1. Globular Clusters and Streams(?) around the LMC. The LMC has a known globular cluster population (Bennett et al. 2022), and hints of some stellar streams (Navarrete et al. 2019). In this project, the student will first produce a homogeneous catalog of observations, and then examine the correspondence between the inferred orbits for globular clusters and stellar streams around the LMC to discern whether the streams could be disrupted globular clusters.

2. A (star's) journey to the centre of the galaxy. Galaxies seem to largely have concentrations of stars at their centre -- often called a 'bulge' -- and the Milky Way is found to be no different. Simulations largely reproduce this feature, but it is not clear if one mechanism driving stars to journey to the galactic centre, or if several factors compete to create the bulge. Worse, progress is severely hampered by a lack of clear definition for a 'bulge' (See also a recent discussion of data here) In this project, the student will develop definitions for bulges by applying creative new methods to simulated galaxies, and then using the definitions to examine Milky Way data (including full kinematic information from Gaia and chemical information from APOGEE). At the end of the project, we will have chosen a new definition for bulges that can be generically applied by simulators and observers alike. Time permitting, we will also look at pathways for individual stars to join the bulge feature and predict how some specific stars may have gotten to the centre of the Milky Way.

3. Pulsar Pairs Probe Potential (of the Milky Way) By detecting changes in the period of a binary pulsar orbit, one can compute the direct acceleration of the binary pulsar relative to Earth -- despite the accelerations being on the order of 0.00000000001 metres/second$^2$. This direct acceleration measurement is a new and unique probe of the Milky Way gravitational potential. However, the sample of binary pulsars only numbers in the 10s at present, which limits the confidence with which the galactic potential may be measured. In this project, we will use simulated Milky Way galaxies (see here and here) to model a binary pulsar population near Earth and investigate how well we can recover the Milky Way potential, both near Earth and beyond. In particular, we'll see if we can confirm or deny the existence of a population of massive, unseen objects.

4. Build-a-bar workshop. Models for galactic bars (e.g. NGC 1300) have previously taken two approaches: analytic models (such as for the Milky Way) or fully numerical simulations (such as the AURIGA simulation suite). Recently, we released a high performance computing software library -- EXP -- that can be used to represent galactic bars using basis function expansions. The basis function expansion technique allows for flexible construction of bar models, even directly from data. In this project, we will use the EXP machinery to expand a range of bar models from the literature to demonstrate the robustness of the basis function expansion technique. Then, we will integrate stars in the potential fields, and compare with observational data from external galaxies, constraining the range of possible bar orbital families.

5. Collecting halo star spectra. One of the major limitations in probing the outer reaches of our Milky Way galaxy is the lack of tracers. However, several studies have either targeted, or seredipitously discovered, distant halo stars. In this project, we will review the literature, looking for additional reports of halo stars. The product will be a collection of halo star positions, that can then be cross-matched with other data sources -- primarily Gaia -- and used to make a fuller picture of the Milky Way halo.

6. A stars in SDSS spectra. A-type stars come in several varieties, with two particular kinds I am interested in: Blue Horizontal Branch (BHB) and Blue Stragger (BS) stars. However, separating the two types of stars has proved to be difficult (Lancaster et al. 2019). In this project, we will use new summary statistics for BHB and BS stars to try and develop a classification system that more cleanly delineates the two.

1. Computing galaxy property uncertainties using the Bayesian beta distribution quantile technique. When considering a population of objects with a binary classification system (e.g. 'Does this galaxy contain a bar? yes/no'), it is straightforward to compute the number of each binary classification. However, estimating the uncertainty is not straightfoward. One technique to estimate confidence intervals relies on the binomial distribution. Following the algorithm laid out in Cameron (2010), in this project we will apply the binomial classification to barred galaxies in a cosmological simulation, and design software for release.

2. Dark matter velocity distribution descriptions with Bayesian blocks histogram technique. Binning quantities to create a histogram of values is a fundamental technique for compactly displaying data (see, e.g. here). Recently (Donaldson et al 2022), we characterised velocity distributions for dark matter particles in the solar neighbourhood using histograms. However, we can improve on the histogram using a novel technique called 'Bayesian blocks' (Scargle 1998). In this project, we will design a software package to perform Bayesian block calculations and apply the software to velocity distributions of particles in the solar neighbourhood, looking for features that depart from a smooth distribution -- possible indications of relic substructure from undigested galaxies. Extensions to the project will also consider generalised ways to find continuous-function generalisations of relevant functions (see, e.g. examples in this introduction).

3. Tilted ring models for galactic discs. Galactic discs in the real universe are observed in every possible orientation, yet simulations tend to prefer a single face-on view. In this project, we will bring published models for tilted ring dynamics to a public release, and then explore the implications of bringing in satellites to these systems. Extensions to the project will consider how thin galaxies may actually become, and designing models that represent the thinnest observed galaxies: proposed to be in tension with current cosmological models (e.g. as described here).

4. The orbital inclination instability. A newly-discovered instability in Keplerian systems is called the orbital inclination instability. Along with a dynamical description, the researchers published some code, but it can be refactored and made accessible. In this project, we will refactor and release the orbital inclination instability code, specifically asking whether this mechanism could be at play in barred galaxies.

1. Supercomputer energy analysis. One source of energy usage in astronomy is through supercomputers. See several recent works here, here, here, and mhere. As astronomers have largely not been trained as computer scientists, much of the software written by astronomers is inefficient and uses more energy than necessary. In this project, the student will build an accounting tool for simple software applications to try and inspire users to develop more efficient astronomical software. The student will also develop general recommendations for the IfA regarding computational efficiency and 'greening' of the computer systems. In particular, the student will make recommendations to optimise hardware usage (dynamically turning machines on and off) and/or make a software improvement 'cheatsheet'.

2. 3d orbit printing. The orbits of stars in the Milky Way can be hard to visualise -- particularly when the orbit is part of a larger structure, such as the galactic bar. Using the program Blender, the student will extract orbit data from high-resolution galaxy simulations and make novel visualisation of the orbits in 3d. Then, the 3d visualisations will be printed for both scientific study and public engagement purposes. The student will have an opportunity to engage with the ROE Visitor Centre.

3. History of the Royal Observatory Edinburgh. The Royal Observatory Edinburgh (ROE) was created with a donation by a wealthy patron, the Earl of Crawford. Several of the patron's writings are held in the Observatory's archives, and other historians have also written about the family (e.g. Hodgson 2020). In this project, we will read through some relevant source documents to add more context to presentations of the history of the ROE.

4. Finding paper diamonds in the rough. The Astrophysics Data System (ADS) is a powerful tool maintained by the Smithsonian Astrophysical Observatory. The service provides a powerful search tool that is presently underutilised by the average astronomer. Additional repositories exist for data (Zenodo) and consolidation of software. In this meta-project, the student will use ADS to design libraries for various research topics, and build a history report (examples: the history of 'supergiants',or non-astronomy papers citation trends in astronomy) on a topic of their choice. The student may also use the 'ads' Python package to perform queries interactively: see this blog post. Possible extensions for the project include research citation metrics/bibliometrics (see the infamous h-index and a cheeky take on the h-index), studying the promotion of papers (including the new service Altmetric), or building a web scraping tool to find 'trendy' papers. Or what about reflecting on changing author lists?

1. Analysing RR Lyrae stars with M-SSA (Multichannel Singular Spectral Analysis).In a recent paper, we brought a machine learning technique from climate science to astrophysics (Weinberg & Petersen 2021). The M-SSA technique has proved particularly fruitful for analysing simulations of galaxies. However, the technique is much more general than just galaxy simulations: M-SSA can pull repeat signals out of (almost) any time series data. In this project, we'll let M-SSA loose on a real data set from the Kepler telescope, which observed a number of bright RR Lyrae-type variable stars. During the project, we will extend the existing M-SSA framework to handle censored (missing) data. We will then look for standard oscillation periods and build templates for even more sparse datasets.

2. Modeling the escaper structure of globular clusters. Globular clusters and dwarf galaxies orbiting in the Milky Way tidal field will lose stars over time as they linger too close to the outskirts. We have recently developed an N-body technique to rapidly simulate different globular cluster orbits in the galaxy, similar to other recent work on the topic (Gieles et al. 2021). The student will analyse these simulations of globular clusters orbiting a Milky Way-like galaxy and examine their destruction. The student may also develop algorithms to classify the structure that develops in the tidal tails as a result of resonances, disc crossings, pericentre passages, and more.

3. Wavelet techniques for modelling gravitational fields. One limitation of current basis function expansion techniques is that they are global (i.e. no compact support). Spline bases are one way around this, but another is wavelet bases. In this project, the student will lay the groundwork by building a 1d wavelet representation of a gravitational model (parallel planes), and compare with a global basis solution.

Multiscale disequilibrium in the Milky Way, revealed by Gaia and dark matter models Disc galaxies are fragile structures that are constantly being pushed away from equilibrium -- not just by encounters with other galaxies, but sometimes by their own internal evolution. Even a protective dark matter halo can act as an amplifier for distortions -- through the dynamics of these processes are poorly understood. The next release of Gaia data will bring a new level of detail to observations of the Milky Way, our home galaxy. From stars that have been funnelled to the inner galaxy, to delicate stellar streams probing orbits in the galaxy, to distant halo stars recording the history of every interaction, a new generation of modelling techniques is required to make sense of deluge of data. In this PhD, a suite of projects will be undertaken around the theme of disequilibrium in the Milky Way, across all scales. The primary tool will be the development of a statistical treatment of disequilibrium features, with a focus on astrophysical 'noise' from small-scale potential fluctuations, induced by giant molecular clouds and dark matter subhalos. The statistical tool, once developed, will be coupled to high performance computing software to model the entire Milky Way. When combined with new Gaia data, this Milky Way model will be a rich galactic dynamics playground for studying regimes of disequilibrium in the Milky Way. The disequilibrium probes will get at a fundamental mystery in the Milky Way: how does dark matter constructively or destructively influence dynamical evolution?

1. Triaxiality measurement in idealised galaxies. Most galaxies in cosmological simulations appear to be triaxial. What does this mean for morphological structure?

2. Spin parameter and distribution in cosmological halos. We've known for more than twenty years that galactic dark matter halos have some angular momentum (Bullock et al. 2001). The angular momentum distribution has implications for the type of structure that can form in the disc inside these halos. In some pilot simulations, I found that the galactic bars that formed in dark matter halos were sensitive to the structure of the angular momentum profile (an idea also developed in Collier et al. 2021). In this project, the student will investigate these implications with more rigor by designing a tandem suite of analytic linear stability models, and also releasing more N-body models. This project will also be undertaken with a large-scale structure team at the University of Edinburgh. For more recent context, see this TNG100 paper.

1. What stars are in the Sagittarius stream? The Sagittarius dwarf galaxy has completed a handful of orbits around the Milky Way, leaving behind stars that escape the dwarf. Many of these left-behind stars have been detected (Belokurov et al. 2014), but at larger distances, it is less clear which stars used to be a part of Sagittarius. In this project, the student will look through a compiled list of stars with accurate distances to find those that may have been a part of the Sagittarius dwarf galaxy. The student will then compare the data against published models (Peñarrubia et al. 2010) for Sagittarius to help prepare for future generations of models.

2. The wandering Black Hole at the centre of the Milky Way. The centre of the Milky Way galaxy hosts a massive black hole, known as Sgr A*. The location of Sgr A* is well-determined (Gravity Collaboration 2019), but what is not known is how the location of Sgr A* relates to the centre of mass of the entire Milky Way. Several processes could dislodge Sgr A* from the exact centre of the galaxy, with a leading candidate being the infall of a massive satellite galaxy, the Large Magellanic Cloud (LMC). The LMC pulls the stellar disc of the Milky Way (Petersen & Peñarrubia 2020), but Sgr A* may not respond with the same intensity, leading to an offset between Sgr A* and the centre of the galaxy. In this project, the student will analyse a model of the Milky Way stellar disc, Sgr A*, and the LMC, measuring the displacement of Sgr A* from the centre of the galaxy.

3. Correcting velocities of satellite galaxies in light of the pull of the Large Magellanic Cloud. The Milky Way galaxy has dozens of orbiting satellite galaxies. The most massive of these satellites is the Large Magellanic Cloud. Because the LMC is approximately 20% of the mass of the Milky Way, it is able to provoke a reaction from the Milky Way disc, where the disc is pulled towards the LMC (Petersen & Peñarrubia 2020). As observers located in the disc of the Milky Way, our observations of the motions of satellite galaxies are biased by the pull of the LMC. Previous studies have used these biased satellite motions to propose groupings and/or alignments among satellites (Patel et al. 2020). In this project, the student will compute corrected velocities using a model for the LMC-induced motion. The student will then analyse the velocities of the satellites to look for unbiased groupings or alignments of satellites.

4. Predicting the density of Dark Matter from the Large Magellanic Cloud on Earth. Physicists are conducting many experiments on Earth in an attempt to detect elusive Dark Matter particles directly. A key ingredient in designing these experiments and interpreting the results is knowing the Dark Matter flux at Earth's location in the Milky Way, which may be strongly affected by galactic evolution (Petersen, Katz, Weinberg 2016). In addition to evolution taking place within the galaxy, the Milky Way is currently being influenced by its most-massive satellite, the Large Magellanic Cloud. With its centre only 50 kpc from the Milky Way centre, the Large Magellanic Cloud's Dark Matter halo likely reaches all the way to Earth, providing additional density for Dark Matter experiments to detect (Besla et al. 2019). In this project, the student will analyse a model of the Dark Matter structure in the combined Milky Way-Large Magellanic Cloud system to characterise the distribution of Dark Matter near Earth, making predictions for the affect on direct-detection experiments.

1. Quantifying the effect of resonances on solar neighbourhood kinematics. (Summer 2020) The Milky Way Galaxy is a complex system containing many stars which form the large-scale structure associated with being a "Spiral Bar Galaxy". The central bar is a region densely populated with stars which are thought to have been pulled in and gravitationally trapped over time. The central bar gravitationally influences the stars in the galaxy, which can result in changes to the orbital behaviour. The stars showing this behaviour can be identified using our modern galaxy simulation. The changes in orbital behaviour cause the galactic structure as a whole to evolve, for example forming denser stellar regions such as the spiral arms. The project will analyse the orbital behaviour of stars in the Milky Way and identify orbits in the solar neighbourhood which are influenced by the central bar. By looking at the early stages of the Milky Way's evolution, the origins of these orbital paths will be analysed.

2. Spiral structure kinematics of Milky Way analogues in the local Universe. (Summer 2020) Our vantage point on Earth makes determining Milky Way spiral structure more complicated than that of external galaxies. However, one can make progress on trying to interpret the local observations of the Milky Way through comparison to nearby galaxies. New data has recently become available that allows for the determination of the stellar motions, or kinematics, in nearby galaxies (SDSS MaNGA, an integral field unit survey). The project will focus on a subset of galaxies that are similar to the Milky Way in terms of spiral structure: How can we describe the kinematics, and what are the interesting features? How diverse are the kinematics between galaxies? Can we build models that explain the kinematic features? How can we use the measurements to inform models of the Milky Way? The student will learn to process spectra of galaxies to measure stellar kinematics and compare the measurements with a library of disc models. The project will use Python, and some experience is desirable, but not necessary.

3. Predictions for direct detection of Large Magellanic Cloud dark matter. (Summer 2021) Direct detection experiments seek to capture the nuclear recoil induced by weakly interacting massive particle (WIMP) dark matter interactions with baryonic matter. The inclusion of the Large Magellanic Cloud (LMC) in models of the Milky Way (MW) potential is expected to alter the signal for direct detection experiments. However, the LMC is not currently well-constrained, and thus, models for the direct detection signal are highly uncertain. In this project, the student will explore a selection of MW-LMC models to build relationships between detection rates and LMC+MW properties.

4. The role of the interloping Triangulum galaxy in sculpting the Andromeda galaxy. (Summer 2022) In this project the student will investigate the ongoing interaction between the two galaxies Andromeda and Triangulum: First, the student will build up-to-date numerical models of the two galaxies. Second, the student will search for plausible orbits of Triangulum around Andromeda, using the latest proper motion data from the Gaia satellite. Third, the student will design high performance N-body simulations to study the full time-dependent evolution of the interaction. The models will be used to diagnose the state of dark matter disequilibrium around Andromeda, resulting in predictions for the distribution around both galaxies.

5. Comparing dark matter velocity distributions from simulations, using the upgraded Kolmogorov-Smirnov techniques and survival analysis. (Summer 2022) Recently (Donaldson et al 2022), we characterised velocity distributions for dark matter particles in the solar neighbourhood using cumulative density functions (CDFs). CDFs allow for direct comparison between multiple distributions, with a half-century of statistics underpinning. In the first part of the project, we will develop a software package that is a clean implementation of CDF comparison techniques.

6. Closed disc orbits in 3d. (Summer 2023) Most orbits in a galactic disc (or halo) will fill an entire torus, given enough time. However, orbits that are in resonance will repeat tracks that only probe a small fraction of the torus. This was an idea I used in an earlier paper on commensurate orbits in discs. Following the commensurability paper, the student will extend the algoritm to 3d. This is computational geometry at its heart (Delaunay Triangulation). The first algorithm can be published (see here for code that needs refactoring), and then extended to 3d. This project can also be designed as a more computationally heavy project, with JAX integration of orbits.

7. Derivation of 2d basis functions for surface density decomposition of MaNGa galaxies. There is a whole industry built around describing the structure of galaxies using computational techniques (e.g. for a recent example, see Miller & van Dokkum 2021). Basis function expansions are a natural way to compress information, but haven't been applied in any significant way to galaxy data (despite the idea being around for almost 50 years for simulations: Kalnajs 1976) In Section 5.3 of Weinberg & Petersen (2021), we lay out some mathematics to do face-on descriptions of galactic discs, using a Fourier-Laguerre expansion on simulated data. In this project, we will extend the Fourier-Laguerre basis to real data. The project is primarily focused on developing the mathematics behind the expansions, and then applying the expansions to real data. There are some big improvements to be made to the Fourier-Laguerre basis: in particular, we could use PCA-like procedures to define a new empirical basis to even more efficiently compress the information. The point of the information compression is to have some sort of uniform way of describing galaxies so that we can look for structural trends, such as describing the structure of spiral arms.