Averaged Phase Curves for Several Taxonomic Types of Asteroids

A method is proposed for constructing averaged phase curves of asteroid brightness for various taxonomic types. The method is based on a large number of astrometric observations published in the Minor Planet Center catalog, for which the apparent visual magnitudes of asteroids were measured simultaneously. Thousands of asteroids of each taxonomic type S, C, E, V, Q, L, D, and X were selected, and numerical integration of the equations of motion was performed. In the course of integration, for each observation, the component of the apparent magnitude dependent on the phase angle was determined. For asteroids of a given type, all obtained values were averaged over the phase angle. As a result, averaged phase curves characterizing each taxonomic type were constructed. The large volume of observational data makes it possible to clearly reveal the character of the opposition effect for different types. A shift of the phase curves with respect to zero at a zero phase angle was noted. This shift depends on asteroid size and differs among taxonomic types. The presence of such a shift indicates a systematic error in the absolute magnitudes of asteroids published in the Minor Planet Center catalog.