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Full-Text Articles in Physical Sciences and Mathematics

Observation And Modelling Of Meter-Class Earth Impacting Asteroids, David L. Clark Sep 2023

Observation And Modelling Of Meter-Class Earth Impacting Asteroids, David L. Clark

Electronic Thesis and Dissertation Repository

Earth is constantly bombarded by solar system objects of a wide variety of sizes, from micron-sized meteoroid stream and sporadic meteor dust, to meter-sized and larger meteoroids observed as fireballs. Fireball event characteristics directly point to the properties and structure of the parent body from which the meteoroid originated. In-atmosphere fireball data paired with in-space observations bring much context to both observations. This thesis centres on three published papers that grew out of my Masters project to identify precovery in-space images of meteoroids first observed as fireballs.

The first article describes the first successful identification of an in-space image of …


The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi Apr 2023

The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi

Electronic Thesis and Dissertation Repository

Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a …


Nearby Galaxies: Modelling Star Formation Histories And Contamination By Unresolved Background Galaxies, Hadi Papei Jan 2023

Nearby Galaxies: Modelling Star Formation Histories And Contamination By Unresolved Background Galaxies, Hadi Papei

Electronic Thesis and Dissertation Repository

Galaxies are complex systems of stars, gas, dust, and dark matter which evolve over billions of years, and one of the main goals of astrophysics is to understand how these complex systems form and change. Measuring the star formation history of nearby galaxies, in which thousands of stars can be resolved individually, has provided us with a clear picture of their evolutionary history and the evolution of galaxies in general.

In this work, we have developed the first public Python package, SFHPy, to measure star formation histories of nearby galaxies using their colour-magnitude diagrams. In this algorithm, an observed colour-magnitude …


The Spectro-Temporal Relationships Of Repeating Fast Radio Bursts, Mohammed Afif Chamma Oct 2022

The Spectro-Temporal Relationships Of Repeating Fast Radio Bursts, Mohammed Afif Chamma

Electronic Thesis and Dissertation Repository

Fast radio bursts (FRBs) are short and extremely energetic bursts of radiation detected from galaxies across the universe that occur thousands of times a day. Despite advances in instrumentation, it is difficult to explain the enormous implied energy reservoirs of FRBs, their emission mechanism and the existence of repeating and periodic sources. This thesis explores the spectro-temporal properties of repeating FRBs and details the discovery of several new relationships between them, providing valuable information on the nature of FRBs. By measuring the spectro-temporal properties of a sample of bursts from the repeating source FRB20121102A I show that the magnitude of …


The Role Of Nonideal Magnetohydrodynamic Effects, Gravitational Instability, And Episodic Accretion In Star-Formation, Indrani Das Jul 2022

The Role Of Nonideal Magnetohydrodynamic Effects, Gravitational Instability, And Episodic Accretion In Star-Formation, Indrani Das

Electronic Thesis and Dissertation Repository

My dissertation focuses on the effect of magnetic fields on disk and core evolution during star-formation. We investigate the fragmentation scales of gravitational instability of a rotationally-supported self-gravitating protostellar disk using linear perturbation analysis in the presence of two nonideal magnetohydrodynamic (MHD) effects: Ohmic dissipation and ambipolar diffusion. Our results show that molecular clouds exhibit a preferred lengthscale for collapse that depends on mass-to-flux ratio, magnetic diffusivities, and the Toomre-Q parameter. In addition, the influence of the magnetic field on the preferred mass for collapse leads to a modified threshold for the fragmentation mass, as opposed to a Jeans mass, …


Probing The Inner Structure Of Active Galactic Nuclei Through Reverberation Mapping, Viraja Chandrashekhar Khatu Jun 2022

Probing The Inner Structure Of Active Galactic Nuclei Through Reverberation Mapping, Viraja Chandrashekhar Khatu

Electronic Thesis and Dissertation Repository

In the centres of massive galaxies, active galactic nuclei (AGN) are supermassive black holes, surrounded by an accretion disk of ionized gas, that release tremendous energy in the form of electromagnetic radiation. Because AGN are unresolved through telescopes, we employ reverberation mapping (RM) to study their structure. RM capitalizes on the fact that AGN are variable – the continuum emission from the accretion disk varies, and surrounding gas (in the broad-line region, BLR) responds to those variations with a positive time lag. RM translates the measured time lag into a size of the BLR. Combined with gas velocities (measured from …


The Dynamical Evolution Of Classical Be Stars, Keegan Marr Feb 2022

The Dynamical Evolution Of Classical Be Stars, Keegan Marr

Electronic Thesis and Dissertation Repository

This thesis focuses on the evolution of the disks of two classical B-emission (Be) stars, 66 Ophiuchi and Pleione, and on the thermal structure for disks tilted out of the star's equatorial plane.

We used a hydrodynamic code to model the disk of the Be star 66 Ophiuchi. Observations from 1957 to 2020 were compiled to follow the growth and subsequent dissipation of the disk. Our models are constrained by new and archival photometry, spectroscopy and polarization observations. Using Markov chain Monte Carlo methods, we confirm that 66 Oph is a B2Ve star. We constrain the density profile of the …


Brown Dwarf Atmospheres At High Cadence And Spectral Resolution: A Speed Limit On Brown Dwarf Rotation And A Spectroscopic Atlas Of A 1050 K Atmosphere, Megan E. Tannock Dec 2021

Brown Dwarf Atmospheres At High Cadence And Spectral Resolution: A Speed Limit On Brown Dwarf Rotation And A Spectroscopic Atlas Of A 1050 K Atmosphere, Megan E. Tannock

Electronic Thesis and Dissertation Repository

Brown dwarfs are sub-stellar objects that form like stars but are not sufficiently massive to sustain hydrogen fusion in their cores. Characterized by cool, molecule-rich atmospheres, brown dwarfs demonstrate great diversity in spectroscopic appearance and share many properties with giant exoplanets. In this thesis I present two investigations: the first is a detailed photometric and spectroscopic study of the three most rapidly rotating brown dwarfs. The second examines a spectrum of a cool brown dwarf at unprecedented spectral resolution and signal-to-noise ratio to study the accuracy of theoretical model photospheres.

Photometric monitoring of brown dwarfs has revealed that periodic variability …


Revisiting Polycyclic Aromatic Hydrocarbon Emission In Photodissociation Regions, Ameek K. Sidhu Aug 2021

Revisiting Polycyclic Aromatic Hydrocarbon Emission In Photodissociation Regions, Ameek K. Sidhu

Electronic Thesis and Dissertation Repository

The mid-infrared (IR) spectrum of almost all objects in the Universe is dominated by a set of strong emission features characteristic of a class of large organic molecules made of carbon and hydrogen known as polycyclic aromatic hydrocarbons (PAHs). These molecules account for ~15% of the cosmic carbon and ~20% of the total IR power of the Milky Way and star-forming galaxies. They are strong absorbers of ultraviolet (UV) photons and release the absorbed energy through vibrational transitions that result in strong IR emission features. PAHs play a critical role in the evolution of the interstellar medium (ISM) as they …


Investigation Of Shocked Basalts From Vargeão Dome And Vista Alegre: Implications For The Search For Life On Mars, Nikol Posnov Jul 2021

Investigation Of Shocked Basalts From Vargeão Dome And Vista Alegre: Implications For The Search For Life On Mars, Nikol Posnov

Electronic Thesis and Dissertation Repository

Impact craters represent excellent astrobiological targets for planetary exploration missions to Mars. The impact of an asteroid or comet into a crystalline, H2O-bearing target may result in development of a hydrothermal system and increase the habitability of the substrate for the colonization of endolithic microorganisms. Given that Mars’ surface is covered by cratered basaltic rock, this study investigated target rocks and impact breccias from Vargeão Dome and Vista Alegre impact structures that formed in basalt in the Paraná Basin of Brazil.

Utilizing petrography and micro-X-ray diffraction (μXRD), the degree of shock metamorphism in plagioclase was quantitively determined. Measuring …


Mathematical Modelling & Simulation Of Large And Small Scale Structures In Star Formation, Gianfranco Bino Jun 2021

Mathematical Modelling & Simulation Of Large And Small Scale Structures In Star Formation, Gianfranco Bino

Electronic Thesis and Dissertation Repository

This thesis aims to study the magnetic and evolutionary properties of stellar objects from the prestellar phase up to and including the late protostellar phase. Many of the properties governing star formation are linked to the core’s physical properties and the magnetic field highly dictates much of the core’s stability.

The thesis begins with the implementation of a fully analytic magnetic field model used to study the magnetic properties governing the prestellar core FeSt 1-457. The model is a direct result of Maxwell’s equations and yields a central-to-surface magnetic field ratio in the equatorial plane in cylindrical coordinates. The model …


Formation Of Supermassive Black Holes In The Early Universe, Arpan Das Apr 2021

Formation Of Supermassive Black Holes In The Early Universe, Arpan Das

Electronic Thesis and Dissertation Repository

The aim of the work presented in this thesis is to understand the formation and growth of the seeds of the supermassive black holes in early universe. Supermassive black holes (SMBH) with masses larger than 108MSun have been observed when the Universe was only 800 Myr old. The formation and accretion history of the seeds of these supermassive black holes are a matter of debate. We consider the scenario of massive seed black hole formation which allows gas to directly collapse into a black hole (DCBH) of similar mass. Considering this scenario, we show that the mass …


Mid-Infrared Studies Of Galactic Sources: Probing The Relationship Between Polycyclic Aromatic Hydrocarbons And Their Physical Environment, Collin Matthew Knight Oct 2020

Mid-Infrared Studies Of Galactic Sources: Probing The Relationship Between Polycyclic Aromatic Hydrocarbons And Their Physical Environment, Collin Matthew Knight

Electronic Thesis and Dissertation Repository

Over the past 50 years, prominent mid-infrared (MIR) emission features from 3--20 $\mu$m have been observed ubiquitously in the interstellar medium (ISM) of Galactic and extragalactic sources. These emission features arise from the vibrational relaxation of polycyclic aromatic hydrocarbons (PAHs) after the absorption of a far-ultraviolet (FUV) photon. PAHs are astronomically significant in that they contain up to 15\% of the cosmic carbon inventory and play an important role in the physical and chemical processes of the ISM such as, for example, the gas heating and the ionization balance. Variations in the relative strengths of the major PAH bands can …


Point Process Modelling Of Objects In The Star Formation Complexes Of The M33 Galaxy, Dayi Li Apr 2020

Point Process Modelling Of Objects In The Star Formation Complexes Of The M33 Galaxy, Dayi Li

Electronic Thesis and Dissertation Repository

In this thesis, Gibbs point process (GPP) models are constructed to study the spatial distribution of objects in the star formation complexes of the M33 galaxy. The GPP models circumvent the limitations of the two-point correlation function employed in the current astronomy literature by naturally accounting for the inhomogeneous distribution of these objects. The spatial distribution of these objects serves as a sensitive probe in understanding the star formation process, which is crucial in understanding the formation of galaxies and the Universe. The objects under study include the CO filament structure, giant molecular clouds (GMCs) and young stellar cluster candidates …


Physical Dispersions Of Meteor Showers Through High Precision Optical Observations, Denis Vida Apr 2020

Physical Dispersions Of Meteor Showers Through High Precision Optical Observations, Denis Vida

Electronic Thesis and Dissertation Repository

Meteoroids ejected from comets form meteoroid streams which disperse over time due to gravitational perturbations and non-gravitational forces. When stream meteoroids collide with the Earth's atmosphere, they are visible as meteors emanating from a common point-like area (radiant) in the sky. Measuring the size of meteor shower radiant areas can provide insight into stream formation and age. The tight radiant dispersion of young streams are difficult to determine due to measurement error, but if successfully measured, the dispersion could be used to constrain meteoroid ejection velocities from their parent comets. The estimated ejection velocity is an uncertain, model-dependent value with …


Quantification Of Surface Roughness Of Lava Flows On Mars, Carolina Rodriguez Sanchez-Vahamonde Dec 2019

Quantification Of Surface Roughness Of Lava Flows On Mars, Carolina Rodriguez Sanchez-Vahamonde

Electronic Thesis and Dissertation Repository

Volcanism has played a significant role throughout Mars’ geologic history. Extensive lava flows are widely spread across Mars’ equatorial region, shaping the surface in a very distinct way. In radar images (at the decimeter scale), these flows are bright, which is a typical characteristic of extremely rough, blocky lavas flows seen on Earth. Although the source of the extreme roughness of Martian lava flows is unknown, their surface roughness parameters can be constrained to 1) gain information about Mars’ interior processes, 2) find appropriate analogues on other planetary bodies, and 3) ideally infer the emplacement style of such lavas. Here, …


Multiwavelength, Machine Learning, And Parallax Studies Of X-Ray Binaries In Three Local Group Galaxies, Robin Arnason Dec 2018

Multiwavelength, Machine Learning, And Parallax Studies Of X-Ray Binaries In Three Local Group Galaxies, Robin Arnason

Electronic Thesis and Dissertation Repository

X-ray binary stars are rare systems consisting of a black hole or neutron star and a main-sequence companion star. They are useful probes of galaxy properties and interesting laboratories for extreme physical conditions. In this thesis, I investigated the X-ray binary population of three galaxies in the Local Group.

The Sculptor Dwarf Spheroidal Galaxy offers the chance to study a primordial low-mass X-ray binary (LMXB) population in an isolated, low-metallicity environment. Combining X-ray, optical, and infrared observations, I have studied nine previously-identified and discovered four additional LMXB candidates in this galaxy. Of these candidates, all but one are either background …


Mapping Debris Disks At Extreme Contrast: Near-Ir Polarimetric Differential Imaging With The Gemini Planet Imager., Juan Sebastian Bruzzone Sep 2018

Mapping Debris Disks At Extreme Contrast: Near-Ir Polarimetric Differential Imaging With The Gemini Planet Imager., Juan Sebastian Bruzzone

Electronic Thesis and Dissertation Repository

Debris disks are gas-poor evolved circumstellar disks that show decreased near- to mid- infrared thermal excess emission because of lack of material close to the star. Regarded as massive analogues to the Main Asteroid or Kuiper Belts in the Solar System, these often young dust-rich disks comprise second-generation dust created by disruptive collisions of planetesimals and the decay products of asteroids and comets. Of the dozen or so directly imaged planets to date many share a distinctive characteristic: they reside in stellar systems known to also possess circumstellar dust. High-angular resolution characterization of debris disks, whose morphology is thought to …


The Periglacial Landscape Of Mars: Insight Into The 'Decameter-Scale Rimmed Depressions' In Utopia Planitia, Arya Bina Aug 2018

The Periglacial Landscape Of Mars: Insight Into The 'Decameter-Scale Rimmed Depressions' In Utopia Planitia, Arya Bina

Electronic Thesis and Dissertation Repository

Currently, Mars appears to be in a ‘frozen’ and ‘dry’ state, with the clear majority of the planet’s surface maintaining year-round sub-zero temperatures. However, the discovery of features consistent with landforms found in periglacial environments on Earth, suggests a climate history for Mars that may have involved freeze and thaw cycles. Such landforms include hummocky, polygonised, scalloped, and pitted terrains, as well as ice-rich deposits and gullies, along the mid- to high-latitude bands, typically with no lower than 20o N/S. The detection of near-surface and surface ice via the Phoenix lander, excavation of ice via recent impact cratering activity as …


Impact Melt Emplacement On Mercury, Jeffrey Daniels Jul 2018

Impact Melt Emplacement On Mercury, Jeffrey Daniels

Electronic Thesis and Dissertation Repository

Impact cratering is an abrupt, spectacular process that occurs on any world with a solid surface. On Earth, these craters are easily eroded or destroyed through endogenic processes. The Moon and Mercury, however, lack a significant atmosphere, meaning craters on these worlds remain intact longer, geologically. In this thesis, remote-sensing techniques were used to investigate impact melt emplacement about Mercury’s fresh, complex craters. For complex lunar craters, impact melt is preferentially ejected from the lowest rim elevation, implying topographic control. On Venus, impact melt is preferentially ejected downrange from the impact site, implying impactor-direction control. Mercury, despite its heavily-cratered surface, …


From Large-Scale Molecular Clouds To Filaments And Cores : Unveiling The Role Of The Magnetic Fields In Star Formation, Sayantan Auddy Jul 2018

From Large-Scale Molecular Clouds To Filaments And Cores : Unveiling The Role Of The Magnetic Fields In Star Formation, Sayantan Auddy

Electronic Thesis and Dissertation Repository

I present a comprehensive study of the role of strong magnetic fields in characterizing the structure of molecular clouds. We run three-dimensional turbulent non-ideal magnetohydrodynamic simulations (with ambipolar diffusion) to see the effect of magnetic fields on the evolution of the column density probability distribution function (PDF). Our results indicate a systematic dependence of the column density PDF of molecular clouds on magnetic field strength and turbulence, with observationally distinguishable outcomes between supercritical (gravity dominated) and subcritical (magnetic field dominated) initial conditions. We find that most cases develop a direct power-law PDF, and only the subcritical clouds with turbulence are …


High Resolution Spectroscopy Of The Hyades Giants, Antonio Martinez Apr 2018

High Resolution Spectroscopy Of The Hyades Giants, Antonio Martinez

Electronic Thesis and Dissertation Repository

The four K0IIIHyades red clump giants, γ , δ , ϵ , and θ 1Tauri, are ideal candidates for cool star research. They are easily observable at a distance of only 47 pc and one star, ϵ Tauri, is a suspected Maunder minimum star. These stars also provide a useful opportunity to investigate the nature of the photospheric velocity field, and assess the effectiveness of a range of spectroscopic tools including the merits of the microturbulence-macroturbulence approach to the study of cool star spectra. High resolution (λ /Δ λ ∼ 100,000) exposures, taken from January 2001 to October 2008 in …


Physical Properties Of Faint Meteors Through High-Resolution Observations, Dilini Subasinghe Nov 2017

Physical Properties Of Faint Meteors Through High-Resolution Observations, Dilini Subasinghe

Electronic Thesis and Dissertation Repository

Small, faint meteors (with masses between 10-7 and 10-4 kg) were once part of an asteroid or comet, and collide with Earth's atmosphere daily. Studying meteors is an effective way to survey the physical properties of their parent bodies. Meteor light curves and orbital information is easily obtained from wide-field observations, from which meteoroid structure can be inferred through meteoroid ablation modelling. A high-resolution narrow-field camera can provide much more detail about the poorly understood ablation processes and physical properties of the meteoroid. The goal of this thesis is to better understand the physical properties of meteors using …


Using Bolide Airwaves To Estimate Meteoroid Source Characteristics And Window Damage Potential, Nayeob Gi Jul 2017

Using Bolide Airwaves To Estimate Meteoroid Source Characteristics And Window Damage Potential, Nayeob Gi

Electronic Thesis and Dissertation Repository

We examined the far-field infrasonic signals produced by 78 bolides simultaneously detected by U.S. government sensors to determine the mechanisms responsible for interstation spreads in infrasound signal period. These signal period spreads lead to large variances in source energy estimates. Our analysis suggests that while acoustic source height contributes to some extent to the variance in signal periods, the range from the source to the station and in particular station noise plays a more significant role.

By simulating the near-field weak shocks from a suite of well-observed energetic fireballs, we have empirically estimated how often fireball shocks produce overpressure ( …


Investigating Brown Dwarf Atmospheres: Gravity, Dust Content, Cloud Structure And Metallicity, Kendra Kellogg Jul 2017

Investigating Brown Dwarf Atmospheres: Gravity, Dust Content, Cloud Structure And Metallicity, Kendra Kellogg

Electronic Thesis and Dissertation Repository

Brown dwarfs are the lowest mass products of star formation. Their low masses don't allow them to sustain, or sometimes even begin, the thermonuclear processes that provide stars with internal energy and the thermal pressure necessary to maintain hydrostatic equilibrium. Thus, their radii and effective temperatures decrease as they age, continually changing their spectral classification. However, it is now a well-known fact that the spectral appearance of ultra-cool dwarfs is governed by more than just temperature. Factors such as gravity, metallicity and cloud distribution play an important role in the structure and composition of ultra-cool dwarf atmospheres and ultimately their …


Detection And Characterization Of Extrasolar Planets Through Planet-Disk Dynamical Interactions, Maryam Tabeshian Apr 2017

Detection And Characterization Of Extrasolar Planets Through Planet-Disk Dynamical Interactions, Maryam Tabeshian

Electronic Thesis and Dissertation Repository

Structures observed in circumstellar disks may be caused by gravitational interaction with planetary or stellar companions. These perturbed disks are often signposts of planet birth in exoplanetary systems, and offer insights into the properties of both the disk and the perturbing planets. Therefore, structures observed in these disks provide a powerful tool for detecting and studying extrasolar planetary systems. In this work, we examine the link between disk structures and nearby/embedded planets using numerical simulations of both hypothetical and observed disk systems.

We demonstrate that gaps can be opened in dynamically cold debris disks at the mean-motion resonances (MMRs) of …


The Geometry And Density Of B-Emission Star Disks From Statistical Analysis And Numerical Simulations, Isabelle H. Cyr Nov 2016

The Geometry And Density Of B-Emission Star Disks From Statistical Analysis And Numerical Simulations, Isabelle H. Cyr

Electronic Thesis and Dissertation Repository

This thesis is divided into 3 investigations. First we present a novel method to estimate the opening angles of Be star disks from interferometric axis ratio measurements, using Bayesian statistics and Monte Carlo techniques. A large set of theoretical axis ratios generated from disk models were compared to observational samples to determine which distribution best reproduces the observations. We find that the observed axis ratio distributions in the K-, H-, and N-band can best be explained by the presence of thin disks while measurements over the H$\alpha$ line point toward slightly thicker disks. Second, using a smoothed particle hydrodynamics (SPH) …


The Circumstellar Environments Of B-Emission Stars By Optical Interferometry, Bethany Grzenia Oct 2016

The Circumstellar Environments Of B-Emission Stars By Optical Interferometry, Bethany Grzenia

Electronic Thesis and Dissertation Repository

A series of B-emission (Be) stars was observed interferometrically and numerically modelled to be consistent with the observations. Uniform geometrical disks were used to make first-order inferences about the configuration of the disk systems’ extended structures and their extent on the sky. Later, the Bedisk-Beray-2dDFTpipeline was used to make sophisticated non-local thermodynamic equilibrium (LTE) calculations of the conditions within the disks. In the first instance, sixteen stars were observed in the near-infrared (K-band, 2.2 micron) with the Palomar Testbed Interferometer (PTI). The Bedisk portion of the pipeline was used to model disk temperature and density structures for B0, B2, B5 …


Formation And Past Evolution Of The Meteoroid Complex Of Comet 96p/Machholz, Abedin Yusein Abedin Sep 2016

Formation And Past Evolution Of The Meteoroid Complex Of Comet 96p/Machholz, Abedin Yusein Abedin

Electronic Thesis and Dissertation Repository

The past dynamical evolution of the meteoroid streams associated with comet 96P/Machholz is investigated. The goal is to obtain a coherent picture of the past capture of this large comet into a short period orbit, and its subsequent breakup hierarchy. In particular, the aim is to constrain the earliest epoch that this large first precursor started to supply meteoroids into the interplanetary space. The fragments and meteoroid streams of that past cometary decay constitute a wide multiplex of interplanetary bodies, knows as the 96P/Machholz complex. The largest presently surviving fragment is comet 96P/Machholz, followed by a large amount of debris …


Emplacement Of The Foy, Hess And Pele Offset Dykes At The Sudbury Impact Structure, Canada, Eric A. Pilles Sep 2016

Emplacement Of The Foy, Hess And Pele Offset Dykes At The Sudbury Impact Structure, Canada, Eric A. Pilles

Electronic Thesis and Dissertation Repository

The 1.85 Ga Sudbury impact structure is the remnant of what is generally considered to have been an ~150–200 km diameter impact basin in central Ontario, Canada. The so-called Offset Dykes are impact melt dykes that are found concentrically around – and extending radially outward from – the Sudbury Igneous Complex (SIC), a ~3 km thick differentiated impact melt sheet. The dykes are typically composed of two main phases of granodiorite: an inclusion- and sulfide-rich granodiorite in the centre of the dyke, and an inclusion- and sulfide-poor granodiorite along the margins of the dyke. This study uses a combination of …