Understanding the structure and composition of gas giants is of basic importance to planetary astrophysics. Our local exemplars Jupiter and Saturn permit spatially resolved observations from Earth as well as sensitive in situ observations by spacecraft. This intersection of physical accessibility and conceptual importance for the planet formation process renders Jupiter and Saturn essential for establishing baseline truth for exploration of the assembly and evolution of planetary systems in general. In this thesis I develop new models for the structure and evolution of these solar system gas giants, bringing spacecraft observations to bear on our understanding of the physical processes at work in giant planet interiors.
I first describe evolutionary models for Jupiter and Saturn that incorporate results from first-principles simulations of hydrogen-helium mixtures at high pressures to address how the helium distribution is likely to evolve in these planets as they cool. Bayesian parameter estimation is used to retrieve the distribution of likely thermal histories for Jupiter and Saturn. I present models that reconcile Jupiter and Saturn’s observed heat flow, and Jupiter’s atmospheric helium depletion, at the solar age. These solutions put stringent limits on the uncertain physics of helium immiscibility, and translate to a precise prediction for the unknown atmospheric helium content of Saturn.
Second, I describe seismology of Saturn using ring waves driven by gravitational perturbations from the planet's nonradial oscillations. I present a family of Saturn interior models together with their normal mode eigenfrequencies and corresponding resonances with orbits in Saturn’s C ring, where more than twenty otherwise unexplained waves have been characterized using Cassini stellar occultation data. I identify the fundamental modes of Saturn at the origin of these ring waves, and use their observed frequencies and azimuthal wavenumbers to estimate Saturn’s rotation period to within ±2 minutes. This yields a period significantly faster than those in Saturn’s kilometric radiation, the traditional proxy for Saturn’s unknown rotation period. The global fit does not exhibit any clear systematics indicating strong differential rotation in Saturn's outer envelope.