Compositional interpretation of the geometric albedo of asteroids - I. Solar phase effects

Aims. In this first paper we investigate the dependence of the geometric albedo on the phase function of the particles that cover it, and derive the expected geometric albedo of bodies for a given mineralogy, taking into account the constraints imposed by the observed phase functions of the asteroids. Methods. A genetic fitting algorithm is used to fit Hapke integral phase functions to Lumme-Bowell integral phase functions described by values of the slope parameter G of the IAU HG system. The resulting geometric albedo of laboratory samples are then compared to the observed values of asteroids with assumed similar mineralogy. Results. Because of the weak dependence of (theta) over bar. on the integral phase functions it is not possible to find a unique set of Hapke parameters that fit the Lumme-Bowell function for a given value of G, at least for phase angles < 60 degrees. Instead, unique solutions can be found if we leave <(theta)over bar> as a free parameter. It is shown that the laboratory derived scattering parameters in general fail to match the geometric albedo and slope parameter of asteroids of presumed equal mineralogy. It is also shown that a given value of the single scatter albedo can lead to very different values of p(v), depending on G and (theta) over bar. The methodology developed is used to compare the observed pv and G of the asteroids (4) Vesta and (21) Lutetia with laboratory measurements of materials with suposedly similar compositions. As expected, it is found that the albedo and slope parameter of Vesta are compatible with measurements of unweathered terrestrial basalts with grain sizes <= 250 mu m. The albedo and slope parameter of Lutetia are found to be compatible with samples of the Allende CV3 meteorite for grain sizes < 500 mu m. The routines that allow the conversion between w and p(V) (and vice-versa) are available at http://funk.on.br/similar to carvano/albedo/albedo.html.