The Physical Meaning of Phase Coefficients

Abstract

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.

Asteroid Photometry

“…Bowell and Lumme, 1979 and references therein). In addition, higher surface roughness also contributes to the steeper slope of a phase function (e.g., Veverka, 1971), although it is not possible to entirely disentangle the effects of multiple scattering and surface roughness from a disk-integrated phase function.…”

Aegaeon (Saturn LIII), a G-ring object

“…The phase coefficients of Anthe, Pallene and Methone are reasonable values for small airless objects (compare with values for asteroids in Bowell and Lumme 1979), while the coefficient for Aegaeon is somewhat on the low side, which may be because a residual unsubtracted G-ring signal adds a slightly forward-scattering component to its phase curve. Alternatively, Aegaeon may have a smoother surface than the other moons (Veverka 1971).…”

Opposition Effect of Asteroids

“…On the other hand, numerous laboratory experiments and theoretical considerations (for references, see survey by Shkuratov 1994a,b) have also shown a great dependence of phase coefficients on surface texture, in particular on surface roughness and size of particles. Veverka (1971) concluded that it is impossible to interpret a phase coefficient unambiguously because of its dependence both on the photometric properties of an individual surface element and on the degree of large-scale roughness which cannot be separated based on disk-integrated measurements. Later Bowell and Lumme (1979) suggested it is possible to determine an asteroid's albedo from photometric observations since, to a first approximation, the surfaces of almost all asteroids are believed to have similar surface texture.…”