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Das Magnetfeld Des Merkur: Über Den Einfluss Der Magnetosphäre Auf

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Das Magnetfeld Des Merkur: Über Den Einfluss Der Magnetosphäre Auf Das Magnetfeld des Merkur: Über den Einfluss der Magnetosphäre auf den Dynamo im Planeteninneren Von der Fakultät für Elektrotechnik, Informationstechnik, Physik der Technischen Universität Carolo-Wilhelmina zu Braunschweig zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr.rer.nat.) genehmigte Dissertation von Daniel Heyner aus Wolfsburg 1. Referentin oder Referent: Prof. Dr. Karl-Heinz Glaßmeier 2. Referentin oder Referent: Priv.-Doz. Dr. Dieter Schmitt eingereicht am: 23.07.2013 mündliche Prüfung (Disputation) am: 16.10.2013 (2013) Veröffentlichungen Teilergebnisse aus dieser Arbeit wurden mit Genehmigung der Fakultät für Elektrotech- nik, Informationstechnik, Physik, vertreten durch den Mentor der Arbeit, in folgenden Beiträgen vorab veröffentlicht: Publikationen Heyner, D., Schmitt, D., Wicht, J., Glassmeier, K.-H., Korth, H., Motschmann, U., 2010, The initial temporal evolution of a feedback dynamo for Mercury, Geophysical & Astro- physical Fluid Dynamics, 104, 419–429 Heyner, D., Schmitt, D., Glassmeier, K.-H., Wicht, J., 2011a, Dynamo action in an am- bient field, Astronomische Nachrichten, 332, 36–42 Heyner, D., Wicht, J., Gomez-Perez, N., Schmitt, D., Auster, H. U., Glassmeier, K. H., 2011b, Evidence from Numerical Experiments for a Feedback Dynamo Generating Mer- cury’s Magnetic Field, Science, 334, 1690–1693 Heyner, D., Glassmeier, K.-H., Schmitt, D., 2012, Stellar Wind Influence on Planetary Dynamos, The Astrophysical Journal, 750, 133 Tagungsbeiträge Heyner, D., Concerning the Temporal Evolution of Mercury’s Feedback Dynamo, (Pos- ter), COSPAR-Tagung, Montreal, Kanada, 2008 Heyner, D., Gomez-Perez, N., A Hermean Feedback Dynamo, (Vortrag),3rd MESSENGER- Flyby, Laurel, USA, 2009 Heyner, D., Glassmeier, K.-H., Schmitt, D., Feedbackdynamo des Merkur, (Vortrag), DPG Frühjahrstagung, Greifswald, 2009 Heyner, D., A Hermean Feedback Dynamo, (Vortrag), EGU, Wien, 2009 3 Veröffentlichungen Heyner, D., J. Mueller, N. Gomez-Perez, J. Wicht, D. Schmitt, K.-H. Glassmeier, Magne- tospheric Feedback on the Dynamo of Mercury, (Poster), AGU-Jahrestagung, San Fran- cisco, USA, 2009 Heyner, D. Recent Topics About the Hermean Magnetosphere, (Vortrag),HEWG-Meeting, Mykonos, Griechenland, 2009 Heyner, D., Gomez-Perez, N., Initial Conditions, Chaotic Branching and Feedback-Stabilization in Numerical Dynamos, (Poster), SEDI-Tagung, Santa Barbara, USA, 2010 Heyner, D., Gomez-Perez, N., Initial Conditions, Chaotic Branching and Feedback-Stabilization in Numerical Dynamos, (Poster), Geodynamik Workshop, Münster, 2010 Heyner, D., Feedbackdynamo des Merkur, (Poster), DGG Jahrestagung, Köln, 2011 Heyner, D., J. Wicht, N. Gomez-Perez, D. Schmitt, H.-U. Auster und K.-H. Glassmeier, The Feedback Dynamo of Mercury, (Vortrag), EPSC, Nantes, Frankreich, 2011 Heyner, D., J. Wicht, N. Gomez-Perez, D. Schmitt, H.-U. Auster, K.-H. Glassmeier, The Feedback Dynamo of Mercury, (eingeladener Vortrag), EGU, Wien, 2012 Heyner, D., J. Wicht, N. Gomez-Perez, D. Schmitt, U. Auster, K.-H. Glassmeier, The Feedback Dynamo of Mercury, (eingeladener Vortrag), AGU-Jahrestagung, San Francis- co, USA, 2012 Heyner, D., Magnetic Field Generation at Mercury, (eingeladener Vortrag),MESSENGER- BepiColombo Workshop, Chicago, USA, 2013 Heyner, D., Wird der Dynamoprozess im Planeten Merkur durch den Sonnenwind ge- schwächt?, (Vortrag), DGG-Jahrestagung, Leipzig, 2013 4 Inhaltsverzeichnis Veröffentlichungen 3 Zusammenfassung 9 1 Einleitung 11 2 Beschreibung von Magnetfeldern und ext. Magnetfeldquellen beim Merkur 15 2.1 Interne und externe Magnetfelder . 15 2.2 Externe Magnetfeldtopologien . 17 2.3 Trennungsmethoden in interne und externe Anteile . 19 2.4 Magnetosphärische Stromsysteme beim Merkur . 22 2.4.1 Das Chapman-Ferraro Problem . 24 2.4.2 Der Neutralschichtstrom . 25 2.4.3 Der Ringstrom . 25 2.5 Trennungsproblem bei Merkur . 26 2.6 Diffusion und Filterung des externen Feldes . 26 3 Modellierungsansätze des externen Feldes 29 3.1 Konzeption der magnetosphärischen Antwortfunktion . 29 3.2 Planare Magnetopause . 30 3.3 Ringförmiger Magnetopausenstrom . 33 3.4 Kugelmagnetosphäre . 36 3.5 Anpassung eines semi-empirischen, terrestrischen Modells . 40 3.6 Parabolisches Modell . 46 3.6.1 Das Chapman-Ferraro-Feld im parabolischen Modell . 47 3.6.2 Druckbilanz am subsolaren Punkt . 51 3.6.3 Antwortfunktion basierend auf dem parabolischen Magnetopau- senmodell . 52 4 Hybridsimulation der Magnetosphäre 57 4.1 Motivation . 57 4.2 Modellbeschreibung und Simulationskonfiguration . 58 4.3 Ergebnisse einer Parameterstudie mit verschiedenen Dipolmomenten . 61 4.4 Lage und Ausprägung des Neutralschichtstroms . 65 4.5 Vergleich der Modell- und Simulationsergebnisse . 67 4.6 Ausblick auf zukünftige Hybridsimulationsstudien . 67 5 Inhaltsverzeichnis 5 Kernentwicklung und Dynamotheorie 69 5.1 Die Induktionsgleichung als Grundlage der Dynamotheorie . 69 5.2 Der Scheibendynamo . 72 5.3 Planetare Dynamos . 75 5.4 Evolution des Merkurkerns . 76 5.5 Bifurkation und Dynamogleichgewichte . 76 5.6 Mean-Field Dynamotheorie . 82 5.7 Dynamo-Skalierungsgesetze . 84 6 Vereinfachende Modelle zum Feedbackdynamo 89 6.1 Dynamos im externen Feld . 89 6.2 Bisheriges Modell des Feedbackdynamos . 93 6.3 Kinematisches Modell zum Feedbackdynamo . 94 6.3.1 Mathematische Formulierung . 94 6.3.2 Numerische Behandlung des kinematischen Dynamomodells . 98 6.3.3 Modellierungsergebnisse . 99 6.4 Analytische Analyse eines kinematischen Dynamos mit einem externen Feld..................................... 103 6.4.1 Das vereinfachte Grundmodell des kinematischen Feedbackdyna- mos................................. 104 6.4.2 Vereinfachter kinematischer Dynamo mit konstantem externen Feld106 6.4.3 Vereinfachter kinematischer Dynamo mit variablem externen Feld 107 6.4.3.1 Analytische Antwortfunktion I . 107 6.4.3.2 Analytische Antwortfunktion II . 108 6.5 Einfluss der Lorentzkraft: Einschätzung mit einem Scheibendynamo-Modell111 7 Dynamische Simulation des Feedbackdynamos mit einem dreidimensionalen Modell 115 7.1 Grundgleichungen . 115 7.2 Randbedingungen an der Kern-Mantel-Grenze . 122 7.2.1 Thermische Randbedingungen . 122 7.2.2 Mechanische Randbedingungen . 122 7.2.3 Übergangsbedingung des Magnetfeldes . 123 7.2.4 Approximativer Größenvergleich der Internen und Externen Felder 126 7.3 Der Feedback bei schwach überkritischen Dynamos . 128 7.4 Einfluss der Größe des inneren Kerns auf den Feedbackmechanismus . 140 8 Erweiterung des Feedbackdynamo-Modells 147 8.1 Sternentwicklungsmodell für die Sonne . 147 8.2 Feedbackdynamos in der Frühzeit des Merkur . 149 8.3 Falsifizierungsmöglichkeiten bei Exoplaneten . 151 8.4 Auswirkungen des schwachen Magnetfeldes auf die Habitabilität eines Planeten . 157 6 Inhaltsverzeichnis 9 Magnetfeldmessdaten der Messenger-Mission 161 9.1 Der Offsetdipol des Merkur . 161 9.2 Vergleich der Modelle zum Merkurdynamo mit den Messergebnissen . 165 10 Diskussion und Ausblick 173 Literaturverzeichnis 175 Danksagung 185 Curriculum Vitae 187 7 Zusammenfassung Der Planet Merkur besitzt ein sehr schwaches Dipolfeld. Als Erklärung für das planetare Magnetfeld wird ein Dynamoprozess im Inneren angenommen. Nach gängigen Skalie- rungsgesetzten der Dynamotheorie, sollte aber das Dipolfeld an der Oberfläche um ein bis zwei Größenordnungen stärker sein. Um diesen scheinbaren Widerspruch aufzuklären, wurden verschiedene Dynamomodelle vorgeschlagen, die eine spezielle innere Struktur voraussetzen. Die den Planeten umgebende Magnetosphäre kann ebenfalls einen dämp- fenden Effekt auf den Dynamoprozess ausüben. Dies stellt eine Alternative oder auch eine Erweiterung zu den anderen vorgeschlagenen Dynamomodellen dar. In dieser Arbeit wird das Feedbackdynamomodell für den Merkur vorgestellt und dis- kutiert. Der Effekt des magnetosphärischen Feedbacks bedarf keiner speziellen inneren Struktur, aber eines starken Sonnenwindes wie beim Merkur. Die Wechselwirkung des Sonnenwindes mit einem merkurähnlichen Dipolfeld, wird anhand einer Reihe verein- fachter Magnetosphärenmodelle untersucht. Dazu wird das interne Dipolmoment vari- iert und das sich jeweils ergebende externe Feld bestimmt. Dieses Feld besteht zu einem Großteil aus dem Feld der Magnetopause. Auf Grund der Energieerhaltung ist das Ma- gnetopausenfeld in seiner Amplitude unabhängig vom internen Feld und wird nur vom Sonnenwinddruck bestimmt. Dieser Effekt bestätigt sich in einer realistischeren Sonnen- windsimulation. Die Wechselwirkung des planetaren Dipolfeldes wird als magnetosphäri- sche Antwortfunktion abstrahiert, um es in Dynamomodellen einfügen zu können. Dieses parameterisierte Magnetopausenfeld wird auf ein vereinfachtes kinematisches Dynamo- modell angewendet und das sich ergebende System einer Stabilitätsanalyse unterzogen. Es zeigt sich, dass es einen Lösungsbereich gibt, bei dem der Dynamo durch den Feedback frühzeitig stabilisiert wird. Der Dynamo darf allerdings nicht zu stark angetrieben und das Saatfeld darf nicht zu stark sein, damit des externe Feld einen ausreichend dämpfenden Effekt haben kann. Die analytische Analyse ergibt, dass stabile, schwache Dynamos beim Anstieg der Antwortfunktion, also mit zunehmenden externen Feld existieren. Die Brei- te des Lösungsbereichs mit schwachen Dynamos wird von der Höhe des Maximums des Verhältnisses vom externen zum internen Magnetfeld bestimmt. Der dynamische Druck des Sonnenwindes legt die Höhe dieses Maximums fest. In der Frühzeit des Sonnensys- tems herrschte ein um Größenordnungen stärkerer Druck, was den Effekt des externen Feldes auf den Merkurdynamo verstärkt, wie in einer vereinfachten kinematischen
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