1. Thermal modeling of rocky bodies
Maria Teresa Capria, Maria Cristina De Sanctis, Jeremie Lasue, Gianfranco Magni, Angioletta Coradini, Fabrizio Capaccioni
Rosetta VIRTIS Science Team meeting, Paris, May 2010

2. THERMAL MODELING IN THE ROME GROUP
Since many years we are working on thermal modeling of icy bodies. We have used these models to study the thermal evolution and differentiation of comets and Kuiper Belt objects.
Different codes have been developed, from 1D to quasi-3D. These codes are solving heat transportation and gas diffusion equations.
In the last 2 years codes have been written solving only the heat transport equation. They are used to study the thermal properties of rocky, iceless bodies (Mercury, Vesta, asteroids).

3. THERMAL MODELING – ROCKY BODIES
A tool for deriving surface and subsurfaces temperatures of rocky bodies has been derived, with the aim of analyzing the dependence of the temperature on the surface and in the subsurface layers on a wide range of assumptions on the soil properties.
The 1D version of the code has been already used to test various hypotheses on the composition and thermal properties of the surface and upper crust of Mercury and Vesta.
A quasi-3D version has been very recently implemented.

4. THE MODEL – ROCKY BODIES
The problem is solved in spherical symmetry, one dimension. We are assuming that heat is transferred only by conduction. Heat conductivity equation is solved:
Boundary condition on the surface:

5. INPUT AND OUTPUT INPUT PARAMETERS OUTPUT Orbit Size Rotation period
Axial tilt
Albedo
Emissivity
Density
Initial temperature
Thermal conductivity expression
Specific heat expression
(for each layer):
Temperature
Thermal conductivity
Thermal inertia

6. INPUT PARAMETERS – THERMAL PROPERTIES
In order to express density, thermal conductivity and specific heat we can use both constant values and expressions, that can be complicated at will. For example, we can use empirical expressions derived from measurement of lunar samples [SCI-F/BC/TN/01]

7. THERMAL CONDUCTIVITY
Thermal conductivity of particulate materials depends on bulk density, constituent materials, size and distribution of the grains and temperature. Data available are coming from measurements of lunar soils and measurements on particulates of terrestrial minerals.
Even small disturbances to the in situ configuration of the porous lunar fines have shown relatively large effects on their bulk thermal properties.
The equation expresses the contribution of the conductive transfer across the grains (Kc) and the contribution of the radiative transfer across the empty space between grains (Kr).

8. 1D MODEL – (2867) STEINS Spherical equivalent radius: 2.65 km
Rotation period: hrs
Axial tilt: 169.5°
Albedo: 0.41
Emissivity: 0.9

9. 1D MODEL – (2867) STEINS
We are assuming that the surface is covered with regolith, taken into account both in thermal conductivity and density expressions. We are using “lunar” expressions.

10. 1D MODEL – STEINS
Using the low (green) curve

11. 1D MODEL – STEINS
Using the higher (red) curve
F 3 high

12. 1D MODEL – STEINS
Thermal inertia in the first 10 meters, aphelion

13. 1D MODEL – STEINS
No regolith layer, two different constant values for thermal conductivity (2 W/K/m and 4 W/K/m)

14. 3D MODEL – CURRENT DEVELOPMENTS
A quasi-3D version of the “rocky” model has been written.
Non-spherical shapes can be taken into account.
Influence of the shape and topography on the thermal properties can be simulated.

15. BODY SHAPE – BASIC ASSUMPTIONS
The shape of the body can be described through a two-dimensional discreet grid defined with the angles θ and ϕ corresponding to the latitude and longitude of the points considered on the comet.
A global shape thus defined can be altered by the presence of a crater-like depression.
The local illumination is calculated by taking the cosine of the angle between the local normal to the surface and the direction to the Sun.
Shadowing effects are taken into account : for each shape or altered shape, the shadow of each point on the surface of the body is calculated.
Temperature is computed locally, using as input the solar illumination and the physical properties of the material.
Lateral heat transfer is negligible with respect to the normal heat transfer.

16. 3D MODEL - VESTA

17. EARLY RESULTS - VESTA
T min = 40K
T max = 246K
Before perihelion A

18. CONCLUSION AND NEXT STEPS
Surface temperature is mainly determined by solar input. Internal temperatures (and skin depth) depend on unknown parameters.
Surface temperature is not very diagnostic of thermal properties, subsurface measurements needed.
We are looking for better expressions of thermal conductivity and specific heat. We will perform extensive testing of different values/expressions of thermal conductivity and density, to study the dependence of temperature on the soil physical properties. The aim is to obtain a grid of parameters that will help us in interpreting VIRTIS data.
The code can be improved (complicated…) almost at will. Local surface topography could be included.
Next version of the 3D code will be able to read shape models.