Systematic biases in radiometric diameter determinations

Abstract

Radiometric diameters and albedos of asteroids and other Solar System bodies have generally been determined with the aid of a standard thermal model, which assumes a smooth nonrotating surface and relies on an empirical beaming factor to adjust model fluxes to the values observed for objects of known radius. It has been assumed that the need for a correction factor is generally due largely to the effects of roughness on the thermal emission from real surfaces. We show that in many cases the effects of rotation are also important and must be considered in radiometric diameter determinations. The thermal effect of rotation depends not only on the object's thermal inertia, rotation rate, and pole orientation, but also on its temperature: colder objects with constant rotation rate and thermal inertia radiate proportionally less of their heat on the day hemisphere and more on the night hemisphere. If the asteroids Ceres and Pallas have lunarlike thermal inertias the effect of rotation on their thermal emission is very important: in particular, large variations in thermal emission correlated with variations in subsolar latitude around their orbits are expected. Such variations are not observed, and we therefore suggest that these and other main-belt asteroids have thermal inertias ≤1.5 × 10 4 erg cm −2 sec −1 2 K −1 , ≤30% that of the Moon. We determine a disk-integrated beaming parameter of 0.72 for the Moon and use this value to correct empirically for roughness effects in our thermophysical models. As a result of the influence of temperature on the thermal effects of rotation, the standard thermal model systematically underestimates the diameters (and overestimates the albedos) of cold objects. For example, assuming a thermal inertia 20% of the lunar value and the Sun in the equatorial plane, a Trojan asteroid would be 11% larger than the diameter determined radiometrically at 10 μm, and if it had a lunar thermal inertia, it would be 67% larger than determined radiometrically at 10 μm. Errors at 20 μm are smaller. The error in radiometric diameter varies with the body's albedo, thermal inertia, and subsolar latitude in ways that we describe.