It has been longer than I intended since my previous post, however the scientific cogs have still been whirring. I am extremely pleased to say that I will be moving back to theoretical physics, after my brief foray into the world of the astrophysicists. From the new academic year I will be moving to the University of Southampton to start a PhD in the gravity group, working on gravitational waves and binary systems. This, I could not be happier about – an area at the forefront of theoretical physics, combining my love for gravity, black holes and space missions! So what better to do first, than write a post presenting an overview of why this area of research is exciting and what hopes it has for advancing our understanding of the universe.

Back in 2017, I wrote a post on gravitational waves here at RTU, describing how such waves are generated. I briefly explained that, in order for the waves to be currently detectable, the sources need to be extremely massive i.e. colliding neutron stars or black holes. Just as with any other astronomical observation, to pick out a clear signal, one needs to know what they are looking for in the data. Here’s where the theory comes in; systems such as black hole binaries (two black holes locked in orbit around each other) are complex solutions, but of course solutions nonetheless to Einstein’s equations of motion. The field of numerical relativity uses numerical methods and algorithms to solve Einstein’s equations for such complex, dynamical systems. Solutions of the Einstein Field Equations that we can solve fully by hand represent only trivially simple systems in nature and astrophysical binaries certainly don’t fall into this box. Equipped with computer clusters, we can now computationally model these systems and theoretically compute the templates of the gravitational waves they would emit.

Such computational methodology works well when the two objects in the binary system are roughly the same size – i.e. when their mass ratio is roughly 1. The two objects circle each other a handful number of times before spiralling inward and amalgamating into one fat mass. This process is known as an inspiral. Key point being, the number of orbits undertaken during the inspiral in this case is relatively small and consequently, the evolution of the system can be computationally run in a reasonable amount of time. When the two entities of the binary are of roughly equal mass it is known as a Comparable Mass Ratio Inspiral (CMRI). Our success with numerical relativity in this area has led to the LIGO gravitational wave detector spotting eleven of such events since 2015! Detailed descriptions of such inspirals have been a major computational effort in gravitational research for recent decades. The ability to predict the exact pattern of gravitational waves for such systems, allows for meaningful observation and it can be safely said that gravitational waves have now firmly entered the domain of the observational.

*Artists impression of the gravitational waves from a CMRI system*

The challenge comes when we move from objects of comparable mass to those of disparate mass. Of particular interest is the set up where the larger object is a factor of 10,000 *or more* heavier than it’s partner in the system. This type of binary system is called an Extreme Mass Ratio Inspiral (EMRI) and is often embodied in nature by a supermassive black hole at the center of a galaxy, being orbited by a stellar mass black hole. Because the little black hole is so much smaller than its partner, it exhibits between *10^(5)-10^(6)** *orbits before eventually plunging in. The examination of the gravitational waves from such a system would provide us with a wealth of knowledge. Due to the thousands of orbits, the gravitational wave signal encodes highly detailed mapping of the spacetime geometry surrounding the super massive black hole. You can think of the little black hole as tracing out the structure of spacetime with each encircling and transmitting this information in the form of gravitational waves.

*Artists impression of an EMRI system’s spacetime curvature*

Results from such set ups would be extremely accurate tests for the predictions of Einstein’s theory of General Relativity in the regime of strong gravity – a regime which has largely been untestable thus far. Additionally, the data from such an inspiral would give in profound insight into parameters of the components, such as mass and angular momentum. This would hugely help theoretical physicists validate their hypotheses on the *types* of black holes that exist.

Due to the colossal number of orbits in an EMRI system, modelling the gravitational waveforms with numerical relativity would be highly computationally expensive, if not impossible. However, large mass difference in the EMRI case *can* be used to our advantage, providing us with a highly accurate approximation scheme to solving the Einstein equations. Approximation schemes, are often used in theoretical physics and center around expanding equations about a small perturbative parameter – in the case of EMRI’s we expand in one over the mass ratio of the two objects. The Einstein equations are perfectly accepting of a perturbative expansion in powers of such a parameter and in the case of EMRI systems the mass ratio can be as small as 10^(-6). At first order of the expansion, the path of the lighter object is simply treated as that of a massive test particle, affected solely by the gravity created by the larger black hole. Then, order by order we add corrections into the equations, to account for the mass of the lighter object and the small effective force it imposes. This force is known as the gravitational self-force. In fact, it has been estimated that reaching the second-order expansion will be sufficient for accuracy in the gravitational waveform templates, allowing for detection of EMRI systems from data gathered by the upcoming gravitational wave detector, LISA. This analysis of EMRI systems is a key area of research of my supervisors to be, Professor Leor Barack and Dr. Adam Pound, and one where they have already had great success.

*Artists impression of the LISA space mission*

LISA, a space-based observatory to detect gravitational waves, is planned to launch in the early 2030s. The sensitivity of LISA will peak in the mililihertz band, the frequency range at which EMRI systems will emit gravitational waves. However, even if an EMRI system is very close, its signal will still be much weaker than the instrumental noise gathered by LISA. Such is the problem when trying to catch such extraordinarily sensitive signals that are buried in detector noise. To maximise the science return from the multi-billion dollar mission it is vital that the theoretical waveform models are derived accurately, in advance. Then, the data from LISA can be matched up against these theoretical templates, acting as a filter against the noise, allowing us to clear signals. Getting the EMRI waveforms right would unlock a wealth of scientific information. The encoding of the geometry of spacetime in the gravitational waves, would provide profound insight into our understanding of gravity in the strong regime – we just need the wave template cipher.

To recap, we have the comparable mass binary systems (i.e. two similar size black holes) whose gravitational waves have been detected by LIGO, for which numerical methods have proved fruitful to model. And, the extreme mass binary systems, key LISA targets, for which we are using our perturbative tricks to model. A third system sits between these, the logically named Intermediate Mass Ratio Inspiral (IMRI). IMRI systems are those for which the mass ratio is around 1000. They would be embodied in nature by either an intermediate mass black hole around a supermassive black hole (case 1) *or *a stellar mass black hole around a intermediate mass black hole (case 2). There is doubt around the existence of such systems however, as intermediate black holes have not *yet* been proven to exist.

Being the middle sibling in this situation, means neither of our above methods for theoretical waveform modelling can do the trick. The accuracy of the perturbative expansion in the mass ratio method severely deteriorates as the parameter is no longer small, yet the number of orbits remains large. Such a set up thus requires a hybrid approach and this is what my PhD will hope to investigate. But let me end by telling you why this last case is worth cracking. As well as providing the first confirmation of the existence of an intermediate mass black hole, observations of IMRI gravitational waves will allow us to probe the dynamical processes in globular clusters and galactic nuclei. Rich astrophysical insights are up for grabs, along with fundamental knowledge on black hole formation and morphology. In case 1 IMRI’s, since the central object is large, gravitational waves are produced at a low frequencies. Such systems would then be detectable by the capabilities of LISA in the future. In case 2, IMIRI’s the central object is smaller, producing higher frequency gravitational waves which could actually be detectable by the currently running Advanced LIGO instrument. Tantalising prospects, whereby discoveries are theoretically possible as soon as we have the correct gravitational wave templates against which to filter the LIGO data.

Gravitational waves, black holes and all things gravity will return to being a central theme here at RTU. Posts in the near future will also include a more in-depth look at IMRI systems and the workings of the LISA instrument. A journey to catching waves starts here.