The work performed here studies particle dynamics in local two-dimensional simulations of self-gravitating accretion discs with a simple cooling law. It is well known that the structure which arises in the gaseous component of the disc due to a gravitational instability can have a significant effect on the evolution of dust particles. Previous results using global simulations indicate that spiral density waves are highly efficient at collecting dust particles, creating significant local over-densities which may be able to undergo gravitational collapse. This thesis expand on these findings, using a range of cooling times to mimic the conditions at a large range of radii within the disc. The PENCIL Code is used to solve the 2D local shearing sheet equations for gas on a fixed grid together with the equations of motion for solids coupled to the gas solely through aerodynamic drag force. The work contained here shows that spiral density waves can create significant enhancements in the surface density of solids, equivalent to 1-10cm sized particles in a disc following the profiles of Clarke (2009) around a solar mass star, causing it to reach concentrations several orders of magnitude larger than the particles mean surface density. These findings suggest that the density waves that arise due to gravitational instabilities in the early stages of star formation provide excellent sites for the formation of large, planetesimal-sized objects. These results are expanded on, with subsequent results introducing the effects of the particles self-gravity showing these concentrations of particles can gravitationally collapse, forming bound structures in the solid component of the disc.

Simulations were performed to determine the effect of turbulence on protoplanets as they accrete inside of a planetary gas disk at the stage of planet formation that involves interactions between relatively large, similar sized bodies. The effect of turbulence was implemented into an existing N-Body code using a parameterization of magnetohydrodynamic (MHD) turbulence performed by Laughlin et. al. (2004). The investigation focussed on the effect of turbulent perturbations on planetary dynamics and accretion at various locations in the disk, particularly at large semimajor axis. At these distances, protoplanet collisions are generally less frequent due to the large induced eccentricities from close encounters and due to the trapping of protoplanets in mutual resonances. It is, however, essential that large protoplanets develop at these distances since some must eventually grow large enough to accrete the massive gas envelopes indicative of the giant planets. The interaction between a protoplanet and the surrounding gas disk creates a torque imbalance acting on the protoplanet, which is generally believed to result in the rapid inward spiraling of the protoplanet. In order to create a fixed region in the disk within which protoplanets may interact without migrating into the central star, two scenarios were considered that would inhibit the inward migration of the protoplanets. The first scenario involved a gas disk that had been truncated at the inner edge, referred to as a planet trap, and the second involved the existence of a stationary giant planet within a gap in the disk, referred to as a planet barrier. Each scenario was tested using different density profiles of the gas disk, different numbers and masses of initial protoplanets, various rates of gas disk decay and also four different levels of turbulence intensities. The results demonstrated that the addition of turbulence to the gas disk promotes planet mixing and results in an increased number of collisions between planets, even at large heliocentric distances. A turbulent disk has the tendency to create a final system where the planets are, on average, larger than those produced in a non-turbulent disk. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-09-17 14:41:52.607

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis is a comprehensive investigation into the mechanics of evaporation experienced by planetesimals during accretion, a planet-building process. The evaporation events that these rocky bodies experience govern their chemical evolution, impacting the chemistry of the final body – a planet. Studying these planet-building processes is notoriously difficult (e.g., Sossi et al., 2019). There are still many unknowns surrounding what controls the degree of evaporation these bodies experience, and the resulting chemical signatures. The current study was designed to attempt to define some important parameters that govern silicate melt evaporation. Here, we isolate and evaluate the effects of (1) pressure, (2) oxygen fugacity and (3) the activity coefficient of MgO on evaporating planetesimals through a series of computational models. The model introduced in this study, the ƒO2 Modified KNFCMAS Model, uses a robust stepwise routine for calculating evaporative fluxes from a shrinking sphere. The modelling results are then compared to data from partial evaporation experiments of synthetic chondrite spheres to demonstrate the validity of this model, and to expose unknowns about the physicochemical conditions of high temperature silicate melts experiencing evaporation (in this case, the effective pressure, and the activity coefficient of MgO). Major element-oxide and isotope data from the models yielded two main conclusions concerning planetesimals: (1) the rate of evaporation is controlled by pressure and oxygen fugacity and (2) the chemical composition of the residual melt is controlled by oxygen fugacity and the activity coefficient of MgO. Results from computational modelling and evaporation experiments were used to determine an approximation for the activity coefficient of MgO in a simplified chondritic composition, as well as the effective pressure experienced by the evaporating spheres during the partial evaporation experiments. This study outlines the controls on planetesimal chemistry during evaporation and provides a more accessible means of studying these complex processes.

In recent years, thousands of exoplanets have been discovered around a variety of stellar hosts. The disks of gas and dust surrounding young stars are the location and source of material for planet formation. The properties of these protoplanetary disks therefore directly affect the planetary systems that may form. However, the details of the planet formation process are still unclear. In this dissertation, I constrain planet formation mechanisms by measuring the properties of protoplanetary disks, focusing on mass, dust grain growth, and dust settling. I use physically-motivated models and an Artificial Neural Network along with a Markov Chain Monte Carlo (MCMC) fitting procedure to obtain these and other disk properties. This dissertation compiles the largest sample to date of consistently-modeled protoplanetary disks, probing how disk properties vary with host mass and age. The occurrence of planetary companions increases as stellar mass decreases. Thus, brown dwarfs (BDs), with smaller masses than pre-main-sequence stars, may commonly host planets. Studying properties of BD disks and comparing them to pre- main-sequence star disks is therefore important for constraining their planet-forming potential. I present spectral energy distribution (SED) models for BD and pre-main- sequence star disks in four star-forming regions. The SEDs consist of archival photometry data spanning optical to millimeter wavelengths. I model the BD disk SEDs using physically-motivated radiative transfer code; pre-main-sequence star SEDs are modeled using a newly-developed MCMC fitting procedure that allows for a more complete analysis of the disk properties. I compare disk masses and dust settling in these two disk categories to gauge how host mass affects these properties. Typical disk lifetimes are a few tens of millions of years; planet formation likely occurs within the first few million years or less. Comparing how disk properties vary between star-forming regions of different ages can help pinpoint the timeline for planet formation. I present SED models for BDs in four star-forming regions and pre-main-sequence stars in eleven star-forming regions. I obtain the disk masses, dust grain sizes, and amount of dust settling in the disks and discuss the differences and similarities of these properties across regions of varying age.

At the edge of the Solar System lies the Kuiper Belt, a ring of leftover planetesimals from the era of planet formation. Collisions between the Kuiper Belt Objects produce dust grains, which absorb and re-radiate stellar radiation. The total amount of stellar radiation so absorbed is perhaps one part in ten million. Analogous to this, Sun-like stars at Sun-like ages commonly have dusty debris disks, which absorb and re-radiate as much as one part in ten thousand of the stellar radiation. We set out to understand this difference. In chapter 1, we outline the relevant observations and give a feel for the relevant physics. In chapter 2, we turn to the extrasolar debris disks. Using disks spanning a wide range of ages, we construct a pseudo-evolution sequence for extrasolar debris disks. We apply a straightforward collision model to this sequence, and find that the brightest disks are a hundred to a thousand times as massive as the Kuiper Belt, which causes the difference in dust luminosity. Current theoretical models of planetesimal growth predict very low efficiency in making large planetesimals, such that the Kuiper Belt should be the typical outcome of Minimum Mass Solar Nebula type disks. These models cannot produce the massive disks we find around other stars. We revisit these models in chapter 3, to understand the origin of this low efficiency. We confirm that these models, which begin with kilometer sized planetesimals, cannot produce the observed extrasolar debris disks. Instead, we propose an alternate model where most mass begins in centimeter sized grains, with some kilometer sized seed planetesimals. In this model, collisional cooling amongst the centimeter grains produces a new growth mode. We show in chapter 4 that this can produce the Kuiper Belt from a belt not much more massive than the Kuiper Belt today. We follow in chapter 5 by showing that this model can also produce the massive planetesimal populations needed to produce extrasolar debris disks.

At the edge of the Solar System lies the Kuiper Belt, a ring of leftover planetesimals from the era of planet formation. Collisions between the Kuiper Belt Objects produce dust grains, which absorb and re-radiate stellar radiation. The total amount of stellar radiation so absorbed is perhaps one part in ten million. Analogous to this, Sun-like stars at Sun-like ages commonly have dusty debris disks, which absorb and re-radiate as much as one part in ten thousand of the stellar radiation. We set out to understand this difference. In chapter 1, we outline the relevant observations and give a feel for the relevant physics. In chapter 2, we turn to the extrasolar debris disks. Using disks spanning a wide range of ages, we construct a pseudo-evolution sequence for extrasolar debris disks. We apply a straightforward collision model to this sequence, and find that the brightest disks are a hundred to a thousand times as massive as the Kuiper Belt, which causes the difference in dust luminosity. Current theoretical models of planetesimal growth predict very low efficiency in making large planetesimals, such that the Kuiper Belt should be the typical outcome of Minimum Mass Solar Nebula type disks. These models cannot produce the massive disks we find around other stars. We revisit these models in chapter 3, to understand the origin of this low efficiency. We confirm that these models, which begin with kilometer sized planetesimals, cannot produce the observed extrasolar debris disks. Instead, we propose an alternate model where most mass begins in centimeter sized grains, with some kilometer sized seed planetesimals. In this model, collisional cooling amongst the centimeter grains produces a new growth mode. We show in chapter 4 that this can produce the Kuiper Belt from a belt not much more massive than the Kuiper Belt today. We follow in chapter 5 by showing that this model can also produce the massive planetesimal populations needed to produce extrasolar debris disks.

The properties of planet-forming midplanes of protostellar disks remain largely unprobed by observations due to the high optical depth of common molecular lines and continuum. However, rotational emission lines from rare isotopologues may have optical depth near unity in the vertical direction, so that the lines are strong enough to be detected, yet remain transparent enough to trace the disk midplane. In this thesis, we present a chemical model of an MRI-active protoplanetary disk including different C, O isotopes and detailed photochemical reactions. The CO condensation front is found to be at 1.5 AU on the disk midplane around a solar like star, and its location remains almost unchanged during 3Myr of evolution. The optical depth of low-order rotational lines of C¹⁷O are around unity, which suggests it may be possible to see into the disk midplane using C¹⁷O. Such ALMA observations would provide estimates of the disk midplane temperature if the CO ice lines were spatially or spectrally resolved. With our computed C¹⁷O/H₂ abundance ratio, one would also be able to measure the disk masses by measuring the intensity of gas emission. / text

In this thesis, I discuss two studies concerned with modelling protoplanetary discs around stars from different ends of the stellar mass range. In Chapters 1 and 2, I give an introduction to the field of protoplanetary discs, both from an observational and a modelling point of view, and describe the radiative transfer methods I have employed. In Chapter 3, I present my work regarding the disc around the Herbig Ae star HD 163296. I show the results of applying a new modelling technique to this disc: I combine SED modelling with fits to the CO snowline location and C$^$O $J=2-1$ line profile from ALMA. I find that all of the modelling steps are crucial to break degeneracies in the disc parameter space. The use of all of these constraints favours a solution with a notably low gas-to-dust ratio ($g/d < 20$). The only models with a more interstellar medium (ISM)-like $g/d$ require C$^$O to be underabundant with respect to the ISM abundances and a significant depletion of sub-micron grains, which is not supported by scattered light observations. I propose that the technique can be applied to a range of discs and opens up the prospect of being able to measure disc dust and gas budgets without making assumptions about the $g/d$ ratio. In Chapter 4, I present my work on characterising the disc around the very low mass star V410 X-ray 1. Protoplanetary discs around such low mass stars offer some of the best prospects for forming Earth-sized planets in their habitable zones. The SED of V410 X-ray 1 is indicative of an optically thick and very truncated dust disc, with my modelling suggesting an outer radius of only 0.6 au. I investigate two scenarios that could lead to such a truncation, and find that the observed SED is compatible with both. The first scenario involves the truncation of both the dust and gas in the disc, perhaps due to a previous dynamical interaction or the presence of an undetected companion. The second scenario involves the fact that a radial location of 0.6 au is close to the expected location of the H$_2$O snowline in the disc. As such, a combination of efficient dust growth, radial migration, and subsequent fragmentation within the snowline leads to an optically thick inner dust disc and larger, optically thin outer dust disc. I find that a firm measurement of the CO $J=2-1$ line flux would distinguish between these two scenarios by enabling a measurement of the radial extent of gas in the disc. Many models I consider contain at least several Earth-masses of dust interior to 0.6 au, suggesting that V410 X-ray 1 could be a precursor to a system of tightly-packed inner planets, such as TRAPPIST-1. In Chapter 5, I summarise the work presented in this thesis, give an overview of future applications of the methods outlined in this dissertation, and an outlook on potential future projects.

Recent studies suggest that many protoplanetary disks around pre-main sequence stars with inferred ages of 1-5 Myr (known as Class II protostars) may contain insufficient mass to form giant planets. This may be because by this stage much of the material in the disk has already grown into larger bodies, hiding the material from sight. If this is the case, then these older disks may not be an accurate representation of the initial mass budget in disks for forming planets. To test this hypothesis, I have observed a sample of protostars in the Taurus star forming regions identified as Class I in multiple independent surveys, whose young (<1 Myr old) disks are more likely to represent the initial mass budget of protoplanetary disks. For my dissertation I have used detailed radiative transfer modeling of a multi-wavelength dataset to determine the geometry of the circumstellar material and measure the mass of the disks around these protostars. I discuss how the inferred disk mass distribution for this sample compares with results for the existing 1-5 Myr old disk samples, and what these results imply for giant planet formation. Next, I discuss the cases of three separate, individual Class I protostars discovered through my ongoing survey of Class I protostars whose disks are all of particular interest, each for its own reasons. Each of these disks may provide clues that even at the young ages of Class I protostars, planet formation may already be well underway in their disks. Finally, large disk mass surveys of large star forming regions like the Orion Nebula Cluster may be contaminated by free-free emission from disks that are being photoevaporated by nearby massive stars. I discuss my work with the VLA to constrain the free-free emission spectra for these sources so that current and future millimeter surveys can accurately measure disk masses in the ONC.

A long-standing question in planet formation is the origin of planetesimals, the kilometre-sized precursors to protoplanets. Asteroids and distant Kuiper Belt objects are believed to be remnant planetesimals from the beginnings of our Solar system. A leading mechanism for explaining the formation of these bodies directly from centimetre-sized dust pebbles is the streaming instability (SI). Using high resolution numerical simulations of protoplanetary discs, we probe the behavior of the non-linear SI and planetesimal formation in previously unexplored configurations. Small variations in initial state of the disc can lead to different macroscopic outcomes such as the total mass converted to planetesimals, or the distribution of planetesimal masses. These properties can vary considerably within large simulations, or across smaller simulations re-run with different initial perturbations. However, there is a similar spread in outcomes between multiple smaller simulations and between smaller sub-regions in larger simulations. In small simulations, filaments preferentially form rings while in larger simulations they are truncated. Larger domains permit dynamics on length scales inaccessible to the smaller domains. However, the overall mass concentrated in filaments across various length scales is consistent in all simulations. Small simulations in our suite struggle to resolve dynamics at the natural filament separation length scale, which restricts the possible filament configurations in these simulations. We also model discs with multiple grain species, sampling a size distribution predicted from theories of grain coagulation and fragmentation. The smallest grains do not participate in the formation of planetesimals or filaments, even while they co-exist with dust that readily forms such dense features. For both single-grain and multiple-grain models, we show that the clumping of dust into dense features results in saturated thermal emission, requiring an observational mass correction factor that can be as large as 20-80\%. Finally, we present preliminary work showing that the critical dust-to-gas mass ratio required to trigger the SI can vary between 3D and 2D simulations. / Thesis / Doctor of Philosophy (PhD)