CCD Time-Series Photometry of White Dwarf Stars

<p>This thesis describes a practical programme that focused on CCD photometry of pulsating white dwarf (WD) stars. The first part of this thesis describes the development of two high-speed CCD photometer instruments and their data reduction pipeline, while the remainder describes the observation and analysis of several pulsating WDs and other targets. The two photometers (Puoko-nui North and South) share a common hardware design that is optimized for acquiring efficient photometry with integration periods of milliseconds through to minutes. The design integrates a commercial CCD (Charge-Coupled Device) camera and GPS (Global Positioning System) receiver with custom timing electronics and control software. The reduction and visualization software developed for these instruments provide detailed real-time information to the observer, and a streamlined data reduction pipeline. EC04207-4748 is a pulsating helium atmosphere WD that shows significant non-sinusoidal intensity variations. We show that the pulsation spectrum of this WD can be described by four independent pulsation eigenmodes plus linear combinations that arise from non-linear energy transport through a sub-surface convection layer. Our results are consistent with similar analyses that have been made for similar stars, and add an additional data point to the growing catalogue of these convection measurements. We argue that the convection layer depth may form a useful substitute for the effective temperatures of these WDs. GWLibrae is the class prototype of the accreting WD pulsators. These stars exist in cataclysmic variable (CV) systems, and show a mix of CV and pulsating WD-related phenomena. Our observations of GW Librae four - six years after its 2007 outburst show signs of quasi-stable intensity modulations that we believe may be caused by non-radial pulsations, but these are not convincingly explained by existing WD or CV models. L19-2 is a hydrogen atmosphere WD pulsator that shows extremely stable pulsation behaviour. We combine new observations with archival observations dating back to the mid 1970's, and derive a preliminary estimate of the period rate of change Ṗ for two of the pulsation modes in this target. We show a clear result for the main 192 s pulsation mode Ṗf₂ ≾ 10⁻¹⁴ s s-¹, and discuss the improvements that we plan to make in order to convincingly improve this constraint by an additional order of magnitude. Observations of other rapidly variable targets include two extremely low mass (ELM) WDs, which exhibit variability due to their orbital motion (J0751) as well as non-radial pulsations (J1518); the 33 ms optical period of the Crab Pulsar; the helium atmosphere WD pulsators EC05221-4725 and EC20058-5234; the stable hydrogen atmosphere pulsator G117–B15A; and the eclipsing sdB binary system PG1336-018.</p>

CCD Time-Series Photometry of White Dwarf Stars

<p>This thesis describes a practical programme that focused on CCD photometry of pulsating white dwarf (WD) stars. The first part of this thesis describes the development of two high-speed CCD photometer instruments and their data reduction pipeline, while the remainder describes the observation and analysis of several pulsating WDs and other targets. The two photometers (Puoko-nui North and South) share a common hardware design that is optimized for acquiring efficient photometry with integration periods of milliseconds through to minutes. The design integrates a commercial CCD (Charge-Coupled Device) camera and GPS (Global Positioning System) receiver with custom timing electronics and control software. The reduction and visualization software developed for these instruments provide detailed real-time information to the observer, and a streamlined data reduction pipeline. EC04207-4748 is a pulsating helium atmosphere WD that shows significant non-sinusoidal intensity variations. We show that the pulsation spectrum of this WD can be described by four independent pulsation eigenmodes plus linear combinations that arise from non-linear energy transport through a sub-surface convection layer. Our results are consistent with similar analyses that have been made for similar stars, and add an additional data point to the growing catalogue of these convection measurements. We argue that the convection layer depth may form a useful substitute for the effective temperatures of these WDs. GWLibrae is the class prototype of the accreting WD pulsators. These stars exist in cataclysmic variable (CV) systems, and show a mix of CV and pulsating WD-related phenomena. Our observations of GW Librae four - six years after its 2007 outburst show signs of quasi-stable intensity modulations that we believe may be caused by non-radial pulsations, but these are not convincingly explained by existing WD or CV models. L19-2 is a hydrogen atmosphere WD pulsator that shows extremely stable pulsation behaviour. We combine new observations with archival observations dating back to the mid 1970's, and derive a preliminary estimate of the period rate of change Ṗ for two of the pulsation modes in this target. We show a clear result for the main 192 s pulsation mode Ṗf₂ ≾ 10⁻¹⁴ s s-¹, and discuss the improvements that we plan to make in order to convincingly improve this constraint by an additional order of magnitude. Observations of other rapidly variable targets include two extremely low mass (ELM) WDs, which exhibit variability due to their orbital motion (J0751) as well as non-radial pulsations (J1518); the 33 ms optical period of the Crab Pulsar; the helium atmosphere WD pulsators EC05221-4725 and EC20058-5234; the stable hydrogen atmosphere pulsator G117–B15A; and the eclipsing sdB binary system PG1336-018.</p>

Deep learning in turbulent convection networks

We explore heat transport properties of turbulent Rayleigh–Bénard convection in horizontally extended systems by using deep-learning algorithms that greatly reduce the number of degrees of freedom. Particular attention is paid to the slowly evolving turbulent superstructures—so called because they are larger in extent than the height of the convection layer—which appear as temporal patterns of ridges of hot upwelling and cold downwelling fluid, including defects where the ridges merge or end. The machine-learning algorithm trains a deep convolutional neural network (CNN) with U-shaped architecture, consisting of a contraction and a subsequent expansion branch, to reduce the complex 3D turbulent superstructure to a temporal planar network in the midplane of the layer. This results in a data compression by more than five orders of magnitude at the highest Rayleigh number, and its application yields a discrete transport network with dynamically varying defect points, including points of locally enhanced heat flux or “hot spots.” One conclusion is that the fraction of heat transport by the superstructure decreases as the Rayleigh number increases (although they might remain individually strong), correspondingly implying the increased importance of small-scale background turbulence.

A Closure for Updraft–Downdraft Representation of Subgrid-Scale Fluxes in Cloud-Resolving Models

A closure relationship between subgrid-scale (SGS) updraft–downdraft differences and resolvable-scale (RS) variables is proposed and tested for cloud-resolving models (CRMs), based on a data analysis of a large-eddy simulation (LES) of deep convection. The LES flow field is partitioned into CRM-RS and CRM-SGS using a cutoff scale that corresponds to a typical CRM grid resolution. This study first demonstrates the capability of an updraft–downdraft model framework in representing the SGS fluxes of heat, moisture, and momentum over the entire deep convection layer. It then formulates a closure scheme to relate SGS updraft–downdraft differences to horizontal gradients of RS variables. The closure is based on the idea that largest SGS and smallest RS motions are spectrally linked and hence their horizontal fluctuations must be strongly communicated. This relation leads to an SGS scheme that expresses vertical SGS fluxes in terms of horizontal gradients of RS variables, which differs from conventional downgradient eddy diffusivity models. The new scheme is shown to better represent the forward and backscatter energy transfer between CRM-RS and CRM-SGS components than conventional eddy-viscosity models.

Numerical simulations of magnetic structures

We use 3D radiative MHD simulations of the upper turbulent convection layer for investigation of physical mechanisms of formation of magnetic structures on the Sun. The simulations include all essential physical processes, and are based of the LES (Large-Eddy Simulations) approach for describing the sub-grid scale turbulence. The simulation domain covers the top layer of the convection zone and the lower atmosphere. The results reveal a process of spontaneous formation of stable magnetic structures from an initially weak vertical magnetic field, uniformly distributed in the simulation domain. The process starts concentration of magnetic patches at the boundaries of granular cells, which are subsequently merged together into a stable large-scale structure by converging downdrafts below the surface. The resulting structure represents a compact concentration of strong magnetic field, reaching 6 kG in the interior. It has a cluster-like internal structurization, and is maintained by strong downdrafts extending into the deep layers.

Buoyancy statistics in moist turbulent Rayleigh–Bénard convection

We study shallow moist Rayleigh–Bénard convection in the Boussinesq approximation in three-dimensional direct numerical simulations. The thermodynamics of phase changes is approximated by a piecewise linear equation of state close to the phase boundary. The impact of phase changes on the turbulent fluctuations and the transfer of buoyancy through the layer is discussed as a function of the Rayleigh number and the ability to form liquid water. The enhanced buoyancy flux due to phase changes is compared with dry convection reference cases and related to the cloud cover in the convection layer. This study indicates that the moist Rayleigh–Bénard problem offers a practical framework for the development and evaluation of parameterizations for atmospheric convection.