Folie 1 MUPUS Team Meeting, Graz> I. Pelivan> Thermal Model > Comet Engineering Thermal Model I. Pelivan, E. Kührt

Folie 2 MUPUS Team Meeting, Graz> I. Pelivan> Thermal Model > Reference: CSTM Rosetta lander surface temperatures significantly depend on ambient temperatures -> comet surface temperatures needed as input to lander thermal mathematical model (TMM) Outdated CSTM restricted to equator shall be replaced by more suitable model predicting the surface temperature depending on time and location Intended for operational use with the Philae TMM (planning and ground-testing operational sequences, NOT landing site selection)

Folie 3 MUPUS Team Meeting, Graz> I. Pelivan> Thermal Model > CSTM overview Solve the 1D heat transport problem (ignore the lateral heat transfer) for a sphere Include the time dependent (diurnal and seasonal) solar insolation at the surface boundary. Assumes a no-heat transfer at the bottom boundary (adiabatic condition). Set the simulation domain depth to 8 times the seasonal thermal penetration (necessary for high latitudes to achieve the required accuracy of the surface temperature) One material component (no layering) was defined according to the parameters given in CSTM document Energy consumption due to sublimation of water ice can be switched on and off Sublimation is allowed only at surface. The model was run for 3 orbital periods to ensure the convergence of the surface temperature (independent on initial conditions) Approximations:  Heliocentric distance remains constant during one rotational period

Folie 4 MUPUS Team Meeting, Graz> I. Pelivan> Thermal Model > Model input parameters SymbolParameterValue (or range), unit ε IR Emissivity (hemispherical)0.9 kThermal conductivity, effective 0.001…0.1 W/m/K, temperature independent ρDensity of surface materialNominal 370 (range 100 ‐ 1000) kg/m³ AB AB Bond Albedo 0.01 (geometric albedo 0.053, phase integral ~0.2 by analogy with Tempel ‐ 1, Borrelly, Wild ‐ 2) S Solar constant (TSI) 1 AU W/m² [ASTM 2000] All other parameters (e.g., Specific heat capacity at constant pressure) Agreed upon between teams (“best estimate”)

Folie 5 Model equations MUPUS Team Meeting, Graz> I. Pelivan> Thermal Model > Heat conduction: -Upper boundary condition (conservation of energy): -Lower boundary condition: -Initial condition:

Folie 6 US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Case study For 15 latitudes (89N, 85N, 75N, 60N, 45 N, 30N, 15N, 0, 15S, 30S, 45S, 60S, 75S, 85S, 89S) Surface temperature from 3.25AU to 1.25 AU heliocentric distance in (inbound orbit) in steps of 0.25 AU Outputs were generated for each of 6 cases in steps of 5 deg in hour angle

Folie 7 US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Case study For 15 latitudes (89N, 85N, 75N, 60N, 45 N, 30N, 15N, 0, 15S, 30S, 45S, 60S, 75S, 85S, 89S) Surface temperature from 3.25AU to 1.25 AU heliocentric distance in (inbound orbit) in steps of 0.25 AU Outputs were generated for each of 6 cases in steps of 5 deg in hour angle

Folie 8 US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Model output parameters For 15 latitudes (89N, 85N, 75N, 60N, 45 N, 30N, 15N, 0, 15S, 30S, 45S, 60S, 75S, 85S, 89S) Surface temperature from 3.25AU to 1.25 AU heliocentric distance in (inbound orbit) in steps of 0.25 AU Outputs were generated for each of 6 cases in steps of 5 deg in hour angle CaseDust Thermal Conductivity (W/K m) Sublimation 10.1Off 20.01Off Off 40.1On 50.01On On

Folie 9 Some results: active vs. inactive comet Sphere Parameters used: recommended, with k = 0.1, 0.01, W/m/K US Rosetta Co-I Workshop> I. Pelivan> Thermal Model >

Folie 10 Some results: active vs. inactive comet, k = W/m/K US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > active inactive

Folie 11 Some results: comparison with data from MIRO team US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > min(our model) = max(our model)= min(MIRO) = max(MIRO) = our model: red Miro: blue.. k1 - k01 -. k001 => 5 deg shift detected and corrected in MIRO model

Folie 12 Sphere results summary US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Changing the dust thermal conductivity from 0.1 to can change the surface temperature by as much as 35K. Sublimation has a max. 35K effect on the surface temperature at 3AU but can differ by more than 150K at 1.25 AU. The sublimation effect is stronger for a smaller thermal conductivity.

Folie 13 US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Case study For 15 latitudes (89N, 85N, 75N, 60N, 45 N, 30N, 15N, 0, 15S, 30S, 45S, 60S, 75S, 85S, 89S) Surface temperature from 3.25AU to 1.25 AU heliocentric distance in (inbound orbit) in steps of 0.25 AU Outputs were generated for each of 6 cases in steps of 5 deg in hour angle

Folie 14 Shape model(s) US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Inclusion of any shape model with triangular (or quadrilateral elements) Shape model preprocessing finished (check of normal vector orientation, processing of element data) Validation of revised source code for shape model inclusion and other apects with data for sphere Wrong normal vector orientation vs. corrected, validation example

Folie 15 Shape model(s) – cont‘d + some open points US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > New subroutines  calculation of solar incidence angle for shape elements (boundary condition)  Determination of Sun vector and element normal vector  Frame for NAIF SPICE ephemerides as option to kepler (actual implementation pending, see next slide) Open:  Model-specific transformation routines  For arbitrary location on comet surface: implement point-in-triangle routine  NAIF SPICE interface for other products?  Test implementations!

Folie 16 Some design decisions US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > C instead of Fortran:  Compiler difficulties (solved) btw. NAG Fortran and Fortran SPICE Toolkit, still existing: run time problems (segmentation inaccessible NAG routine (TO BE REPLACED?)  CSPICE vs. Fortran Toolkit: also implemented with IDL and Matlab

Folie 17 Profile analysis – more to do US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Profiles: ____ k = constant k=c_k*T^3 Temperature dependance of k leads to overall temperature increase Surface temperature practically not depend on k

Folie 18 Thermal engineering model summary and outlook US Rosetta Co-I Workshop> I. Pelivan> Thermal Model > Original Fortran code re-implemented in C – update for shape model to follow Final ephemerides implementation (only tested with separate program so far) Physics updates where required (TBD) Test new implementations and changes