Distribution of spin-axes longitudes and shape elongations of main-belt asteroids

Context: Large all-sky surveys provide us with a lot of photometric data that are sparse in time (typically few measurements per night) and can be potentially used for the determination of shapes and rotational states of asteroids. The method which is generally used to derive these parameters is the lightcurve inversion. However, for most asteroids their sparse data are not accurate enough to derive a unique model and the lightcurve inversion method is thus not very efficient. Aims: To fully utilize photometry sparse in time, we developed a new simplified model and applied it on the data from the Lowell photometric database. Our aim was to derive spin axis orientations and shape elongations of asteroids and to reconstruct distributions of these parameters for selected subpopulations to find if there are some differences. Methods: We model asteroids as geometrically scattering triaxial ellipsoids. Observed values of mean brightness and the dispersion of brightness are compared with computed values obtained from the parameters of the model -- ecliptical longitude $\lambda$ and latitude $\beta$ of the pole and the ratios $a/b$, $b/c$ of axes of the ellipsoid. These parameters are optimized to get the best agreement with the observation. Results: We found that the distribution of $\lambda$ for main-belt asteroids is not uniform (in agreement with findings of Bowell et al., 2014, M&PS, 49, 95) and is dependent on the inclination of orbit. Surprisingly, the non-uniformity of $\lambda$ distribution is larger for asteroids residing on low-inclination orbits. We also studied distributions of $a/b$ for several groups of asteroids and found that small asteroids ($D<25\,$km) are on average more elongated than large ones.