This thesis studies the formation of planets and the destruction of stars that explode as supernovae. To understand planet formation and recreate the diversity of exoplanets that we see in our galaxy, we need a better understanding of protoplanetary disks. We develop a time-evolving model for the solid particles in these disks, tracking maximum particle size and surface density in their outer regions. This time dependent particle modeling shows us that disks pass through several regimes as more particles drift inwards, lowering maximum particle sizes and surface densities. By combining this model with our model for pebble accretion, we are able to estimate growth rates for injected protoplanetary cores. Applying our models to a sample of seven disks, we find that planetesimals should grow rapidly, particularly early in the disk's lifetime before it has drained too much. To reproduce observed planetary masses, we find that protoplanetary cores must reach planetesimal sizes before the ages of typically observed disks.

Turning our attention to smaller particles, we develop a new model for pebble accretion to explore the growth of lower mass protoplanetary cores. We apply full gas effects to the dynamics of small cores, finding that their new velocities play a crucial role in understanding their growth. Additionally, we model full probability distributions for the relative velocities of interacting particles, rather than simply studying the mean velocity. As we extend the model down to cm scales, we find that gas interactions play the dominant role in setting relative velocities for inter-particle collisions. At these small scales especially, particles in the low velocity tail of the velocity distribution can be accreted particularly rapidly, enhancing growth. In examining these rare growth interactions, our model suggests a path for solid body growth across the meter-scale barrier, up to planetesimal masses.

Finally, I also present my work statistically modeling the ages of Type Iax supernova progenitor stars. In this study, we use Hubble Space Telescope photometry of the stellar regions around Type Iax supernovae explosion sites to estimate ages for these regions. This is performed by statistically rigorous fitting of theoretical stellar models to our multi-band photometry. We are ultimately able to generate probability distributions for the ages of each supernova we consider, generating strong constraints on the formation channel for these events.

An inquiry into atmospheric escape driven by photoionization. We begin with a brief survey of the relevant historical development of atmospheric escape, spanning from the origins of kinetic theory to the age of exoplanets. Collisional mechanisms justifying the continuum assumption, central to the hydrodynamic framework, are scrutinized. Given the inherent presence of ions in photoionized outflows, we argue for the pervasive application of the hydrodynamic framework. Prefatory investigation of the multifrequency problem is undertaken. Results uncover notable differences from those invoking the monochromatic approximation. Notably, outflows are cooler and slower, yet denser and of higher mass-loss rates. Moreover, of importance to observations, the outflows are less ionized near the optical planetary radius and more ionized further from the planet. Supplementary to these results is our detailed procedure for generating synthetic observations.

To enable both expedited and detailed examination of the problem, a one-dimensional and three-dimensional model are prescribed. The one-dimensional modeling should provide the wider community with access to inexpensive and accurate results. On the other hand, the three-dimensional modeling can be used for precise exploration of more complicated physics. Unique to the three-dimensional results are the inclusion of asymmetric heating, the Coriolis force, and stellar winds. The large-scale morphology of three-dimensional outflows is elucidated. Energetic arguments for the extent of the outflow are presented, along with the prediction of a Coriolis shock. The consequences of varying stellar wind strengths are explored. Results predict a yet unseen, and unsearched for, transitory pretransit signal.

A newborn star is encircled by a remnant disc of gas and dust. A fraction of the disc coalesces into planets. Another fraction spirals inward and accretes onto the star(1). Accreting gas not only produces observed ultraviolet radiation, but also drags along embedded planets, helping to explain otherwise mysterious features of observed extrasolar systems. What drives disc accretion has remained uncertain. The magneto-rotational instability (MRI), driven by coupling between magnetic fields and disc rotation, supplies a powerful means of transport(2), but protoplanetary disc gas might be too poorly ionized to couple to magnetic fields(1-6). Here we show that the MRI explains the observed accretion rates of newly discovered transitional discs(7,8,) which are swept clean of dust inside rim radii of similar to 10 AU. Stellar coronal X-rays ionize the disc rim, activating the MRI there. Gas flows steadily from the rim to the star, at a rate set by the depth to which X-rays ionize the rim wall. Blown out by radiation pressure, dust largely fails to accrete with gas. Our picture supplies one concrete setting for theories of how planets grow and have their orbits shaped by disc gas(9), and when combined with photo-evaporative disc winds(10) provides a framework for understanding how discs dissipate.

In this thesis, I will explore three ideas that relate to giant planet formation, an incredibly dynamic process that affects not only the orbital configurations, but also the atmospheric structure and processes driven by the often extreme environments in which these planets are embedded:(1) The formation of our solar system's ice giants may have involved significant migration due to a disk dynamical instability, as well as concurrent accretion of solids and gas from the protoplanetary disk, that may have consequences for their current atmospheric composition and evolution. (2) In exoplanetary systems, gas giants have been discovered on orbits that are extremely eccentric, and in the inner regions corresponding to the traditionally rocky planet region of our own solar system. These exotic systems may have undergone a phase of giant impacts, analogous to the phase that shaped our solar system's inner planet region and resulted in the Moon-forming impact. Such a phase produces outcomes that reproduce interesting features of the population: the correlation of mass with eccentricity, and eccentricity with stellar metallicity. (3) Finally, the atmospheres of the close-in planets are bathed in stellar irradiation. Photochemical reactions occur as the upper layers of the atmospheres are irradiated, and the massive amounts of deposited energy drive hydrodynamic winds from the planets. This results in mass loss that can not only be observed in the cases of giants, but can shape the global structure of smaller planets, leaving an imprint on entire populations of these planets.

With the rapid increase in our ability to observe exoplanets and exoplanetary systems over the past two decades, the amount of data available to planet formation theorists has grown considerably. This in turn has spurred development in our understanding of the physics of planet formation. In this dissertation, I discuss the work I have done to understand the physical processes that shape the architectures of the planetary systems we observe. This work can broadly be broken down into studies that cover three distinct epochs of planet formation, which I roughly term the "early," "middle," and "late" stages.

Chapters 2-5 discuss a new paradigm for the early stages of planetary growth generally referred to as "pebble accretion." In Chapter 2, I discuss in detail an analytic model I developed to calculate how planets grow through pebble accretion, with a focus on how this process varies as a function of planetary mass, particle size, and the level of turbulence in the protoplanetary disk. I demonstrate that over a wide range of parameter space turbulence can greatly reduce the efficiency of pebble accretion. In Chapter 3 I apply these considerations to the growth of gas giant planets at wide orbital separations. I derive an inverse relationship between the level of turbulence in a protoplanetary disk and the semi-major axis at which the core of giant planet can form. In Chapter 4 I discuss how our modeling of pebble accretion naturally predicts an upper mass limit that planets can reach, which I term the "flow isolation mass." I discuss the characteristics of this mass scale, and discuss predictions for the architectures of planetary systems that reach the flow isolation mass in the context of new observations. Finally, in Chapter 5 I contrast growth limited by flow isolation to another limiting mass scale known as the "pebble isolation mass." I demonstrate that because of the top-down manner in which pebble isolation inhibits particle accretion, analytic estimates of the pebble isolation mass can be off by factors as large as ~5, and analytic estimation of the planet's final mass is considerably more difficult. I also show that if pebble accretion is simultaneously inhibited by pebble and flow isolation, growth generally stops at observed super-Earth mass scales over a wide range of disk parameters, and final planet masses can once again be estimated analytically in a straightforward manner.

Chapter 6 discusses the intermediate stage of planet formation, where the cores of giant planets have reached sufficient size to undergo runaway gas accretion. I discuss the two-way feedback process between the growing planet and the protoplanetary disk it feeds from. I derive analytic expressions for the planet's perturbation to the surface density, which I broadly classify into the "consumption" and "repulsion" regimes. These analytic expressions are vetted against 1D numerical simulations, both for viscous disks that accrete due to local kinematic viscosity, and inviscid disks which accrete via magnetized winds.

Chapter 7 is concerned with the late stages of planet formation, where giant planets interact under their mutual gravity. I develop a method to fit radial velocity signals of planets where the mutual gravitational interaction is strong and the system must be tested for long-term stability, and apply this method to the planetary system around the star HD 200964. I demonstrate that the increased time baseline from additional observations moves the best-fit period ratio from 4:3 closer to 7:5, with the 3:2 also providing plausible fits that exhibit long-term stability. I discuss these different period ratios in the context of different formation pathways.

An understanding of planetary histories and characteristics requires an empirical connection between planet formation and evolved planets---a long-sought goal of astrophysics and planetary science. This connection is now increasingly possible due to simultaneous revolutions in the observations of protoplanetary disks and exoplanet atmospheres. A crucial step towards relating these observations of different evolutionary stages is to characterize the fundamental properties of both disks and atmospheres.

The work presented in this dissertation uses microphysics---i.e., the physics that governs the evolution of small particles--- to constrain the fundamental properties of both disks and atmospheres. This dissertation provides evidence that protoplanetary disks are more than an order of magnitude more massive than previously appreciated, that the detailed properties of clouds shape observations of exoplanet atmospheres, and that the physics of modeling clouds gives a new understanding of the solid content and composition in protoplanetary disks.

Clouds on extrasolar worlds are abundant and interfere with observations; however, little is known about their properties. Herein, cloud properties are predicted from first principles and are used to investigate and explain the novel observational properties of hot Jupiters---massive planets close to their host stars. This work describes the use of clouds in tracing fundamental planetary properties and develops a method for probing non-uniform cloud properties using near-future observations.

The total mass available in protoplanetary disks is a critical initial condition for understanding planet formation, however, the surface densities of protoplanetary disks are largely unconstrained due to uncertainties in the dust-to-gas ratio and carbon monoxide (CO) abundance. In this dissertation, a new set of models (dust-line models) are developed that reconcile theory with observations of protoplanetary disks and create a new set of initial conditions for planet formation models. These models use recent, resolved, multiwavelength observations of disks in the millimeter to constrain the aerodynamic properties of dust grains and infer the total disk mass without an assumed dust surface density or tracer-to-total mass ratio. This work provides a picture of protoplanetary disks where they are significantly more massive than was previously appreciated. These qualitative changes to models of protoplanetary disks thus have significant implications for theories of planet formation; particularly for the important processes where the amount of gas determines the evolution of the solids.

The techniques used in modeling clouds in exoplanet atmospheres are then combined with the dust-line models of protoplanetary disks to show that the observed depletion of CO gas in well-studied disks is consistent with freeze-out processes in a moderately diffusive environment. This new model of ice formation and evolution in disks is able to use existing observations to constrain three crucial parameters that control planetary formation, namely: the solid and gaseous CO inventory at the disk midplane where planets form, the bulk disk diffusivities and mixing characteristics, and the disk mass--through resolving inconsistencies in estimates of total mass using different tracers.