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Nucleus, Neutral and Ionized Coma of Comets 67P/Churyumov-Gerasimenko and 46P/Wirtanen Preparations for the ROSETTA Radio Science Investigations

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Nucleus, Neutral and Ionized Coma of Comets 67P/Churyumov-Gerasimenko and 46P/Wirtanen Preparations for the ROSETTA Radio Science Investigations Global modeling of comets: Nucleus, neutral and ionized coma of comets 67P/Churyumov-Gerasimenko and 46P/Wirtanen Preparations for the ROSETTA Radio Science Investigations I NAUGURAL –D ISSERTATION ZUR ERLANGUNG DES DOKTORGRADES DER MATHEMATISCH–NATURWISSENSCHAFTLICHEN FAKULTAT¨ DER UNIVERSITAT¨ ZU KOLN¨ VORGELEGT VON JORG¨ VON OERTZEN AUS BOBLINGEN¨ KOLN¨ 2003 Berichterstatter: Prof. Dr. F. M. Neubauer Hochsch.-Doz. Dr. M. Patzold¨ Tag der mundlichen¨ Prufung:¨ 4.Dezember2003 Contents 1 Introduction 1 1.1 Kurzzusammenfassung . 1 1.2 Abstract..................................... 3 1.3 Motivation.................................... 4 1.4 Cometarymissions ............................... 5 2 The ROSETTA mission 7 2.1 TheROSETTA Spacecraft............................ 7 2.2 RadioScienceInvestigations . .... 8 2.2.1 ScientificObjectives . .. .. .. .. .. .. .. 8 2.2.2 RadioSubsystem............................ 8 2.3 OtherExperiments ............................... 9 3 Possible Target Comets 11 3.1 46P/Wirtanen .................................. 11 3.2 67P/Churyumov-Gerasimenko . .. 11 3.3 OrbitalElements ................................ 12 3.4 TimelineandGeometricConsiderations . ...... 12 4 Thermal model of a cometary nucleus 15 II CONTENTS 4.1 Introduction................................... 15 4.2 TheCometaryNucleus ............................. 16 4.2.1 ObservationsofCometaryNuclei . 16 4.2.2 Structure ................................ 16 4.2.3 Composition .............................. 17 4.2.4 Albedo ................................. 19 4.2.5 ThermalSkinDepth .......................... 19 4.2.6 HeatandGasDiffusionModels . 21 4.3 ThermalModelofaCometaryNucleus . .. 22 4.3.1 EnergyandMassConservationinaPorousMedium . ... 23 4.3.2 SublimationRate ............................ 24 4.3.3 ThermalConductivityandGasFlux . 26 4.3.4 BoundaryConditions. 28 4.3.5 NumericalScheme ........................... 30 4.4 PhysicalParameters. .. .. .. .. .. .. .. .. 30 4.5 CalibrationandResults . .. 32 5 The Neutral Coma 43 5.1 Introduction................................... 43 5.1.1 CompositionoftheComa . 45 5.1.2 Modelsofthecometarycoma . 46 5.2 HydrodynamicSimulationoftheNeutralComa . ...... 47 5.2.1 HydrodynamicApproximation . 47 5.2.2 TheZEUS Code............................. 48 5.2.3 BoundaryConditions. 49 5.2.4 Non-Gravitational Forces acting on ROSETTA ............. 50 5.3 Results...................................... 52 5.3.1 Case1: H2O Sublimationat3AU,67P/C-G. 52 5.3.2 Case 2: StrongSublimationat2AU,46P/Wirtanen . ..... 58 5.3.3 ConsequencesforRSI . 62 5.3.4 Discussion ............................... 63 CONTENTS III 6 Ionized Coma and Interaction with the Solar Wind 65 6.1 Introduction................................... 65 6.2 SolarWindParameters ............................. 67 6.3 SolarActivity&Predictions . ... 69 6.4 CometaryPlasma ................................ 72 6.4.1 SolarUVSpectrum........................... 72 6.4.2 OpticalDepthoftheComaintheUVRange . 74 6.4.3 PhotoionizationandPhotodissociation . ...... 76 6.4.4 ImpactIonizationandChargeExchange . ... 77 6.4.5 TotalIonizationFrequency . 79 6.4.6 Ion-MoleculeReactions . 79 6.4.7 Recombination ............................. 79 6.4.8 ElectronTemperature. 80 6.4.9 ThermalElectronCollisionopause . ... 82 6.5 StationaryPlasmaModel1D . 84 6.5.1 Case 1: with Assumption of Photochemical Equilibrium ....... 84 6.5.2 Case 2: Numerical Solution of the 1D Continuity Equation...... 87 6.5.3 Conclusions............................... 88 6.6 InteractionwiththeSolarWind. .... 89 6.6.1 CometaryPick-upIonsintheSolarWind . .. 90 6.6.2 BowShock/BowWave ........................ 91 6.6.3 Collisionopauseand MagneticPile-Up Boundary . ...... 92 6.6.4 CavitySurface/Ionopause. 94 6.6.5 Results for 67P/Churyumov-Gerasimenko and 46P/Wirtanen .... 96 6.7 TransientSolarEvents . .. .. .. .. .. .. .. .. 98 6.7.1 SolarFlares............................... 98 6.7.2 CoronalMassEjections . 99 6.7.3 PossibleEffectsonRadioScience . .. 99 7 Discussion and Outlook 103 8 Zusammenfassung 107 IV CONTENTS A Physical Constants 113 B Finite Difference Scheme for the Heat Diffusion Equation 114 C The Thermal Model applied to 1P/Halley 115 D Additional results of the coma model 117 D.1 67P/Churyumov-Gerasimenkoat1.3AU. 117 D.2 46P/Wirtanenat1.1AU. .. .. .. .. .. .. .. .. 121 E Observational Geometry for 67P/Churyumov-Gerasimenko 125 Danksagung 143 Erklarung¨ 145 List of Figures 3.1 Distances for the 67P/Churyumov-Gerasimenko mission scenario . 13 3.2 Timelinefor46P/Wirtanen . .. 14 4.1 Variousmodelsofcometarynuclei . .... 17 4.2 Effectiveradiusofcomet46P/Wirtanen . ...... 19 4.3 Pressure ratiop ˜s ps ............................... 26 4.4 Typicalthermalconductivities . ..... 28 4.5 Energybalanceatthesurface . ... 29 4.6 Observationsandmodelresultsfor46P/Wirtanen . ......... 33 4.7 Observations and model results for 67P/Churyumov-Gerasimenko . 35 4.8 Surfacetemperatures,modelM3 . ... 37 4.9 Surfacetemperatures,modelW2 . ... 38 4.10 Surfacetemperatureswithobliquity . ....... 39 4.11 Mapoflocalgasproductionrates,modelM3 . ...... 41 5.1 Accelerationduetosolarradiationpressure . ......... 51 5.2 Number density in the equatorial plane at 3 AU, 67P/C-G . ......... 53 5.3 Extent of the collisional coma in the equatorial plane 3 AU,67P/C-G. 54 5.4 Gaspressureintheequatorialplaneat3AU,67P/C-G . ........ 55 5.5 RadialprofileofHDparametersat3AU,67P/C-G . ..... 56 5.6 Profile of HD parameters in equatorial plane at 3 AU, 67P/C-G........ 57 VI LIST OF FIGURES 5.7 Number density and velocity in the equatorial plane at 2 AU,46P/Wirtanen . 59 5.8 Radial profile of HD parameters at 2 AU, 46P/Wirtanen . ....... 60 5.9 Profile of HD parameters in equatorial plane at 2 AU, 46P/Wirtanen . 61 6.1 Interactionpatternwiththesolarwind . ....... 66 6.2 Variationofsolarwindparameters . ..... 68 6.3 Monthlyaveragedsunspotnumbers . ... 70 6.4 Flareactivity,solar10.7cmfluxandpredictions . .......... 71 6.5 ThesolarUVfluxat1AU ........................... 73 6.6 Cross sections for H2O moleculesintheUVrange . 74 6.7 Opticaldepthatthesubsolarpoint . ..... 75 6.8 Electrontemperatureprofilesat1P/Halley . ........ 81 6.9 Exemplaryelectrontemperatureprofile . ...... 82 6.10 CometocentricdistanceoftheTEC. ..... 83 6.11 Characteristictimescalesforions . ....... 85 6.12 Photochemicalcontrolledcomaat 46P/Wirtanen . ......... 86 6.13 Ionnumberdensitiesatvariousdistances. ......... 88 6.14 Standoffdistancesoftheinteractionregions . ........... 96 6.15 Variationofstandoffdistances . ......100 C.1 Thermalmodelappliedto1P/Halley . 116 D.1 Number density and velocity in the equatorial plane at 1 3AU,67P/C-G . 118 D.2 Radial profile of HD parameters at 1 3AU,67P/C-G . 119 D.3 Profile of HD parameters in equatorial plane at 1 3AU,67P/C-G . 120 D.4 Number density and velocity in the equatorial plane at 1 1 AU, 46P/Wirtanen 121 D.5 Radial profile of HD parameters at 1 1AU,46P/Wirtanen . 122 D.6 Profile of HD parameters in equatorial plane at 1 1AU,46P/Wirtanen . 123 E.1 Observational geometry for 67P/Churyumov-Gerasimenko ..........126 CHAPTER 1 INTRODUCTION 1.1 Kurzzusammenfassung Das thermische Verhalten eines Kometenkernes, die Entstehung und Entwicklung der Neu- tralgasumgebung (der sogenannten kometaren Koma), der Plasmaumgebung des Kometen, sowie seine Interaktion mit dem Sonnenwind werden in dieser Arbeit studiert. Das Ziel ist es, ein umfassendes Modell eines Kometen und seiner Umgebung zu entwickeln. Mit diesem Modell lassen sich dann physikalische Parameter in der Kometenumgebung und deren Ent- wicklung in Abh¨angigkeit vom heliozentrischen Abstand der Kometen 46P/Wirtanen und 67P/Churyumov-Gerasimenko bestimmen. Insbesondere soll untersucht werden, welche Ef- fekte die Kometenumgebung auf das Radiosondierungs-Experiment (RSI = Radio Science Investigations) auf der Raumsonde ROSETTA haben wird. Die Mission ROSETTA soll im Februar 2004 gestartet werden und etwa 10 Jahre sp¨ater den Kometen 67P/Churyumov- Gerasimenko bei einem Abstand von ca. 4 Astronomischen Einheiten (AE) erreichen, und ihn dann auf seiner Bahn begleiten. Urspr¨unglich war Komet 46P/Wirtanen als Zielkomet f¨ur die Mission vorgesehen. Nachdem der Start von ROSETTA im Januar 2003 aufgrund von Problemen mit der vorgesehenen Startrakete verschoben werden musste, war der Zeit- plan der Mission nicht einzuhalten und es wurde ein neuer Zielkomet ausgew¨ahlt. Komet 46P/Wirtanen dient nun noch als m¨ogliches Ersatzziel, falls in der n¨achsten Startphase wieder Probleme auftauchen sollten. Die hier entwickelten Modelle beziehen sich im allgemeinen auf beide Kometen, da diese sich in vielen Dingen ¨ahnlich sind, wie zum Beispiel Orbitpa- rameter, Gr¨oßenordnung des Kometenkerns und Zusammensetzung. Im Einzelnen werden die Unterschiede in der Diskussion der Ergebnisse ausgearbeitet. Die W¨armediffusion im Kometenkern wird hier mit einem eindimensionalen Modell be- schrieben. Um eine Aussage ¨uber die Temperaturverteilung und das Sublimationsverhalten f¨ur die gesamte Oberfl¨ache des Kometen machen zu k¨onnen, wird ein Gitter von eindimen- 2 INTRODUCTION sionalen Modellen ¨uber den Kometenkern verteilt. Die physikalischen Bedingungen an der Oberfl¨ache werden durch ein Energiegleichgewicht beschrieben und gehen als Randbedin- gung in die Modellrechnungen ein. Viele der in den Modellen zu ber¨ucksichtigenden Para- meter sind derzeit nur ungenau bekannt. Diese nicht zu vermeidende Ungenauigkeit spiegelt sich in der Variationsbreite der Ergebnisse wieder. Die W¨armediffusion im Kometenkern wird mit einer Energie-Erhaltungsgleichung
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