# Jeremy Heyl

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#### Supervision Enquiry

## Graduate Student Supervision

##### Doctoral Student Supervision (Jan 2008 - Mar 2019)

In the first part of this thesis, we solve the coupled Einstein-Vlasov system in spherical symmetry using direct numerical integration of the Vlasov equation in phase space. Focusing on the case of massless particles we study critical phenomena in the model, finding strong evidence for generic type I behaviour at the black hole threshold that parallels what has previously been observed in the massive sector. For differing families of initial data we find distinct critical solutions, so there is no universality of the critical configuration itself. However we find indications of at least a weak universality in the lifetime scaling exponent, which is yet to be understood. Additionally, we clarify the role that angular momentum plays in the critical behaviour in the massless case. The second part focuses on type II critical collapse. Using the critical collapse of a massless scalar field in spherical symmetry as a test case, we study a generalization of the BSSN formulation due to Brown that is suited for use with curvilinear coordinates. We adopt standard dynamical gauge choices, including 1+log slicing and a shift that is either zero or evolved by a Gamma-driver condition. With both choices of shift we are able to evolve sufficiently close to the black hole threshold to 1) unambiguously identify the discrete self-similarity of the critical solution, 2) determine an echoing exponent consistent with previous calculations, and 3) measure a mass scaling exponent, also in accord with prior computations. Our results can be viewed as an encouraging first step towards the use of hyperbolic formulations in more generic type II scenarios, including the as yet unresolved problem of critical collapse of axisymmetric gravitational waves. In the last part, we present simulations of nonlinear evolutions of pure gravity waves. We describe a new G-BSSN code in axial symmetry that is capable of evolving a pure vacuum content in a strong gravity regime for both Teukolsky and Brill initial data. We provide strong evidence for the accuracy of the numerical solver. Our results suggest that the G-BSSN is promising for type II critical phenomena studies.

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This thesis details three distinct projects that explore stellar populations in Milky Way globular clusters. In the first, a method of modelling mass segregation in clusters is presented. The model is fit to 54 clusters and the best fit parameters are presented in tabular form. The newly derived parameter that indicates the amount of mass segregation correlates strongly with other dynamical cluster parameters. In the second study, white dwarf data in the cluster 47 Tucanae are used to construct an empirical relation between temperature and time for these stars. The modified data are compared to theoretical cooling models from four different research groups. We find disagreement between all of the models and the data. The models are also inconsistent with each other. In thethird investigation, new UV white dwarf data in 47 Tuc is used to constrain the hydrogen mass fraction and neutrino production rates in cooling white dwarfs. A much different approach from the second project is used. The data are left untouched and the model is transformed to the space in which the data exist. Using the unbinned maximum likelihood statistic, the model’s parameter space is explored with MCMC sampling. A constraint on the rate of neutrino production in white dwarfs comes from this analysis.

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This thesis constitutes a numerical study concerning the dynamics of an inviscidfluid subject to Newtonian gravity. Type-II critical phenomena has been previously measured in gravitational collapse simulations of isothermal-gas-spheres in Newtonian gravity. Our first objective was to extend this work by applying the more general polytropic-gas equation-of-state to the spherically symmetric fluid. We showed that under generic conditions of critical collapse, the polytropic gas allows for scale-invariant solutions. These solutions display self-similarity of the first kind with non-linear scaling between the space and time variables. One of these solutions was identified as the critical solution in critical collapse simulations. Such solution was found to have a single unstable mode with a Lyapunov exponent whose value depends on the polytropic index (Γ) from the equation of state. We argued that this behavior constitutes evidence of type-II critical phenomena with a transition from type-II to type-I behavior occurring at Γ ≥ 6/5. Thus, the polytropic gas exhibits both types of critical behavior. These phenomena was investigated dynamically and also from perturbation analysis. In the second phase of the project we extended the hydrodynamic model to treataxi-symmetric gravitational collapse. This allowed us to study the effect of angular momentum on the critical solution. As previously predicted, infinitesimal initial rotation introduces a non-spherical, unstable axial mode into the dynamics. The measured scaling behavior of the specific angular momentum of the collapsed core agrees with the predicted growth rate (Lyapunov exponent) of the axial perturbation. This two-mode linear regime modifies the scaling laws via the introduction of universal functions that depend on the two-parameter family of initial data. The predicted universality of these functions was confirmed through careful measurements of the collapsed mass and its angular momentum near the collapse threshold. A two-parameter space survey reveals a universal behavior of the order-parameters, with no mass-gap even in the presence of finite initial rotation. The behavior changes slightly beyond some initial rotation threshold. The results then, can be interpreted as an intermediate convergence to a non-spherical self-similar critical solution with a single unstable mode.

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This thesis investigates the merging of horizons which occurs when a black hole crosses a cosmological horizon. We study the simplest spacetime which has both a black hole and cosmological horizon, namely Schwarzschild-deSitter (SdS) spacetime. First we develop a new coordinate system for SdS spacetime, which allows us to properly illustrate and analyze the merging of horizons. We then use a combination of numerical and analytical methods to study the structure of the merging horizons, including the null generators which make up the horizon, as well as the presence of caustic points on the horizon. We find an analytical formula for the location in spacetime where the black hole and cosmological horizon first touch. Next we study the area of the horizons. Using numerical methods, we find several intriguing results regarding the behavior of horizon area on time, and in the limit of small black hole mass. The first result is that the time at which the black hole first touches the cosmological horizon is also the time at which the rate of horizon area increase is maximal. The second and third results concern the horizon area in the limit of small black hole mass. The second result is that in this limit, all of the increase in horizon area occurs prior to horizon merger. The third and final result is that in the limit of small black hole mass, the increase in horizon area can be thought of as being due in equal parts to two effects: to the joining of new generators not previously on the horizon, and the expansion of generators on the horizon for all times. The first and third results just mentioned are both corroborated using analytical techniques. Finally, we conclude by discussing how the study of merging horizons in this thesis is a valuable first step to undertaking a similar study of the horizons which occur in merging black hole binaries.

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We investigate the implications of a magnetic field in the late stages of stellar evolution, in relation to the process of mass-loss via a stellar wind. We develop the very first hybrid magnetohydrodynamic-dust-driven wind model for intermediate-mass Asymptotic Giant Branch (AGB) stars. This model consists of incorporating a canonical Weber-Davis magneto-centrifugal scenario with the effects of radiation pressure on dust grains in the envelope of an AGB star. This results in a dual-fluid description, the solution of which is seen to possess traits of both types of winds. In this context, we additionally investigate the implications of spots on the photosphere that alter the location of dust formation and hence the wind solutions. This model is adapted to tackle the case of the red supergiant Betelgeuse. The underlying motivation is to delineate a new mechanism for solving the problem of transport of stellar material from the photosphere out to the dust formation radius, many stellar radii away. Various dust formation scenarios are investigated and it is concluded that the simplest of such scenarios, with silicate dust forming at a large distance, is the most viable one as well. This theory is also applied to the low-mass end of AGB stars; the star Mira. By applying a modified wind model we solve for a hybrid MHD-dust-driven wind solution and find that the magnetic field required to model the observed wind is about 4 G, well within the range of current estimates for AGB stars. We also formulate a hot-spot model to rationalise dust shells at a distance of several stellar radii. Finally, we study the effects of a strong magnetic field in post-AGB compact objects; magnetised white dwarfs and neutron stars. We develop a fast and efficient solution for Hartree-Fock atoms in strong magnetic fields using pseudospectral methods. The atomic structure package developed for this purpose is seen to be many orders of magnitude faster than finite-element based methods. We also obtain for the first time, estimates for the binding energies of certain low-lying states of the lithium atom, that have not been reported thus far in the literature.

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The interaction of strong magnetic fields of compact objects with the surrounding plasma leads to novel and puzzling astrophysical phenomena. In this dissertation, we examine some of the properties of strongly magnetized plasmas as outlined in the following. A fully relativistic treatment of Bernstein waves in a uniform, magnetized, relativistic electron-positron pair plasma has remained too formidable a task owing to the very complex nature of the problem. We perform contour integration of the dielectric response function and numerically compute the dispersion curves. If coupled to electromagnetic modes, these waves may be important for generating radiation in pulsar magnetospheres. The soft gamma-ray repeaters, classified as magnetars, unleash large amounts of magnetically stored energy in a spectacular event called the giant flare. What causes these flares to develop is an open question. We examine two trigger mechanisms, one internal and the other external to the neutron star. In the internal mechanism, we propose that the strongly wound up poloidal magnetic field develops tangential discontinuities and dissipates its torsional energy in heating the crust. Alternatively, we argue that the shearing motion of the external magnetic field footpoints causes the materialization of a Sweet-Parker current layer in the magnetosphere. The thinning of this macroscopic layer powers the giant flare. The extreme environments of compact objects are conducive to the creation of exotic particles, that may not be discovered in laboratories. The light pseudoscalar particle, dubbed the axion, borne out of the Peccei-Quinn solution to the strong CP problem in QCD is one such particle which remains elusive. We present a novel way of constraining its properties by examining the level of linear polarization in the radiation emerging from magnetic white dwarfs. On sub-meV mass scales, our study provides the strongest constraints on axion properties obtained astrophysically. The cooling theory of neutron stars is corroborated by comparison with observations of thermally emitting isolated neutron stars. An important ingredient for such an analysis is the age of the object, which typically is highly uncertain. We conduct a population synthesis study of the nearby isolated thermal emitters and obtain their ages statistically.

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The crust of a neutron star plays an important role in the emission observed from it. The thermal emission generated in the core of the neutron star passes through the crust, thus it is important to know what is in the crust in order to understand how the emission is shaped and altered. The crust itself may be responsible for the observations of glitches from neutron stars and also as a source of gravitational waves. This thesis is two-fold. The first goal is to calculate the composition of the neutron star crust of a non-accreting neutron star. The second is to use the calculated crustal compositions in molecular dynamics simulations in order to determine the shear modulus and breaking strain of the crustal material.The composition of the crust is found to be dependent on how the neutron star cooled. Nuclear reactions within the crust are quenched as the star cools. The composition of the crust, envelope, and atmosphere are calculated after the nuclear reactions are quenched. With the settling timescales of the various isotopes in the crust, some of these isotopes are able to float up to the neutron star surface and form the atmosphere. Three different cooling methods were used in these calculations – modified Urca cooling, a thick crust and a thin crust – each produces different atmospheric and crustal compositions.The calculated crustal abundances are then used as initial conditions in molecular dynamics simulations. A shear force is introduced by deforming the simulation box. The shear modulus and breaking strain are calculated for the three different crustal compositions as well as for perfect pure face-centered cubic (FCC) and body-centered cubic (BCC) systems. The upper limit, from the perfect crystal lattice structure, on the breaking strain is found to ~0.11 − 0.12 and the shear modulus is found to be 6.5 × 10³º dyne/cm². These properties predict glitch amplitudes of ∆Ω/Ω∼10⁻³. The gravitational wave strain amplitudes for PSR J2124- 3358 are also predicted to be greater than the observed upper limits. This indicates that the neutron star crust is not a perfect BCC lattice which deformed to 10% of the maximum.

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The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for exploring the physics of quantum field theories. In this dissertation, we explore this idea in three astrophysical scenarios.In the early universe, quantum fluctuations of a scalar field result in the generation of particles, and of the density fluctuations which seed the large- scale structure of the universe. These fluctuations are generated through quantum processes, but are ultimately treated classically. We explore how a quantum-to-classical transition may occur due to non-linear self-interactions of the scalar field. This mechanism is found to be too inefficient to explain classicality, meaning fields which do not become classical because of other mechanisms may maintain some evidence of their quantum origins.Magnetars are characterized by intense magnetic fields. In these fields, the quantum vacuum becomes a non-linear optical medium because of interactions between light and quantum fluctuations of electron-positron pairs. In addition, there is a plasma surrounding the magnetar which is a dissipative medium. We construct a numerical simulation of electromagnetic waves in this environment which is non-perturbative in the wave amplitudes and background field. This simulation reveals a new class of waves with highly non-linear structure that are stable against shock formation.The dense nuclear material in a neutron star is expected to be in a type-II superconducting state. In that case, the star’s intense magnetic fields will penetrate the core and crust through a dense lattice of flux tubes. However,depending on the details of the free energy associated with these flux tubes, the nuclear material may be in a type-I state which completely expels the field. We compute the quantum corrections to the classical energies of these flux tubes by creating a new, massively parallel Monte-Carlo simulation. The quantum contribution tends to make a small contribution which adds to the classical free energy. We also find a non-local interaction energy with a sign that depends on the field profile and spacing between flux tubes.

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