Prof. Dr. Alessandra Buonanno

Research Achievements – Prof. Dr. Alessandra Buonanno

In September 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected for the first time a gravitational wave passing through the Earth – a scientific discovery of historic importance, which was made possible by the forceful and outstanding work of about a thousand scientists over the last three decades. This revolutionary discovery was rewarded with the Physics Nobel Prize in 2017.

The detected gravitational wave was the result of a violent astronomical event – the collision of two black holes. Since this momentous event in 2015, the field of gravitational wave astronomy has been flourishing: Four more mergers of binary black holes were detected, and in August 2017 the first binary neutron-star merger was observed, thanks also to the Vir- go detector, in combination with dozens of electromagnetic follow-up observations, allowing unprecedented insights into these extreme astrophysical objects. Picture 1 (explanation see below)

Gravitational waves were predicted by Albert Einstein over 100 years ago, however he him- self did not believe that they would ever be detected, since the signal of a gravitational wave is extremely small: The minuscule change in length that had to be detected by Advanced LIGO is one hundred thousand times smaller than the size of an atomic nucleus, even for a violent event such as the collision of two black holes of several solar masses, colliding at almost the speed of light. This makes not only the detection a herculean challenge but also the interpretation of the signal, since fingerprints of the source’s characteristics are encoded in the particular shape and time dependence of the gravitational-wave signal. The other challenge is the complexity of Einstein’s field equations: Even with current state-of-the-art com- puters, purely numerical solutions are prohibitively difficult to find due to the high computa- tional cost and very long computation times.

The first of these two challenges was overcome by the ingenuity and tenacity of several ex- perimentalists and the LIGO Scientific Collaboration. Prof. Dr. Buonanno has significantly contributed to solving the second challenge. This consisted in combining analytical techniques, which provide us with approximate solutions to Einstein’s equations, and which can be computed fast and efficiently, with numerical techniques, which are very precise but com- putationally expensive. In 1999, as a postdoctoral researcher, Buonanno invented the so- called effective one-body (EOB) approach together with Prof. Dr. Thibault Damour. Similar to how the two-body problem in Newtonian physics can be significantly simplified to the motion of a reduced mass in an effective central potential, the two-body problem in general relativity can also be reduced to one of a test-body moving in the dynamical space-time of an effective black hole. While still highly complex, this novel approach allows for much more efficient computation and the inclusion of perturbative and non-perturbative effects, and led to the first analytic prediction of the full gravitational waveform from a binary black hole coalescence.

Research Achievements – Gottfried Wilhelm Leibniz Prize 2018 Prof. Dr. Alessandra Buonanno DFG February 2018

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Indeed, the most dynamical and non-linear phase of the binary black hole evolution occurs when they end their long inspiral with a plunge, merge with each other, and leave behind a deformed black hole. The latter eventually settles down to a spherical or oblate shape after getting rid of its deformations by emitting gravitational waves into the surrounding space- time, a process called “ringing”.

Soon after its original formulation, Buonanno and her group worked to improve the new approach, using results from analytic and perturbative methods, and also from numerical relativity. The latter became available only in 2005 thanks first to the work of Prof. Dr. Frans Pre- torius of Princeton University, and then of Prof. Dr. Manuela Campanelli’s group of Rochester Institute of Technology and Prof. Dr. Joan Centrella’s group of NASA Goddard Flight Space Center. Together with Prof. Dr. Cook of Wake Forest University and Prof. Dr. Pretorius, Prof. Dr. Buonanno carried out the first comprehensive analysis of numerical relativity simulations. This work unveiled several important physical characteristics of the three main stages of the coalescence process, notably the inspiral, the merger and the ringdown, and paved the way to subsequent work aimed at building fast, analytic templates for gravitational-wave searches. Buonanno furthermore compared numerical and analytical results, showing that several predictions of the EOB theory were indeed correct. The successes of the EOB formalism where further corroborated by subsequent detailed studies done by Buonanno’s group at the University of Maryland and the Max Planck Institute for Gravitational Physics.

The LIGO problem of finding very weak signals in the data stream is analogous to the problem of recognising voices in an environment with very high background noise. For this pur- pose, LIGO uses several hundred thousand filters and templates and matches them against the detector output. Templates need to be generated fast and very accurately, so that data can be analysed efficiently without missing the signal. Prof. Dr. Buonanno and her group initiated several research directions aimed at developing the most accurate, physical and efficient template bank for the searches of binary black holes by Initial LIGO (2005–2010), and then by Advanced LIGO (2015–present). On one side, this work relies on sophisticated studies to include other physical effects in the waveform models, and extends the EOB theory to binary systems composed of neutron stars, thus including effects due to matter and tides, and black holes with spin, whose presence makes the two-body dynamics and gravitational waveforms even more complicated, creating modulations to the gravitational-wave train. On the other side they improved and completed the EOB formalism by including non-perturbative and non-linear information close to merger, eventually extending the templates to the entire parameter space.

Picture 2 (explanation see below)

Prof. Dr. Buonanno’s ultimate research goal is to exploit current and future gravitational-wave detectors on the ground and in space to test gravity in the strong-field, highly dynamical re- gime, probe extreme matter and fundamental physics. To achieve this goal, her group is de-

Research Achievements – Gottfried Wilhelm Leibniz Prize 2018 Prof. Dr. Alessandra Buonanno DFG February 2018

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Beyond her core expertise in modelling gravitational waves, Buonanno has also pioneered studies in quantum-optical noise and high-precision measurements for gravitational-wave detectors. Those experiments achieve so accurate measurements of position that we have to consider quantum limitations and deal with the Heisenberg uncertainty principle. The latter, if applied naively to the test masses (i.e., hanging mirrors) of a gravitational-wave interferometer, produces a free-mass standard quantum limit (SQL) on the interferometer’s sensitivity: the more accurately we measure the test-mass displacement at a given time, the larger the disturbance we impose onto the test-mass velocity, the less accurately we can measure the test-mass displacement at later times. It is possible to circumvent SQL’s by changing the designs of the instruments.

In 2001, Prof. Dr. Buonanno, and Prof. Dr. Yanbei Chen of Caltech demonstrated that the optical configuration of Advanced LIGO, can beat the free-mass SQL, if thermal noise can be pushed low enough. This is due to correlations between photon shot noise and radiation pressure noise (somewhat resembling test-mass displacement and test-mass momentum, respectively), which until their work were assumed to be uncorrelated. Their analyses re- vealed a new optomechanical effect (optical-spring effect), which was then verified experi- mentally in the 40-metre interferometer at Caltech and in table-top optical-cavity experiments at MIT and AEI in Hannover. Their result predicted new noise curves for Advanced LIGO, and continue to have an impact in the community as studies targeted to next generation of gravitational-wave detectors, which will operate in 10–15 years, are taking off.

Explanation picture 1: Numerical relativity simulation of the first binary black-hole merger observed by the Advanced LIGO detectors on September 14, 2015. The image shows the two inspiraling black holes and the gravitational waves emitted. © S. Ossokine, A. Buonanno (Max Planck Institute for Gravitational Physics), Simulating eXtreme Space-times project, D. Steinhauser (Airborne Hydro Mapping GmbH)

Explanation picture 2: The third gravitational wave signal (GW170104) as observed by the Advanced LIGO detectors in Hanford and Livingston. The maximum-likelihood binary black hole waveform given by the full-precession model developed in Buonanno's division is shown in black. The bottom panel shows the residual detector noises after substracting the model. © LIGO/Phys. Rev. Lett. 118, 221101

Research Achievements – Gottfried Wilhelm Leibniz Prize 2018 Prof. Dr. Alessandra Buonanno DFG February 2018