Professor David Merritt explains his interest in astrophysics and the focus of his current research. Describing the improvements made to the computational algorithms, he highlights the importance of taking into account the effects of relativity in these calculations

Could you describe what led to your interest in modelling complex astrophysical systems?

I’ve long been fascinated by the connection between the microscopic and the macroscopic in physics. A persistent feature of many complex systems is the emergence of coherent (macroscopic) behaviour from the seemingly random interactions of microscopic ‘agents’ – molecules in a gas, individuals in a population, stars in a galaxy, etc. The questions we pose as scientists are usually at the macroscopic level (eg. how does a galaxy evolve?), but the best way we have to address them is via simulations based on the microscopic physics (eg. how do individual stars move?). Such simulations

sometimes reveal modes of behaviour that are strikingly simple yet totally unexpected.

Your current project focuses on the dynamical evolution of dense clusters of stars and stellar remnants around supermassive black holes (SBHs) at the centre of galaxies. Why is this important?

A star like the Sun would be tidally torn apart if it came sufficiently close to an SBH. Partly because of tidal effects, the only objects that we expect to find very near an SBH are ‘compact remnants’: neutron stars and stellar-mass black holes, the dense leftovers from the evolution of massive stars. These remnants can interact through ‘gravitational encounters’: close passages that exchange energy and gradually change orbits. From time to time, such interactions cause a remnant to be scattered into the SBH. The resulting capture event will change the mass and spin of the SBH, but it can also result in an observable burst of gravitational waves. Detecting gravitational waves is currently a major focus for theoretical physicists, who would like to use the observed properties of the waves to test Einstein’s theory of gravity.

Is there anything novel about the computational algorithms that you are using to simulate clusters of stars around SBHs?

Standard N-body algorithms work very well when close encounters between stars are rare and when the simulation time is limited to a few orbital periods. But they

can be inefficient when applied to galactic nuclei, because motion is dominated by the presence of the SBH. A star or stellar remnant will complete millions of orbits around the SBH before coming close enough to another star to be perturbed, but it is those perturbations that are driving the collective evolution. The computer code needs to follow the unperturbed orbit about the SBH with extremely high precision: otherwise the effects of the small perturbations will be swamped by numerical errors.

Why is it important to take into account the effects of relativity when simulating the evolution of nuclear star clusters?

One insight that comes from my group’s research is that the effects of relativity can be crucial even for stars that spend most of their time far away from SBHs. The effects of relativity depend less on the size of an orbit than on its distance of closest approach to the SBH. Very eccentric orbits bring a star near to the SBH once each orbital period, even if that star spends most of its time much farther away.

What is the significance of the extreme mass ratio inspiral (EMRI) problem?

EMRI refers to a particularly interesting mode of stellar remnant capture by an SBH. If the remnant is scattered onto a highly eccentric orbit about the SBH, gravitational waves emitted during times of closest approach will extract energy from the orbit. The prospect of detecting gravitational waves from the

Relativity, torque

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THE ORIGIN AND evolution of the Universe and its components – stars, planets and galaxies – has long fascinated scientists, resulting in considerable research. Today, our knowledge of the Universe is rapidly advancing, enabled by generous funding and expertise behind exploration efforts. One project in particular is attempting to elucidate the processes involved in the formation of galaxies and specifically their central structures.

The centers of galaxies contain supermassive black holes (SBHs), which are believed to provide the gravitational energy underlying quasars and other energetic phenomena. But galactic nuclei have remained largely mysterious, shrouded in a cloak of dust or simply too far away to resolve.

OBSERVATION AND SIMULATION

Using both snapshots in time produced by instruments such as the Hubble Space Telescope and advanced computational modelling algorithms, scientists are gaining important insights into the physical processes that shape galactic centres. Understanding the physical principles that underlie the dynamical evolution of galactic nuclei is the ambition of Professor David Merritt from the Rochester Institute of Technology (RIT) in New York and his colleagues.

Merritt, an experienced astrophysicist, shares the now commonly held belief that the centres of galaxies contain one or more supermassive black holes (SBHs). He and his colleagues want to understand how clusters of stars evolve and congregate near the middle of galaxies under the influence of central SBHs. In an attempt to understand this behaviour, the group has developed advanced algorithms that can simulate these processes.

Finance is central to all modern, large-scale research efforts. Merritt and his team have been highly successful in attracting funding,

having secured US $458,000 in the form of a grant from the NASA Astrophysics Theory

programme – which awarded funding to only 28 projects from a pool of 181

submissions – and an award of US $252,200 from the National

Science Foundation. These

funds have allowed the group to embark upon a three-year research project studying the evolution of galactic nuclei.

FOCUSING ON THE INFREQUENT

Many different types of algorithm are employed in the modelling of stellar interactions. Traditionally, a set of algorithms called N-body codes have been used: “Standard N-body codes follow the evolution of N stars as they move in response to their mutual gravitational attraction,” explains Merritt. These codes are good for understanding infrequent interactions between stars within a limited simulation period, but the conditions in the centres of galaxies are far different, necessitating a new approach.

In the central parts of galaxies, stars and stellar remnants such as neutron stars orbit an SBH millions of times before a close interaction occurs with another stellar body. As these interactions are believed to be the driving force behind the evolution of galactic centres and are poorly understood, they are the main theme of the group’s modelling efforts. One of their key collaborators has helped the group to make headway on this problem by creating a computational code which accurately tracks normal orbits of stellar bodies around SBHs and focuses on moments of interaction which drive the holistic evolution of the galaxy: “My collaborator Seppo Mikkola at Tuorla Observatory developed a new scheme called ‘algorithmic regularisation’ specifically for

Modelling galactic nuclei

A team led by a researcher from the Rochester Institute of Technology has secured significant funding to conduct a three-

year research project into the evolution of galactic nuclei. The aim is to better understand the interactions of supermassive black holes

with stars and stellar remnants, and their role in galaxy evolution

inspirals was one of the primary motivations behind the proposed laser-interferometer space antenna (LISA). LISA could have detected low-frequency gravitational waves from EMRIs occurring almost anywhere in the observable Universe. Unfortunately, NASA chose to withdraw financially from the LISA project in 2011, but design work is continuing on a scaled-down version.

Do you anticipate any new directions for your research?

Astrophysicists believe that SBHs are rapidly spinning. According to general relativity, a spinning black hole exerts a torque on matter orbiting around it. There is also an equal and opposite back-reaction: the orbiting matter exerts a torque on the black hole, causing its spinaxis to precess, in much the same way that a spinning top precesses due to the torque exerted by its weight. This mutual spin-orbit interaction has a number of important consequences for the joint evolution of SBHs and galactic nuclei, but many of the details remain unresolved. N-body algorithms are an ideal tool for exploring this complex problem.

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PROFESSOR DAVID MERRITT

simulating galactic nuclei,” highlights Merritt. Mikkola’s new algorithm is much faster than existing codes, making it more efficient and allowing the research to focus on the events considered most important.

THE PROMISE OF GRAVITATIONAL WAVE

One way that an orbiting object can be captured by a SBH is through gravitational perturbations from other stars, in much the same way that Jupiter scatters comets into the Sun. But a more interesting capture channel is called an EMRI, or extreme-mass-ratio inspiral. An EMRI will follow a more gradual pattern, spiralling inwards over multiple orbits as it emits gravitational waves, causing its orbital energy to decrease. The detection of gravitational waves from EMRIs would enable astrophysicists to accurately measure the mass and angular momentum of the SBH, as well as testing Einstein’s theory of gravity.

Merritt and his colleagues were the first scientists to successfully apply an N-body code to the EMRI hypothesis. When they did so the results were startling: “When we adapted Mikkola’s new algorithm to this problem in 2011, a striking and unexpected phenomenon appeared which we call the ‘Schwarzschild barrier’,” he explains.

This phenomenon acts in such a way as to ‘repel’ inspiralling bodies from the eccentric orbits that would otherwise lead to capture as EMRIs. Critically, the presence of the Schwarzschild barrier reduces the frequency of predicted EMRI events.

Since this discovery, Merritt and his team have worked on understanding the principles behind this new phenomenon: “We believe we now understand each part of this cycle, but we would never have predicted the existence of such an effect if we had not observed it in the N-body simulations,” he underlines.

TO COALESCE OR NOT TO COALESCE

Another aim of Merritt’s research is to better understand the theorised coalescence of two SBHs in a binary system. These massive binaries are predicted to occur during the merger of two galaxies – a relatively common event in the timescale of the Universe. Once the two galaxies have merged, the two central SBHs become locked in orbit a few to a few tens of

parsecs apart. In order for the two SBHs to coalesce into a single body, the system must be stripped of huge amounts of energy. Emission of gravitational waves is one mechanism capable of removing this energy, but before gravitational wave emission can be efficient, the two SBHs must somehow be brought much closer together than a parsec.

Recent work by Merritt and his team has made notable inroads into this problem by illustrating that the interaction between binary SBHs and nearby stars is efficient enough to bridge this gap: “This is important, because while every SBH seems to be accompanied by stars, only a fraction are associated with appreciable amounts of gas,” he explains.

The findings made by the RIT investigators have already provided important contributions to the science of galactic nuclei and their evolution. Their contributions to the EMRI hypothesis and SBH coalescence have also changed the way scientists think about these events. Holding great promise for contributions to tomorrow’s astrophysics, the work represents the forefront of theoretical astrophysics. Despite impressive success, the need for technology capable of detecting gravitational waves in deep space highlights the necessity of continued investment in both the people and tools of future astrophysics. Only with this in place can we hope to unlock more of the deep secrets of the Universe.

DYNAMICAL STUDIES OF THE CENTERS OF GALAXIES

OBJECTIVES

To study the dynamical evolution of dense clusters of stars and stellar remnants – white dwarfs, neutron stars and black holes – around super-massive black holes (SBHs) in the centers of galaxies like the Milky Way. This project will use a new computational algorithm that can efficiently simulate systems with larger numbers of gravitating bodies. The effects of spin of the SBH will be included for the first time; spin induces a frame-dragging torque on the orbits, and an inverse torque exerted by the orbiting bodies on the SBH, altering its spin direction. Further simulations will study clusters containing a distribution of remnant masses and clusters containing binary black holes.

KEY COLLABORATORS

Tal Alexander, Weizmann Institute, Israel

Seppo Mikkola, Tuorla Observatory, Finland

Eugene Vasiliev, Lebedev Physical Institute, Moscow, Russia

Clifford Will, University of Florida, Gainesville, USA

FUNDING

National Science Foundation – award no. 1211602

National Aeronautics and Space Administration – award no. NNX13AG92G

CONTACT

Professor David Merritt Principal Investigator

School of Physics and Astronomy Rochester Institute of Technology Office: CAR A100 85 Lomb Memorial Drive Rochester, New York 14623, USA

T +1 585 475 7973 E merritt@astro.rit.edu

http://ccrg.rit.edu/people/merritt

DAVID MERRITT is an American Astrophysicist and Professor at the Rochester Institute of Technology (RIT), New York. He received his PhD in Astrophysical Sciences from Princeton University and held postdoctoral positions at the University of California, Berkeley and the Canadian Institute for Theoretical Astrophysics in Toronto. His fields of specialisation include dynamics and evolution of galaxies, supermassive black holes, and computational astrophysics. Merritt is a former Chair of the Division on Dynamical Astronomy of the American Astronomical Society. He is founder of the Center for Computational Relativity and Gravitation at RIT.

The findings made by the Rochester Institute of Technology

investigators have provided important contributions to the science

of galactic nuclei and their evolution

THE SCHWARZSCHILD BARRIER (SB) IN A SIMULATION OF EXTREME-MASS-RATIO INSPIRALS

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