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.

Exoplanet atmospheres tell the story of diverse worlds: what they are made of and how they came to be. We use theoretical models to make sense of the narrative encoded in each atmospheric data set. In particular, we extract information with retrievals, which couple statistical tools with high signal-to-noise spectral data to derive and estimate atmospheric properties. The inferred atmospheric structure and molecular abundances then influence our understanding of the Solar System in the context of exoplanets.

Retrievals have become an essential tool in both understanding existing data and quantitatively informing the needs of future missions. Consequently, this thesis focuses on the interplay between data and models, the core components of a retrieval.

First, I demonstrate the need to evaluate model assumptions in order to extract meaningful constraints from spectra. While varying in sophistication, most model-spectra comparisons fundamentally assume ``1D'' model physics. However, we know that planetary atmospheres are inherently ``3D'' in their structure and composition. Within a Bayesian retrieval framework, I show how the assumption of a single 1D thermal profile can bias our interpretation of the thermal emission spectrum of an unresolved hot Jupiter's atmosphere that is composed of two thermal profiles. I extend the application to full spectroscopic phase curves. For modern data, I reveal that the constraint for water vapor abundance is robust independent of model setup; however, methane is artificially well-constrained to incorrect values. Furthermore, I find that the 1D setup is insufficient at fitting data that the James Webb Space Telescope may measure, causing many abundance biases.

Next, I develop an inverse modeling framework to estimate the science return of proposed missions that aim to perform reflected light spectroscopy of rocky exoplanets around Sun-like stars. By combining an albedo model, an instrument noise model, and a Bayesian inference tool, I explore retrievals of atmospheric and bulk properties as a function of data signal-to-noise ratio (SNR) and resolution (R). I present the recommended R and SNR combinations to achieve detection or constraint of key indicators of habitability on rocky planets such as water vapor, oxygen, and ozone.

The spectral resolution of instruments used to characterize substellar atmospheres has greatly increased over the past decade. As we more frequently observe exoplanet and brown dwarf atmospheres at higher spectral resolution, more work is needed to assess both what new information is contained in these improved observations as well as how our current modeling tools fall short in accurately reproducing these spectra. My dissertation has examined this question from multiple angles to ultimately prepare the field to better understand substellar atmospheres through the better quality spectra we will receive from the JWST and the upcoming ELTs. First, I present how high-resolution cross-correlation spectroscopy (R $\sim$ 25,000 to 100,000) will allow us to probe the regions in the atmospheres of sub-Neptune exoplanets above the clouds or hazes which obscure molecular features in observations at low spectral resolution. Using theoretical models of high-resolution observations for a typical hazy sub-Neptune, we calculate the signal-to-noise of these spectra required to robustly detect a host of molecules as a function of spectral resolution and wavelength coverage to aid in planning future observations and instruments.

Next, I present two projects focused on adapting atmospheric retrieval methods for medium-resolution spectra of brown dwarfs. I first describe applying a GPU-version of the CHIMERA retrieval framework to a high signal-to-noise, medium-resolution (R$\sim$6000) FIRE spectrum of a T9 dwarf from 0.85-2.5 $\mu$m. At 60$\times$ higher spectral resolution than previous brown dwarf retrievals, a number of novel challenges arise, which I explore. I show that compared to retrieval results from a R$\sim$100 spectrum of the same object, constraints on atmospheric abundances improve by an order of magnitude or more with increased spectral resolution.

Finally, I apply lessons learned from this project to JWST NIRSpec/G395H (R$\sim$2700, 2.87 - 5.14 $\mu$m) observations of a T8 dwarf, presenting the first retrieval analysis taking full advantage of the maximum spectral resolution available with NIRSpec. I obtain precise ($\sim$ 0.02 dex) abundance constraints for a number of species, which indicate shortcomings in our understanding of disequilibrium chemistry in brown dwarf atmospheres. I also present the measured $^{12}$CO/$^{13}$CO ratio for this brown dwarf, making it the fourth and coldest ($\sim$ 760 K) extrasolar object with such a measurement. Together, these projects illustrate the power of high-quality, medium-to-high resolution spectra to precisely constrain atmospheric properties, furthering our understanding of the formation and atmospheres of substellar objects.

This thesis is focused on utilizing the combination of giant exoplanet mass via radial velocity observations and radius via transit observations to study their structure and evolution. In Chapter 2, Giant planet thermal evolution models are coupled to tidal evolution dynamics, including orbital evolution and planet interior heating. Viable tidal evolution histories are explored to explain inflated radii of hot Jupiters. Tidal evolution is demonstrated to be a viable heating mechanism in some cases, but for other cases it can not explain the large radii. The thesis continues in Chapter 3 by exhibiting cases when the tidal-thermal evolution model, including energy-limited mass loss, can be used to infer interior properties and demonstrate a possible evolution history. Specifically, I utilize the thermal evolution models to examine planets CoRoT-2b, CoRoT-7b, and the Kepler-11 system. In Chapter 4, planets with lower incident irradiation are examined to infer the heavy element composition inside a range of planets. These planets don't appear to be significantly inflated by the unknown radius inflation mechanism, thus the mysterious mechanism can be ignored. It is shown that the heavy element mass inside these planets correlates with the metallicity of the star. The heavy element mass also correlates with the mass of the planet. However, the heavy element enrichment is inversely related to the mass of the planet. In the final chapter, I develop a mixing equation of state code for the MESA stellar evolution project. This code is developed with the intention of studying inhomogeneous thermal evolution of planets.

Exoplanet science is now focusing on characterizing the physics and chemistry of exoplanet atmospheres, including those of terrestrial-class, potentially habitable planets. In this thesis, I use a combination of laboratory experiments and theoretical modeling to understand two themes related to these atmospheres: (1) their primordial outgassing compositions from an experimental cosmochemistry approach, and (2) the planetary context for observable biosignature gases using modeling tools.

There is no first-principles understanding of how to connect a planet’s bulk composition to its initial atmospheric properties. Since terrestrial exoplanets likely form their atmospheres through outgassing, an important step towards establishing this connection is to assay meteorites, remnants of planetary building blocks, by heating and measuring their outgassed volatiles. In the first theme, I use multiple experimental techniques to determine meteorites’ outgassing compositions over a range of temperatures and pressures. I describe the results of heating carbonaceous chondrite samples and measuring their abundances of released volatiles as a function of temperature in a high-vacuum environment. I find that these meteorites outgas significant amounts of H2O, CO, CO2 and smaller quantities of H2 and H2S. I also discuss a complementary bulk element analysis to monitor outgassing of heavier elements (e.g., sulfur, iron, zinc). I compare these experimental results to thermochemical equilibrium models of chondrite outgassing and determine how these experiments can improve atmospheric models and inform the connection between bulk composition and early atmospheres.

For the second theme, I perform a comprehensive analysis of the necessary planetary conditions for atmospheric methane to be a compelling biosignature gas. Methane is one of the only biosignatures that JWST can readily detect in terrestrial atmospheres. Therefore, it is essential to understand methane biosignatures to contextualize these imminent observations. Using a combination of multiphase thermodynamic and atmospheric chemistry models, I investigate abiotic sources of methane and determine the planetary conditions for which these sources could be enhanced on terrestrial planets so as to result in false positives. I determine that known abiotic processes cannot easily generate atmospheres rich in CH4 and CO2 with limited CO due to the strong redox disequilibrium between CH4 and CO2, providing the first tentative framework for assessing methane biosignatures.

Extrasolar planet surveys have identified an abundant new population of highly irradiated planets with sizes that are in between that of the Earth and Neptune. Such planets are unlike anything found in our own Solar System, and many of their basic properties are not understood. As such, these planets provide a fundamental test for models of planets formation and evolution with important implications for the formation of the Earth and planet habitability.

In order to understand these new classes of planets, we have developed planetary structure and evolution models that can be used both to answer questions about individual planetary systems and to study populations of planets as a whole. In brief, these models allow us

to follow a planet's mass, size, internal structure, and composition as it ages; from the time it finishes formation until it is detected billions of years later.

These evolution models are critical because a planet's composition can change substantially over its lifetime. Close-in planets, like most of those found so far, are bombarded by large amounts of ionizing radiation, which over time can completely strip away a planet's atmosphere; even turning a gas-rich Neptune sized planet into a barren rocky super-Earth.

Using these models, we explore the structure, composition, and evolution of sub- Neptune sized extrasolar planets found by NASA's Kepler mission. We examine the relationships between planetary masses, radii, and compositions. We show how these compositions

have been sculpted by photo-evaporation, and we examine the interplay between thermal and evaporative evolution.

The formation of clouds significantly alters the spectra of cool substellar atmospheres from terrestrial planets to brown dwarfs. In cool planets like Earth and Jupiter, volatile species like water and ammonia condense to form ice clouds. In hot planets and brown dwarfs, iron and silicates instead condense, forming dusty clouds. Irradiated methane-rich planets may have substantial hydrocarbon hazes. During my dissertation, I have studied the impact of clouds and hazes in a variety of substellar objects. First, I present results for cool brown dwarfs in- cluding clouds previously neglected in model atmospheres. Model spectra that include sulfide and salt clouds can match the spectra of T dwarf atmospheres; water ice clouds will alter the spectra of the newest and coldest brown dwarfs, the Y dwarfs. These sulfide/salt and ice clouds potentially drive spectroscopic variability in these cool objects, and this variability should be distinguishable from variability caused by hot spots.

Next, I present results for small, cool exoplanets between the size of Earth and Neptune. They likely have sulfide and salt clouds and also have photochemical hazes caused by stellar irradiation. Vast resources have been dedicated to characterizing the handful of super Earths and Neptunes accessible to current telescopes, yet of the planets smaller than Neptune studied to date, all have radii in the near-infrared consistent with being constant in wavelength, likely showing that these small planets are consistently enshrouded in thick hazes and clouds. For the super Earth GJ 1214b, very thick, lofted clouds of salts or sulfides in high metallicity (1000× solar) atmospheres create featureless transmission spectra in the near-infrared. Photochemical hazes also create featureless transmission spectra at lower metallicities. For the Neptune-sized GJ 436b, its thermal emission and transmission spectra combine indicate a high metallicity atmosphere, potentially heated by tides and affected by disequilibrium chemistry. I show that despite the challenges, there are promising avenues for understanding small planets: by observing thermal emission and reflected light, we can break the degeneracies and con- strain the atmospheric compositions. These future observations will provide rich diagnostics of molecules and clouds in small planets.