## Overview

NZGravity is coordinating applications for several PhD scholarships within an interdisciplinary team to work on gravitational wave astronomy and statistical data analysis for the LISA mission. The cross-institutional research team spans astrophysics, cosmology, mathematics and statistics with members at five New Zealand universities as well as international collaborators within the International LISA Consortium.

Space-based gravitational wave science raises deep challenges regarding source modelling and numerical simulation and requires new statistical methodologies. We are seeking highly motivated and skilled students with a strong background in mathematics, statistics, physics or a related discipline, with sound computing skills and a keen interest in interdisciplinary research in gravitational wave science. All PhD and MSc candidates will have the opportunity to join the NZ Gravity Group, obtain academic support from an interdisciplinary supervisory team and will contribute to cutting-edge research for the LISA mission. The PhD scholarships will be available from March 2022 and provide an annual (tax-free) stipend of NZ$35,000 plus tuition fees for three years. Starting dates are flexible throughout the year.

More details about each of the PhD projects including the required skillsets and supervisors can be found below. Admissions decisions will be made by individual universities – please direct initial enquiries to the supervisors of specific projects that interest you or send general queries to Professor Richard Easther and Professor Renate Meyer.

*Please note that all New Zealand universities currently require students and staff to be vaccinated against Covid-19. *

## List of **Projects**

**Supermassive Black Holes and Ultralight Dark Matter****Searching for Dark Matter using Observations of Black Hole Spin****Triple Stars into BPASS****Bayesian tools for gravitational wave data analysis****Bayesian strategies for noise modelling and estimation of the stochastic gravitational wave background with LISA****Searching for the low-frequency stochastic gravitational-wave background using a Pulsar Timing Array****Gravitational wave scattering from black holes**

**Project** Descriptions

**Supermassive Black Holes and Ultralight Dark Matter**

Ultralight dark matter scenarios propose that cosmological dark matter consists of a self-gravitating quantum fluid; matter that obeys the Schrodinger equation and contributes to (and feels) the Newtonian gravitational potential. ULDM models involve very low mass particles (on the order of 10^{-21 }eV) with corresponding Compton wavelengths of up to a kiloparsec. ULDM is of interest as it has the potential to resolve “small scale” problems sometimes attributed to conventional dark matter scenarios while preserving its successes at larger scales. This project will look at the dynamics of SMBH interacting with ULDM at the centres of galaxies — the region in which we expect to see the largest departures from conventional dark matter, focusing on the implications for merger dynamics and gravitational wave production in these systems.

Skillset: Physics (quantum mechanics and dynamics), computing and (ideally, but optionally) some exposure to galactic astrophysics.

**Contact:**

Richard Easther, University of Auckland

**Searching for Dark Matter using Observations of Black Hole Spin **

Observations of rotating black holes have the potential to constrain or detect light bosonic fields that have been proposed as dark matter. Ultralight bosonic fields around spinning black holes can trigger a superradiant instability. The resulting emission extracts angular momentum via gravitational wave emission which can reduce the effective black hole mass by up to a few per cent. This project will utilise current astrophysical observations to place bounds on the presence of light bosonic dark matter and create detailed forecasts for the ability of LISA to constrain these scenarios.

Skillset: General relativity and cosmology; computing.

**Contact: **

Chris Gordon, University of Canterbury

(w. Richard Easther and Jörg Frauendiener)

**Triple Stars into BPASS **

Interacting binary stars play a key role in the evolution of stellar populations and there is growing observational evidence that triple and multiple star systems are also numerous in the Universe. These systems are critical to gravitational wave astronomy as they can source both transient and stochastic backgrounds. This project will create a numerical architecture for the investigation of triple star systems by extending the Binary Population and Spectral Synthesis code (see https://bpass.auckand.ac.nz), identifying systems where the evolutionary pathways differ from those of single or binary stars and then creating new, detailed evolutionary models and adapting extant scenarios [see e.g. Chrimes et al. (2020, MNRAS, 491, 3479] to understand the evolution of these systems. The successful PhD candidate will join the international BPASS team and the NZ Gravity Group.

Skillset: Astrophysics and numerical modelling.

**Contact:**

J.J. Eldridge and Richard Easther, University of Auckland

**Bayesian tools for gravitational wave data analysis**

** **Extreme Mass-Ratio Inspirals (EMRIs) are among the most fascinating LISA sources but the signal templates are challenging to compute with the necessary accuracy. A typical EMRI signal will be observed by LISA for about 10,000 orbits making it especially sensitive to waveform inaccuracies. Consequently, Bayesian inference for features of interest is often computationally expensive and subject to model misspecification.** **This project focuses on statistical computing in Bayesian inference with gravitational wave applications using state-of-the-art statistical methods and machine learning techniques. The goal is to develop novel statistical computing methods to deal with challenges in Bayesian inference with complex models, overcoming current limitations of traditional techniques. In particular, we will focus on Bayesian calibration for posterior approximation, robust inference, and deep learning approaches with accurate numerical waveforms. This PhD position will be at the interesting overlap between computational statistics, Bayesian analysis, machine learning and astrophysics.

Skillset: Statistics, computer science, mathematics, information engineering, astrophysics, or a closely related discipline.

**Contact: **

Matt Edwards and Kate Lee, University of Auckland

**Bayesian strategies for noise modelling and estimation of the stochastic gravitational wave background with LISA**

The research project will investigate novel statistical strategies for parameter estimation of gravitational wave signals observed by the Laser Interferometer Space Antenna (LISA). One aim is to estimate the power spectrum of the stochastic gravitational wave background produced by the emission from all galactic binaries. In collaboration with astrophysicists and data scientists, the candidate will further develop methods to extract, map, and separate the galactic background from the primordial gravitational wave background. Another aim is to develop novel Bayesian methods for mitigating the influence of detector and background noise on the estimation of gravitational wave signals observed by LISA. The focus will be on robust nonparametric Bayesian methods for spectral density estimation that can take the idiosyncrasies of LISA measurements into account such as correlations between the channels, non-stationarities induced by LISA’s orbital motion for long-lived signals, glitches and data gaps.

Skillset: Statistics, astrophysics or a related relevant discipline; time series, Bayesian nonparametrics, strong computing skills.

**Contact: **

Renate Meyer, University of Auckland and Matt Parry, University of Otago

**Searching for the low-frequency stochastic gravitational wave background using a Pulsar Timing Array **

The primary aim of this project is to increase the sensitivity of Pulsar Timing Array (PTA) experiments to the low-frequency stochastic gravitational wave background, such as the signal expected to be generated by a Universe full of supermassive black holes that orbit each other after galaxies merge. This objective will be pursued by developing novel methods of detecting and mitigating correlated systematic errors using Bayesian inference and noise modeling techniques. PTAs require accurate physical and statistical modeling of the definition of time on Earth, the masses of objects in our Solar System, the density of free electrons in both the Solar wind and the interstellar medium, and the orbital dynamics of neutron stars. This project will advance the state-of-the-art in measuring the phase of a pulsar’s periodic signal and detecting and modeling the inaccuracies that are induced by observatory instrumentation. The successful PhD candidate will join an international team of physicists and statisticians as part of the International Pulsar Timing Array community, the ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav), and the NZ Gravity Group.

Skillset: Statistics, astrophysics or a related relevant discipline; Bayesian data analysis, Monte Carlo methods, time series, machine learning methods, strong computing skills.

**Contact: **

Willem van Straten and Patricio Maturana-Russel, Auckland University of Technology

**Gravitational wave scattering from black holes**

Much is known about quasi-normal modes, i.e., the characteristic response of a black hole to small perturbations. Much less is known about the reaction of a black hole to a large deformation. We have developed a computational framework called COFFEE to solve the equations of General Relativity and can use it to study the reaction of a Schwarzschild black hole to the impact of a large burst of gravitational waves and to measure the scattered radiation at infinity. In this way we can determine the energy-momentum and angular momentum transfer between black hole and the incoming and scattered gravitational waves. The preferred starting date is 01/06/2022 or earlier.

*In several PhD projects we want to generalize this to the full family of Kerr-Newman black holes, in particular to the Reissner-Nordström and the Kerr black holes.*

Skillset: Programming skills in Python or similar languages and a good understanding of the general relativistic background are desirable.

**Contact: **

Jörg Frauendiener, University of Otago