The Physical Meaning of Phase Coefficients

The question of what information about an asteroid's surface is contained in a measurement of the phase coefficient between phase angles of 10° and 30° is examined in detail. Contrary to some past claims it is shown that absolute reflectivities cannot be derived from phase coefficients. Furthermore, typical asteroid phase coefficients cannot be interpreted unambiguously. This is because the observed phase coefficient may depend as much on the photometric properties of an individual surface element as on the degree of large-scale surface roughness, and these two effects are impossible to separate if only disk integrated measurements are available. The wavelength dependence of asteroid phase coefficients should be small and should contain little information about the surface. In the case of irregular asteroids with macroscopically rough surfaces, the importance of large-scale shadowing, and hence the observed phase coefficient, will depend on the aspect of the asteroid. In such cases, therefore, phase coefficients must be carefully defined to be meaningful It should be possible, in some cases, to estimate the relative surface roughness of two quasi-spherical asteroids by combining photometric and polarimetric observations. For example, if the two asteroids have almost identical polarization curves but quite different phase coefficients, it is likely that the asteroid with the larger phase coefficient has a macroscopically rougher surface.