Thermal modeling

The most frequent method to determine the size (and volume) of an asteroid is fitting the thermal data observations (typically from IRAS, WISE, and AKARI satellites) by simple thermal models that assume a spherical shape model:

• Standard Thermal Model (STM) of Lebovsky et al (1986) – no rotation and asteroid in opposition. Includes a normalization factor – beaming parameter η that is calibrated by the size of asteroids (1) Ceres and (2) Pallas derived from stellar occultation measurements. This value (η=0.756) is not valid for smaller asteroids! Used to analyze AKARI data, however, η values were re-calibrated to be more realistic for certain populations (MBAs, NEAs).
• Fast Rotating Model
• Near-Earth Asteroid Thermal Model of Harris (1998) – beaming parameter is fitted, still spherical non-rotating (the lightcurve is averaged) object. The thermal flux is computed only for the illuminated and visible part of the surface. Used with WISE data.

The reported size uncertainties for individual asteroids are usually very small (few percent), however, they are not realistic. Indeed, the uncertainties are dominated by the model systematic errors - the spherical shape assumption is too crude and also the role of the geometry is neglected (e.g., the spin axis orientation). In the statistical sense, the sizes determined by thermal models are reliable, but could be easily off for individual objects by 10-30%. This implies a volume uncertainty of 30-90%!

Beaming parameter interpretation

Related to thermal inertia, surface roughness, size, pole, ...

Albedos and sizes from thermal modeling

Thermophysical modeling

Simple thermal models assume spherical, non-rotating asteroids. When shape models, spin vectors, and other physical parameters are known, it is possible to apply more sophisticated methods to infer thermophysical properties such as thermal inertia and/or surface roughness. So far, such thermophysical parameters were derived for less than about 50 asteroids due to the lack of both physical properties (i.e., shape models, spin axis orientations) as well as available thermal infrared observations. However, the number of shape models has grown dramatically in the past decade and the newly obtained thermal infrared data from WISE now open the opportunity to greatly increase the number of thermal inertia determinations.

Thermal inertia, defined by Γ= √ρκC, where ρ is the density of the surface regolith, κ its thermal conductivity, and C its heat capacity, measures the resistance of a material to temperature change, and thus controls the temperature distribution of the surface of an atmosphere-less body. As it affects the symmetry of the temperature distribution on asteroids, the thermal inertia controls the strength of the Yarkovsky effect, which is the rate of change in the semi-major axis of the orbit of an asteroid (da/dt) due to the recoil force of the thermal photons (Bottke et al., 2006, for instance). Thermal inertia is also a sensitive indicator of the nature of the surface regolith as its value is affected by the cohesion of the material in the soil (i.e., between one and several tens of millimeters of the surface layer see, e.g., Mellon et al., 2000; Jakosky, 1986). Knowledge of the grain size of asteroid regolith is of paramount importance for future landing and/or sample-return missions (such as OSIRIS-REx and Hayabusa-2, two different sample return missions to carbonaceous asteroids, Lauretta et al., 2012; Okada et al., 2014). Thermal inertia is strongly affected by the porosity of the material (Zimbelman, 1986). For a given surface composition, the higher the porosity, the lower the values of both j and C. See Vernazza et al. (2012) for a discussion of the effect of porosity on asteroids surfaces.

In order to derive the thermal inertia and other physical parameters of asteroids, such as the diameter and the albedo, a thermophysical model (hereafter TPM, Lagerros, 1996, 1997, 1998) is typically used to analyze thermal infrared data. A TPM calculates thermal infrared fluxes given a set of physical parameters (size D, thermal inertia Γ, Bond albedo A, surface roughness θ) whose values are adjusted to provide the best fit between the model and the observed fluxes, by minimizing a figure of merit (chi-square). Classically, a TPM is used with an a priori knowledge of the shape and the rotational state of the asteroid, which are taken as fixed quantities. Typically, shapes are based on radar imaging (e.g., asteroids 2010 EV5, or (101955) Bennu, Alí-Lagoa et al., 2014; Emery et al., 2014) or on convex inversion of photometric ligthcurves (e.g., asteroids (25143) Itokawa, or (1620) Geographos, Müller et al., 2014; Rozitis and Green, 2014).

References

Lebofsky L. A., Sykes M. V., Tedesco E. F., et al. (1986). A refined ’standard’ thermal model for asteroids based on observations of 1 Ceres and 2 Pallas. Icarus, 68, 239-251.

-- JosefHanus - 21 May 2015