lower side indicate the austral astronomical season: winter (W), spring (Sp), summer (Su) and fall (F). The vertical dashed line indicates December 31, 2000.

Besides these short time scale fluctuations that we have discussed in Sect. 6 and the long term variation due to the solar cycle, one can reasonably expect some effects on intermediate time scales. With this respect we have computed the sky brightness values averaged over three months intervals, centered on solstices and equinoxes. The results for V, R and I are plotted in Fig. 14, where we have used all the available data obtained at Paranal during dark time, with $\Delta_{{\rm twi}}\geq$ 0. This figure shows that there is no convincing evidence for any seasonal effect, especially in the I passband, where all three-monthly values are fully consistent with the global average (thick dashed line). The only marginal detection of a deviation from the overall trend is that seen in R in correspondence of the austral summer of year 2000, when the average sky brightness turns out to be $\sim$ 1.3 $\sigma$ fainter than the global average value. Even though a decrease of about 0.1 mag is indeed expected in the R passband as a consequence of the NaI D flux variation (see Roach & Gordon 1973 and the discussion below), we are not completely sure this is the real cause of the observed effect, both because of the low statistical significance and the fact that a similar, even though less pronounced drop, is seen at the same epoch in the V band, where the NaI D line contribution is negligible (see Fig. 1).

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{MS3223f15.eps} \end{figure}$

Figure 15: Evolution of the night sky spectrum on February 25, 2001 in the wavelength range 5500-6500 Å. The original 1800 s spectra were obtained with FORS1, using the standard resolution collimator and a long slit 1 $^{\prime \prime }$ wide (see also the caption of Fig. 1). In each panel the starting UT time and airmass X are reported. For presentation the four spectra have been normalised to the continuum of the first one in the region 5600-5800 Å.

To illustrate how complex the night sky variations can be, we present a sequence of four spectra taken at Paranal during a moonless night in Fig. 15, starting more than two hours after evening twilight with an airmass ranging from 1.4 to 2.0. For the sake of simplicity we concentrate on the spectral region 5500-6500 Å, right at the intersection between V and R passbands, which contains the brightest optical emission lines and the so called pseudo-continuum (see Sect. 1). Due to the increasing airmass, the overall sky brightness is expected to grow according to Eq. (C.3), which for V and R gives a variation of about 0.2 mag. These values are in rough agreement with those one gets measuring the continuum variation at 5500 Å (0.13 mag) and 6400 Å (0.18 mag). Interestingly, this is not the case for the synthetic V and R magnitudes derived from the same spectra, which decrease by 0.32 and 0.51 mag respectively, i.e. much more than expected, specially in the R band. This already tells us that the continuum and the emission lines must behave in a different manner. In fact, the flux carried by the [OI]5577 Å line changes by a factor 1.9 from the first to the last spectrum, whereas the adjacent continuum grows only by a factor 1.1. For the NaI D lines, these two numbers are 1.4 and 1.2, still indicating a dichotomy between the pseudo-continuum and the emission lines. But the most striking behaviour is that displayed by the [OI]6300, 6364 Å doublet: the integrated flux changes by a factor 5.2 in about two hours and can be easily identified as the responsible for the brightening observed in the R passband. This is easily visible in Fig. 15, where the [OI]6300 Å component surpasses the [OI]5577 Å in the transition from the first to the second spectrum and keeps growing in intensity in the subsequent two spectra. The existence of these abrupt changes is known since the pioneering work by Barbier (1957), who has shown that [OI]6300, 6364 Å can undergo strong brightness enhancements over an hour or two on two active regions about 20 $^\circ$ on either side of the geomagnetic equator, which roughly corresponds to tropical sites. With Cerro Paranal included in one of these active areas, such events are not unexpected. A possible physical explanation for this effect is described by Ingham (1972), and involves the release of charged particles at the conjugate point of the ionosphere, which stream along the lines of force of the terrestrial magnetic field. We notice that in our example, the first spectrum was taken about two hours before local midnight, at about one month before the end of austral summer. This is in contrast with Ingham's explanation, which implies that this phenomenon should take place in local winter, since in local summer the conjugate point, which for Paranal lies in the northern hemisphere, sees the sun later and not before, as it is the case during local winter.

Irrespective of the underlying physical mechanism, the [OI]6300, 6364 Å line intensity changed from 255 R to 1330 R; the fact that the initial value is definitely higher than that expected at these geomagnetic latitudes (<50 R, Roach & Gordon 1973, Figs. 4-12) seems to indicate that the line brightening had started before our first observation. On the other hand, the intensity of the [OI]5577 Å line in the first spectrum is 220 R, i.e. well in agreement with the typical value (250 R, Schubert & Walterscheid 2000).

The case of NaI D lines is slightly different, since these features follow a strong seasonal variation which makes them brighter in winter and fainter in summer, the intensity range being 30-200 R (Schubert & Walterscheid 2000). This fluctuation is expected to produce a seasonal variation with an amplitude of about 0.1 mag in the R passband, while in V the effect is negligible. Actually, the minimum intensity of this feature can change from site to site, according to the amount of light pollution. In fact, most of the radiation produced by low-pressure sodium lamps is released through this transition. For example, Benn & Ellison (1998) report for La Palma an estimated artificial contribution to the sodium D lines of about 70 R. In our first spectrum, the measured intensity is 73 R, a value which, together with the epoch when it was obtained (end of summer) and the relatively large airmass (X= 1.5), indicates a very small contribution from artificial illumination. However, a firmer limit can be set analysing a large sample of low resolution spectra taken around midsummer, a task which is beyond the purpose of this paper.

To search for other possible signs of light pollution, we have examined the wavelength range 3500-5500 Å of the last spectrum presented in Fig. 15, which was obtained at a zenith distance of about 60 $^\circ$ and at an azimuth of 313 $^\circ$ . A number of Hg and Na lines produced by street lamps, which are clearly detected at polluted sites, falls in this spectral region. As expected, there is no clear trace of such features in the examined spectrum; in particular, the strongest among these lines, HgI 4358 Å, is definitely absent. This appears clearly in Fig. 16, where we have plotted the relevant spectral region and the expected positions for the brightest Hg and Na lines (Osterbrock & Martel 1992). In the same figure we have also marked the positions of O₂ and OH main features. A comparison with the spectra presented by Broadfoot & Kendall (1968) again confirms the absence of the HgI lines and shows that almost all features can be confidently identified with natural transitions of molecular oxygen and hydroxyl. There are probably two exceptions only, which happen to be observed very close to the expected positions for NaI 4978, 4983 Å and NaI 5149, 5163 Å, lines typically produced by high pressure sodium lamps (Benn & Ellison 1998). They are very weak, with an intensity smaller than 2 R, and their contribution to the broad band sky brightness is negligible. Nevertheless, if real, they could indicate the possible presence of some artificial component in the NaI D lines, which are typically much brighter. This can be verified with the analysis of a high resolution spectrum. If the contamination is really present, this should show up with the broad components which are a clear signature of high pressure sodium lamps. The inspection of a low airmass, high resolution (R= 43 000) and high signal-to-noise UVES spectrum of Paranal's night sky (Hanuschik et al. 2003, in preparation) has shown no traces of neither such broad components nor of other NaI and HgI lines. For this purpose, suitable UVES observations at critical directions (Antofagasta, Yumbes mining plant) and high airmass periodically executed during technical nights, would probably allow one to detect much weaker traces of light pollution than any broad band photometric survey. But, in conclusion, there is no indication for any azimuth dependency in our dark time UBVRI measurements.

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{MS3223f16.eps} \end{figure}$

Figure 16: Night sky spectrum obtained at Paranal on February 25, 2002 at 04:53 UT (see Fig. 15). Marked are the expected positions for the most common lines produced by artificial scattered light (upper ticks) and natural atmospheric features (lower ticks). The dotted line traces part of the spectrum taken during the same night at 02:39 UT.

There are finally two interesting features shown in Fig. 16 which deserve a short discussion. The first is the presence of CaII H&K absorption lines, which are clearly visible also in the spectra presented by Broadfoot & Kendall (1968) and are the probable result of sunlight scattered by interplanetary dust (Ingham 1962). This is not surprising, since the spectrum of Fig. 16 was taken at $\beta=-$ 3$.^$5 and $\lambda-\lambda_\odot=$ 139$.^$8, i.e. in a region were the contribution from the zodiacal light is significant (see Fig. 5). The other interesting aspect concerns the emission at about 5200 Å. This unresolved feature, identified as NI, is extremely weak in the spectra of Broadfoot & Kendall (1968), in agreement with its typical intensity (1 R, Roach & Gordon 1973). On the contrary, in our first spectrum (dotted line in Fig. 16) it is very clearly detected at an intensity of 7.5 R and steadily grows until it reaches 32 R in the last spectrum, becoming the brightest feature in this wavelength range. This line, which is actually a blend of several very close NI transitions, is commonly seen in the Aurora spectrum with intensities of 0.1-2 kR (Schubert & Walterscheid 2000) and it is supposed to originate in a layer at 258 km. The fact that its observed growth (by a factor 4.3) follows closely the one we have discussed for [OI]6300, 6364 Å, suggests that the two regions probably undergo the same micro-auroral processes.

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{MS3223f17.eps} \end{figure}$

Figure 17: Lower panel: peak signal-to-noise ratio measured for the same star on a sequence of 150 s I images obtained with FORS1 on July 16, 2001. Solid and dashed lines trace Eq. (3) for U and I passbands respectively. Middle panel: seeing measured by the Differential Image Motion Monitor (DIMM, Sandrock et al. 2000) at 5500 Å and reported to zenith (empty circles); each point represents the average of DIMM data over the exposure time of each image. The solid circles indicate the image quality (FWHM) directly measured on the images. Upper panel: sky background (in ke^-) measured on each image.

Such abrupt phenomena, which make the sky brightness variations during a given night rather unpredictable, are accompanied by more steady and well behaved variations, the most clear of them being the inherent brightening one faces going from small to large zenith distances. In fact, as we have seen, the sky brightness increases at higher airmasses, especially in the red passbands, where it can change by 0.4 mag going from zenith to airmass X= 2. For a given object, as a result of the photon shot noise increase, this turns into a degradation of the signal-to-noise ratio by a factor 1.6, which could bring it below the detection limit. Unfortunately, there are two other effects which work in the same direction, i.e. the increase of atmospheric extinction and seeing degradation. While the former causes a decrement of the signal, the latter tends to dilute a stellar image on a larger number of pixels on the detector. Combining Eq. (C.3), the usual atmospheric extinction law $I=I_0\;10^{-0.4\kappa(X-1)}$ and the law which describes the variation of seeing with airmass ( $s=s_0\;X^{0.6}$ , Roddier 1981) we can try to estimate the overall effect on the expected signal-to-noise ratio at the central peak of a stellar object. After very simple calculations, one obtains the following expression:

9 Discussion and conclusions