The statistical study aims at quantifying the average and variability of the column density of neutral sodium present in the upper atmosphere, at different observation sites, in order to establish the minimum laser power necessary for LGS-AO.

3.1 Indirect knowledge about the atmospheric Na: Astronomical observations

High resolution spectroscopic studies of the Na D lines in the interstellar medium (see e.g. [Welsh et al.] 1990; [Welsh et al.] 1994) suggest a methodology whereby the mesospheric neutral sodium column density can be determined from normal astronomical observations, although there has been no systematic attempt to do so until now.

There have been, over the last decade, an increasing number of studies of the local interstellar medium (LISM), defined here as d<200 pc, using both optical and UV absorption lines (see reviews by [Paresce 1984] - and by [Cox & Reynolds 1987]). Thanks to high resolution ground based observations, a large database of information exists concerning the absorption characteristics and galactic distribution of neutral interstellar sodium (Na I) gas. Specifically, this data has been gained over the past 25 years through observations of the Na I D line doublet at 5890 Å seen in the absorption spectra of galactic early-type stars (e.g. [Hobbs] 1978) which have no intrinsic sodium features, either in emission or absorption.

The interesting result for the problem considered here, is the fact that the dense neutral interstellar NaI gas is generally absent from the very local interstellar medium. Indeed no sodium absorption was detected towards any of the stars, observed by [Welsh et al.] (1990), with distances less than 42 pc. This means that it is possible, in principle, to measure the mesospheric sodium column density from observations of sodium absorption in early-type stars closer than $\sim$ 50 pc for which there is little or no interstellar contribution (interstellar equivalent width are typically less than 10 mÅ).

3.2 Archive work

One possibility for a statistical study of column density alone is to use data from astronomical archives. To reduce the work, sites having and/or planning to have LGS-AO have been identified from the list established in [Rigaut (1997)]. In the second part of the work we set out to identify existing archive data for those particular sites that could be used for the statistical study.

It results from this research that there is little high resolution spectroscopic data at the interesting wavelengths in the available data archives. Moreover, the existing data are sparse and spread over time and geographical location. Hence there is no reasonable possibility to make a meaningful statistical study of the atmospheric sodium density above any particular observatory. In the long term a dedicated archive will have to be created.

3.3 What is currently being done

This section will concentrate only on the collaborative efforts of ESO and the National University of Ireland, Galway (NUIG) concerning the problem of measuring the column density of atmospheric sodium with existing intruments, as preparatory work for the laser guide star adaptive optics system planned for the VLT at Paranal. In this framework ESO and NUIG are collaborating within the Training and Mobility of Reasearcher (TMR) program on "Laser guide star for 8 m class telescopes'', funded by the European Commission.

Since it became apparent, from studies of the data archives, that no data exist concerning the abundance of sodium above the Chilean observatories, we decided to make, specifically for this purpose, high resolution spectroscopic measurements of selected stars at ESO La Silla. The only other measurements existing in South America have been done in Brazil by [Clemesha et al. (1992)]. No LGS-AO is planned for La Silla, but for Cerro Paranal, which is $\approx$ 700 km northward ( $\Delta \ell$ = 4 $^{\circ}$ 35'). The Na abundance may, of course, differ somewhat between La Silla and Paranal, however, in the absence of specific measurements at Paranal itself, these observations will give a general idea of the amount of sodium present. They are also interesting for comparison with the results from the Brazilian observations.

The observations aimed at determining the absolute averaged sodium density in the atmosphere above La Silla and the night and day-to-day variations. The data were obtained during one and a half night granted Director Discretionary Time in July 1998, on the ESO Multi Mode Instrument (EMMI, [Dekker et al. 1986]) at the New Technology Telescope (NTT).

The sources, selected from [Welsh et al.] (1994), are unreddened early-type stars closer than 50 pc. This allows to observe pure atmospheric absorption spectra in the vicinity of the NaD doublet free from interstellar absorption and stellar features in absorption or emission. The stars are of type A & B, i.e. with flat spectrum, and have been selected to have m_V < 10, for high incoming flux. Ideally one would like to have short integration times to detect the sporadics and quick variation of the atmospheric sodium. However this is currently impossible for high resolution spectroscopic measurements.

3.3.1 Observations

The minimum resolution necessary to resolve the atmospheric sodium D lines from nearby contaminating water line is of 50000. This thus implied the choice of the EMMI echelle grating #14.

To measure the D₁ equivalent width above a 3 $\sigma$ level, ideally one would like a signal to noise ratio (SNR) of 1000, with:

$\begin{displaymath}\begin{array}{lll} SNR = & \multicolumn{2}{l}{\frac{DQE \time... ...elta \lambda \times N_{\rm sky} \times t) + DN^2}}} \end{array}\end{displaymath}$

(1)

The detector of interest is the CCD#36, which has a read_out_noise of 5 electrons/pixel and a dark of 1.7 electrons/pixel/hour; so that $DN = N \times 5 + (1.7/3600) \times t$ , with t the integration time and N the total number of exposures. This term is however negligible since the observations are dominated by the photon noise. It is thus reasonable to approximate the signal to noise ratio by:

$\begin{displaymath}SNR \approx {\sqrt{(DQE \times \delta \lambda \times N_{\rm obj} \times t)}}\cdot \end{displaymath}$

(2)

For EMMI at the NTT and the echelle grating used, Dekker et al. (1994) quote the arrival of 1 photon/Å/s at 5500 Å for a m_V= 16.6 star, at an airmass of 1. For a m_V=4.7 star, a pixel scale of 0.27'', and taking the quantum efficiency of the detector into account, one finds 403.3 electrons/Å/s arriving on the detector. Since the linearity of the detector is 50000 ADUs, and the gain 2.2 electrons/ADU, in this case, one can integrate for $\approx$ 273 s, without saturating the detector. To reach the desired signal to noise ratio, we will then have to make, e.g. 23 exposures of 4 min, which represents 2 hours on the source when taking the overheads into account.

$\begin{figure}\includegraphics[width=8.8cm,clip]{ds8834fig1.ps}\end{figure}$

Figure 1: Spectrum of $\theta$ Cap (full line). It is the sum of 28 spectra corresponding to 5870 s. of integration on source. The D₁ line is clearly resolved at 5895.96 Å. Overplotted (dotted line) is the spectrum of $\beta$ Lib, corresponding to 2325 s on source

3.3.2 Results

Only 3 sources have been observed and unfortunately, mostly because of bad weather, it was not possible to spend enough time on source to reach the wished signal to noise ratio. $\beta$ Lib, $\theta$ Cap and $\iota$ Cen were observed respectively for a total of 2325, 5870 and 210 s on source.

Figure 1 represents some of the spectra obtained. Each spectrum has been flatfielded individually, wavelength calibrated and finally coadded to the others to create this image. The data reduction has entirely been done under the echelle context of MIDAS ([Banse et al. 1983]). All further data analysis concerns only the $\theta$ Cap data since it has the highest integration time, i.e. the best signal on source.

$\begin{figure}\includegraphics[width=8.8cm,clip]{ds8834fig2.ps}\end{figure}$

Figure 2: Spectrum of $\theta$ Cap. The dotted black line is the original spectrum, the model fitted is represented by the thin full line; the resulting spectrum is overplotted with an artificial offset of 1 (thick full line)

Since the Moon was 80% full during the observation, strong solar lines reflected off the Moon interferes with the observed spectrum. The best illustration is visible in Fig. 1 where at 5895.55 for $\beta$ Lib and 5895.65 for $\theta$ Cap appears a Doppler shifted solar sodium line. Most of the other lines identified in the spectrum correspond to atmospheric water contribution.

To calibrate the spectrum from the atmospheric contribution, except the mesospheric sodium, lines have been identified, fitted and suppressed. The contaminating lines to be suppressed have been identified thanks to table of atmospheric and solar lines (essentially from [Lundström et al. 1991] and [Moore et al. 1966]). Calibration of future observations are planned to be done in two ways: observe a blank sky to determine the exact position of the atmospheric lines; and compare spectra of at least 2 different sources, observed the same night, to identify the lines of solar origin thanks to their relative Doppler shift. It is also expected to be able to use a code creating a synthetic atmospheric spectrum ([Lundström et al. 1991]).

The identified lines were geometrically fitted with Gaussian functions and then merged into a spectrum corresponding to our model of the data (see Fig. 2). The result of the fitting is presented Fig. 3. The signal to noise depends of course on the total integration time. The noise of the background level could however be reduced by using a proper physical model to fit the identified perturbing atmospheric lines. An equivalent width of $\approx$ 0.5 mÅ at 3.5 $\sigma$ was derived from the spectrum Fig. 3.

$\begin{figure}\includegraphics[width=8.8cm,clip]{ds8834fig3.ps}\end{figure}$

Figure 3: Final spectrum of $\theta$ Cap, resulting from the difference between the observed spectrum and the modelled one. Except specified, arrows indicate lines that were not identified and are thus remaining. At $\sim$ 5896 Å, the arrow points at the atmospheric sodium D₁ line, whose equivalent width is 0.5 mÅ

The sodium column density, $N_{\rm Na}$ , has then been derived from the formula ([Spitzer 1978]):

$\begin{displaymath}N_{\rm Na} = W_{\rm D_1} / (8.85 10^{-13} \lambda_{\mu} f_{\rm D_1}) \end{displaymath}$

(3)

3.4 Conclusion

Knowing the Na column density, using the theoretical prediction for sodium laser return ([Milonni et al. 1998]) and assuming no saturation effect in the sodium layer, one can determine the minimum laser power necessary to obtain a given magnitude laser guide star; which is our main interest in this study.

Assuming an atmospheric transmission of 0.7, a $\sim$ 63W projected laser power is necessary to produce a laser guide star of equivalent magnitude, m_V = 6. However this calculation is true only in the case of negligible saturation, which is not the case with such a high power laser. Inverting the problem and considering a 4W laser, assuming there is no saturation effect in the sodium layer at this laser power, one finds that, for a 3 10⁹ cm^-2 sodium column density, a m_V = 8.74 star can be created, which is bright enough to achieve good AO correction.

It is interesting to notice that the sodium column density detected in July 1998 at 29 $^{\circ}$ S is a factor of two fainter than what was detected above Brazil (23 $^{\circ}$ S) in 1991 (Clemesha et al. 1992), which could simply be explained by the latitude difference. This proves the importance of such study. Following this result, ESO is planning on using some time during UVES technical nights to make similar measurements over Paranal.

Due to the dynamic range of the CCD and the minimum exposure time needed on source to reach the requested SNR, when using high resolution spectroscopy, the time resolution on the atmospheric sodium is at best 2 hours, with this type of observation. It is thus impossible to study short time scale variations of the mesospheric sodium column density. However this kind of study has to be persued over at least a period of a year to determine the "absolute'' yearly minimum expected in the Na column density, therefore observations are planned during Chilean summer.

Among the observing facilities present at La Silla, the Coudé Echelle Spectrograph, which is fiber coupled to the ESO 3.6 m telescope, offers the best solution for monitoring atmospheric sodium absorption because it offers a resolution of up to 220000, which would then allow both the Na D₁ and D₂ lines to be resolved from neighbouring water lines. This would enable a double check on the results to be made.