Understanding the interior structure and dynamics of a planet is a key step towards understanding the formation and evolution of a planet. In this thesis, I combine field observation and dynamo modeling to understand planetary interiors. Focus has been put on planets Saturn and Mercury. The Cassini spacecraft has been taking continuous measurements in the Saturnian system since the Saturn orbital insertion in June 2004. Since the Mercury orbital insertion in March 2011, the MESSENGER spacecraft has been examining planet Mercury.;After analyzing the close-in portion of the in-situ Cassini magnetometer measurements around Saturn, I find that Saturn's magnetic field features several surprising characteristics. First, Saturn's magnetic field is extremely axisymmetric. We cannot find any consistent departure from axisymmetry, and have put an extremely tight upper bound on the dipole tilt of Saturn: the dipole tilt of Saturn has to be smaller than 0.06 degrees. Second, we find that Saturn's magnetic field is extremely stable with time. Third, we estimated the magnetic moments of Saturn up to degree 5. This is the first magnetic field model for Saturn which goes beyond degree 3. We find that not only Saturn's intrinsic magnetic field is dominated by the axial moments; among these axial moments the odd degree ones dominate. In addition, the first three odd degree axial moments all take the same sign. This sign pattern of Saturn's magnetic moments is in contrast to that of the Earth's magnetic moments which takes alternative signs for the past century.;The contrast between the geometries of Saturn's magnetic field and the Earth's magnetic field lead us to propose a dynamo hypothesis which speculates that such differences are caused by structural and dynamical differences inside these two planets. Our dynamo hypothesis for Saturn has two essential ingredients. The first concerns about the existence and size of a central core inside Saturn and its influence on Saturn's dynamo action. The second concerns about the possible heterogeneous heat transfer efficiency in the outer envelope of Saturn and its influence on Saturn's dynamo action. We then carried out numerical convective dynamo simulations using the community dynamo code MagIC version 3.44 to test our dynamo hypothesis. In our numerical dynamo experiments, the central core sizes and the outer boundary heat flow heterogeneities are both varied. We find that the central core size is an important factor that can strongly influence the geometry of the dynamo generated magnetic field. Such influence is rendered through the tangent cylinder, which is an imaginary cylinder with its axis parallel to the spin axis of the planet and is tangent to the central core at the equator. We find that both the convective motion and the magnetic field generation efficiency, represented by kinetic helicity, are weaker inside the tangent cylinder than those outside the tangent cylinder. As a result, the magnetic fields inside the tangent cylinder are consistently weaker than those outside the tangent cylinder. Thus the lack of a polar field minimum region at Saturn could be indicative of the absence or a small central core inside Saturn.;MESSENGER observations revealed that Mercury's magnetic field is more unusual than previously thought. In particular, Mercury's magnetic field is strongly north-south asymmetric: the magnetic field strength in the northern hemisphere is three times as strong as that in the southern hemisphere. Yet, there is no evidence for any such north-south asymmetry in the basic properties of Mercury that could possibly influence the present-day dynamo action. Here we propose a mechanism to break the equatorial symmetry of Mercury's magnetic field within the framework of convective dynamos. The essence of our mechanism is the mutual excitation of two fundamental modes of columnar convection in rapidly rotating spherical shells. Such mutual excitation results in equatorially asymmetric kinetic helicity, which then leads to equatorially asymmetric magnetic field. With numerical dynamo experiments, we find two necessary conditions to reproduce the equatorial symmetry breaking of Mercury's magnetic field with equatorially symmetric core-mantle boundary (CMB) heat flows. The first is that buoyancy sources need to be distributed within an extended volume of the outer core rather than being concentrated near the inner boundary. The second is an equatorially peaked CMB heat flow. From this study, we conclude that 1) Mercury's core dynamo is likely powered by distributed buoyancy sources and thus is different from the present-day geodynamo which is predominantly powered by bottom-up inner core growth; 2) Mercury's mantle structure and dynamics could be favoring higher heat flow from the equatorial region of Mercury's core. (Abstract shortened by UMI.).
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