There is a wide range of LISA-related research taking place in Ireland cover topics such as waveform modelling, astrophysics, and instrumentation. We briefly summarize the research of the groups in Dublin, Maynooth, Cork, and Galway below.

## Relativity Group at University College Dublin

The UCD Relativity Group has a broad range of interests in the study of motion in general relativity, especially in the treatment of the two-body problem. In particular, the group has expertise in perturbative methods including the gravitational self-force approach, black hole perturbation theory, post-Newtonian, and post-Minkowskian methods. Using a range of analytic and numerical techniques, these approaches are applied to develop gravitational waveform templates for data analysis with the LISA and LIGO-Virgo-KAGRA interferometers.

A particular focus of the group is the construction of fast and faithful waveform models for extreme mass ratio inspirals (EMRIs). These are a key class of LISA sources in which a much smaller compact object gradually spirals into a supermassive black hole. Such black holes are usually found at the centres of galaxies. Modelling EMRIs is a challenging task, not least because of the complicated orbital motion of the compact object around the massive black hole — see the figure to the left. The slow, multi-year-long inspiral enables the detailed probing of the spacetime around the black hole. Detection and measurement of such systems’ parameters will also inform us about the environments in galactic centres, the multipole nature of the black hole spacetime, and offer new means to test Einstein’s theory of General Relativity.

The UCD group are also a co-leads (with the University of Southampton) in second-order self-force calculations. These models unlock the full potential of EMRI science LISA and also provide a path to model elusive intermediate mass-ratio inspirals (IMRIs).

## Maynooth Black Holes

LISA will have the capacity to detect the mergers of massive black holes out to high-z (z > 10) being particularly sensitive to black holes in the range 1e4 to 1e7 Msolar. This mass range encompasses the so-called “Intermediate Mass Black Holes” range. However, these black holes, due to their intrinsic size and luminosity, are particularly challenging to detect. Moreover, their number densities are completely unknown.

The Maynooth Black Holes group use state-of-the art computational and theoretical models to probe the formation and growth of astrophysical black holes in the early Universe. If, as predicted, black holes grow from seeds (see Figure 1) to eventually form the super-massive black holes we observe today then they must pass through the intermediate stage (see Figure 2). Therefore to know the abundances of the Intermediate mass black holes we need to know the abundances of the seeds. Therefore the question of the abundances of these massive black hole seeds then becomes centre stage. If we know the abundance of the seeds, then we can also estimate how many mergers of intermediate mass black holes should happen in our Universe. This is what LISA should see!

As the time to LISA’s launch decreases, the fidelity of our numerical models increases allowing us to make more and more accurate predictions for the number densities of massive black holes in our Universe. To do so our computer models need to model the formation of virtual universes encompassing galaxy formation, star formation and black hole formation and the multitude of physical processes that accompany all of these observables. The recently launched JWST space telescope has shown us that massive black holes exist and are growing in the early Universe. These (EM) observations are already helping to constrain our models. Of course ultimately what we need is LISA’s observations to constrain our models even further!

## University College Cork

Dr Mark Kennedy studies compact objects in binary star systems. He is interested in what these systems can tell us about the nuclear equation of state and whether the observed mass gap between neutron stars and black holes in our Galaxy is real. LISA will be able to detect new neutron star and black hole binaries to further inform our understanding. As a member of the ULTRACAM team, Mark is involved in the precise timing of ultra compact binaries with periods in the range of minutes. These systems are losing a significant amount of their angular momentum through gravitational wave emission and can be used as verification binaries for LISA once it is operational.

Dr Michael Tremmel uses high resolution cosmological simulations to study the formation, growth, and dynamical evolution of massive black holes in galaxies. Using large-scale simulations like Romulus, his group predicts what the population of MBHs (and binary MBHs) across different environments over cosmic time. His group also uses zoom-in simulations of individual galaxies to study MBHs at unprecedented detail. Such simulations are crucial in predicting and understanding the nature of the MBH binaries and mergers LISA will be detecting.

The image above shows a zoom-in simulation of an early merger between low mass galaxies resulting in a binary MBH (black holes shown as x’s). Mergers like these will likely make up the majority of events detected by LISA and can provide invaluable clues to the formation and early evolution of MBHs in the Universe.

## University of Galway

Nicholas Devaney and Fiona Kenny (now at Atlantic Technological University) have studied Beam propagation simulations for LISA in the presence of telescope aberrations.

Above is an example is from a simulation showing pathlength errors introduced by random combinations of defocus and astigmatism in the transmit telescope where there is +/- 0.1 microradians of tilt jitter, for different beam types (uniform or Gaussian).