Sebastian Höfner, H. Sierks, J.B. Vincent, J. Blum Thermal Analysis of surface and Interior A 3D Thermal model approach to Lutetia and CG Sebastian Höfner, H. Sierks, J.B. Vincent, J. Blum Osiris Full Team Meeting 07.11.2012 Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau

Outline Motivation: thermophysical processes in nucleus active regions Thermal analysis software: ESATAN TMS Description of the modeling method Lutetia thermal analysis CG simple thermal analysis (without sublimation)

Motivation Setup of a 3D thermophysical model of a universal comet nucleus model Focusing on active region modelling including surface geometry and internal/external radiative heat exchange gas production and its contribution to dust jet formation Structures and mass loss First step: Nucleus thermal analysis with commercial software ESATAN-TMS

Thermal analysis software tool (spacecraft industry) ESATAN TMS Thermal analysis software tool (spacecraft industry) http://www.itp-engines.co.uk/ Step 1: Calculating the radiative coupling between facets and the solar irradiation via Monte-Carlo Ray Tracing Step 2: Solving the heat balance equation via a lumped parameter model discretization Convection and Phase-Change modeling possible Capacity Conduction Radiation Source Term: Solar Irradiation

Surface radiative interaction 3D Modeling Method Surface cross-section Model approach with differentiated depth layers Radiative Exchange with environment Radiative and conductive layer exchange Conductive exchange Boundary coupling Increasing thermal inertia Grains Void   Lutetia CG Thermophysical properties 0-10 mm 10+ mm Albedo [ - ] 0.073 0.032 Emissivity 0.97 Surface thermal inertia [ J / Km²s^(-0.5) ] 25 325 10 Bulk density [ kg / m³ ] 1020 2040 350 Heat capacity [ J / kgK ] 1000 778 Conductivity [ W / mK ] 0.0004 0.008 Surface roughness factor 1.2 -- Layer view factor 0.2 0.15 Surface radiative interaction (e.g Massilia Crater)

Surface Thermal Wave Temperature [K]

Surface Thermal Wave Irradiation [W/m²] 30 deg steps Temperature [K]

Location: Massilia Crater Temperature wave [K] in different layer depths for a rotational period [h] Thermal gradient for seven time steps [h] Thermal surface wave lag: 0.2h Thermal wave lag for 10mm depth: 4.5h Temperature [K] Temperature [K] Thermal wave amplitude in 10mm depth: 2.5 K Rotational period [h] Layer depth [mm] Ruling thermal fluxes [W/m²] for one rotational period [h] Location: Massilia Crater Heat Fluxes [W/m²] Rotational period [h] Rotational period [h]

Ruling thermal fluxes [W/m²] for one rotational period [h] Temperature wave [K] in different layer depths for a rotational period [h] Thermal gradient for seven time steps [h] Temperature [K] Temperature [K] Rotational period [h] Layer depth [mm] Ruling thermal fluxes [W/m²] for one rotational period [h] Rim near Northern Pole Heat Fluxes [W/m²] Rotational period [h] Rotational period [h]

VIRTIS Temperature Mapping

Temperature wave [K] in different layer depths for a rotational period [h] Survey of facet 3730 in the equatorial zone 2 AU Temperature [K] Rotational period [h] Hot spot in crater rim: 321K (48 °C) 1.5 AU Temperature [K] Hot spot in crater rim: 325K (52 °C) Rotational period [h]

Thank you for your Attention Any questions? 07.11.2012 Marc Hofmann - Granular flow in low gravity space environment

Emitted Radiative Intensity Sublimation Problem Temperature Vapor Pressure Sublimation Rate Sublimation Enthalpy Emitted Radiative Intensity T Pv Z LZ(T) I [ K ] [ N / m² ] [ kg / m²s ] [ W / m² ] 150 5.1E-06 2.5E-10 6.9E-05 2.8E+01 160 6.7E-05 3.1E-09 8.7E-04 3.6E+01 170 6.4E-04 2.9E-08 8.1E-03 4.6E+01 180 4.8E-03 2.1E-07 5.9E-02 5.8E+01 190 2.9E-02 1.2E-06 3.5E-01 7.2E+01 200 1.5E-01 6.2E-06 1.7E+00 8.8E+01 210 6.4E-01 2.6E-05 7.3E+00 1.1E+02 220 2.4E+00 9.7E-05 2.7E+01 1.3E+02 230 8.2E+00 3.2E-04 8.9E+01 1.5E+02 240 2.5E+01 9.5E-04 2.7E+02 1.8E+02 250 7.0E+01 2.6E-03 7.3E+02 2.1E+02 260 6.6E-03 1.8E+03 2.5E+02 270 4.4E+02 1.6E-02 4.4E+03 2.9E+02 280 9.9E+02 3.5E-02 9.7E+03 3.4E+02 290 2.1E+03 7.3E-02 2.0E+04 3.9E+02 300 4.3E+03 1.4E-01 4.1E+04 4.5E+02 310 8.3E+03 2.8E-01 7.7E+04 5.1E+02 320 1.5E+04 5.1E-01 1.4E+05 5.8E+02 330 2.8E+04 8.9E-01 2.5E+05 6.5E+02 340 4.8E+04 1.5E+00 4.3E+05 350 8.0E+04 2.5E+00 7.1E+05 8.3E+02