Aims. To aid the design of laser guide star (LGS) assisted adaptive optics (AO) systems, we present an analysis of the statistics of the mesospheric sodium layer based on long-term observations (35 years). Methods. We analyze measurements of the Na-layer characteristics covering a long period , acquired at latitude 23 • south, in São José dos Compos, São Paulo, Brazil. We note that Paranal (Chile) is located at latitude 24 • south, approximately the same latitude as São Paulo.Results. This study allowed us to assess the availability of LGS-assisted AO systems depending on the sodium layer properties. We also present an analysis of the LGSs spot elongation over the year, as well as the nocturnal and the seasonal variation in the mesospheric sodium layer parameters. Conclusions. The average values of the sodium layer parameters are 92.09 km for the centroid height, 11.37 km for the layer thickness, and 5 × 10 13 m −2 for the column abundance. Assuming a laser of sufficient power to produce an adequate photon return flux for an AO system with a column abundance of 4 × 10 13 m −2 , a telescope could observe at low geographic latitudes with the sodium LGS more than 250 days per year. Increasing this power by 20%, we could observe throughout the entire year.

Aims. The efficiency of optical pumping that increases the backscatter emission of mesospheric sodium atoms in continuous wave (cw) laser guide stars (LGSs) can be significantly reduced and, in the worst case, eliminated by the action of the geomagnetic field. Our goal is to present an estimation of this effect for several telescope sites. Methods. Sodium atoms precess around magnetic field lines that cycle the magnetic quantum number, reducing the effectiveness of optical pumping. Our method is based on calculating the sodium magnetic sublevel populations in the presence of the geomagnetic field and on experimental measurements of radiance return from sodium LGS conducted at the Starfire optical range (SOR). Results. We propose a relatively simple semi-empirical formula for estimating the effect of the geomagnetic field on enhancing the LGSs photon return due to optical pumping with a circularly polarized cw single-frequency laser beam. Starting from the good agreement between our calculations and the experimental measurements for the geomagnetic field effect, and in order to more realistically estimate the sodium LGSs photon return, we introduce the effect of the distance to the mesospheric sodium layer and the atmospheric attenuation. The combined effect of these three factors is calculated for several telescope sites. Conclusions. In calculating the return flux of LGSs, only the best return conditions are often assumed, relying on strong optical pumping with circularly polarized lasers. However, one can only obtain this optimal return along one specific laser orientation on the sky, where the geomagnetic field lines are parallel to the laser beam. For most of the telescopes, the optimum can be obtained at telescope orientations beyond the observation limit. For the telescopes located close to the geomagnetic pole, the benefit of the optical pumping is much more important than for telescopes located close to the geomagnetic equator.

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The atmospheric turbulence limits the angular resolution of telescopes of tens of meters to that of a telescope of 20 cm diameter. Large telescopes, such as the VLT and the E-ELT, have adopted the Adaptive Optics (AO) system to reduce the undesirable effects of turbulence. The implantation of the technology of “sodium-LGSs” is essential to increase the performances of the AO. The generation of “sodium-LGSs” is the result of the fluorescence of mesospheric Na atoms located between 80 to 105 km of altitude. The laser beam sent from the ground is tuned to the wavelength 589 nm; excites the D2 line of Na. The backscattered light gives necessary information on atmospheric turbulence and their effects on the incoming wave front of an astronomical object. The mesospheric sodium layer is characterized by the abundance of Na, the centroid height and the thickness of the layer. Their behaviors affect the variations of parameters of the “sodium-LGSs”, such as the Return Flux and the elongation of the spot. The characterization of this layer is necessary in order to optimize the performance of the “LGSs-AO” system. We present semi-empirical models based on experimental measurements. These models explain the variations in the abundance and height of the centroid of the sodium layer.