## Final Report Summary - AWE (Accurate Waveforms for Extreme/Intermediate-mass-ratio-inspirals (AWE))

The AWE project aims to further our knowledge about the gravitational-wave emission from small mass-ratio compact binary systems. The direct detection of gravitational-waves by the LIGO/VIRGO collaboration in 2015 has shown the utility of accurate modeling of binary black hole systems in extracting exciting astrophysics from the incoming signals. The future for this field will only become more exciting. One direction is the interest is small mass-ratio systems. In the extreme mass-ratio limit, with stellar mass object orbiting a massive black hole, these are source for the future space-based detector such as the Laser Interferometer Space Antenna, LISA. In the the intermediate mass-ratio case, with a stellar mass object orbiting a roughly one thousand solar mass black hole, these can be sources for ground-based detectors. Both intermediate and extreme mass-ratio inspirals (IMRIs and EMRIs) last a long time in the band of the detector with potential observing times ranging from 10s of seconds (for ground based detectors) to years (for space-based detectors). With all that we have learned from the first two gravitational wave detections, each lasting less than 1 second, one can only imagine the wealth of information we will learn about the universe from the long signals from small mass-ratio systems.

Modeling of small mass-ratio systems is tackled via black hole perturbation theory. The AWE project developed this approach in a number of interesting directions. At the end of the fellowship number of the work packages, as outlined in the Grant Agreement, have been computed and a total of 7 papers have been published in high-impact journals, with more in preparation for publication.

During the outgoing stage, hosted at the Massachusetts Institute of Technology (MIT), the research covered topics such as improved evolutions schemes for highly eccentric orbits; progress assessing the leading inspiral approximation scheme against the most accurate evolutions performed to date; progress extending black hole perturbation theory to second-order-in-the-mass-ratio; and the discovery of a new gravitational wave signature for the inspiral of a compact object into a rapidly rotating black hole. Let us address each of these areas now by describing the work performed and the main results achieved.

During the reintegration phase at University College Dublin (UCD) the project concentrated on adding additional physics to leading inspiral models, extending perturbation theory beyond linear order in the mass-ratio, accelerated motion in Schwarzschild spacetime, improvements to calculating perturbations in Kerr spacetime and the Black Hole Perturbation Toolkit, an open repository of software and results for black hole perturbation theory. Let us address each of these areas now by describing the work performed and the main results achieved.

Highly eccentric inspirals - Astrophysical EMRIs are expected to highly eccentric as the enter the detector band of LISA. Prior work modelling small mass-ratio systems, which the Fellow led during his PhD, had only reached eccentricities up to 0.2. This new work, in collaboration with Prof. Charles Evan's group at the University of North Carolina at Chapel Hill, extended the earlier work of the Fellow to cover the full astrophysical range of eccentricities from 0 up to 0.8.

Assessing the leading inspiral approximation scheme - A leading evolution scheme for EMRIs uses the self-force (which arises from the interaction of the body with its own metric perturbation and causes the smalled body to inspiral) to approximate the inspiral by a sequence of geodesics. It is know that this approximation introduces and error at order unity in the phase evolution of the systems, which could be problematic for accurate gravitational wave astrophysics if the coefficient of that error is not small. Working with Dr. Peter Diener of Louisiana State University and Dr. Barry Wardell at University College Dublin (UCD) has shown the coefficient is small for a scalar-field toy model, but unexpected technical hurdles have had to be overcome in order to make a code accurate enough to precisely quantify the unknown coefficient. This work is now almost complete and we expect to have interesting results in the coming months. After those results are published, we plan to turn to our attention the gravitational case.

Second-order perturbation theory - It is known that in order to model the phase evolution of a small mass-ratio binary to within one radian (a requirement to track the binary over its entire lifespan in the LISA band) we must push black hole perturbation theory beyond linear order. The necessary foundations for this advancement have been laid in the last few years and the Fellow has been part of the lead collaboration aiming to make the first practical calculation within this framework. Making calculations at second-order has required the development of new calculation techniques and the Fellow has published (along with Dr. Wardell) a paper on a aspect of the calculation for the gravitational case. Further collaboration with researchers at the University of Southampton has now brought us close to the first second-order result and there are plans for further work once this is complete. The current work is focused on the case where the massive black hole is not rotating.

The final topic is one that was not included in the original proposal. Working at MIT allowed the researcher to interact with other researchers in the Boston area and in particular the Fellow worked with researchers from Harvard Univesity. Together we explored the gravitational-wave emission from the inspiral of a compact object into an extremely rapidly rotating black hole. This work neatly brought together the numerical skills of the Fellow with the analytic skills of his collaborators Dr Sam Gralla and Achilleas Porfyriadis. The first work from that collaboration was published as Phys. Rev. D 92, 064029 (2015). A later follow up work identified a unique signature of the gravitational radiation from inspirals into rapidly rotating black holes. That work was undertaken by the Fellow and Dr Gralla and Prof. Scott Hughes and was published recently as Class. Quant. Grav. 33:155002 (2016). The Fellow presented this work to science journalists at the American Physical Society April meeting in Salt Lake City which lead to the publication of two popular science articles (http://www.space.com/32723-colliding-black-holes-sing-different-songs.html and https://www.sciencenews.org/article/how-make-gravitational-waves-sing). The Fellow also wrote an article for the Classical and Quantum Gravity blog (https://cqgplus.com/2016/08/23/inspiral-into-gargantua-where-science-meets-science-fiction/).

Evolution of an inspiral with a spinning secondary - This work extends the work undertaken during the first two years of the project to include the effect of the spin of the secondary on the inspiral phase. In particular, working with Prof. Charles Evan's group at the University of North Carolina at Chapel Hill, we extended the previous work of the collaboration to include conservative spin effects. Our calculation also covered binaries where the spin of the secondary was not aligned with the orbital angular momentum. This gave rise to the first calculation of an inspiral in Schwarzschild that was not confined to the equatorial plane of the black hole. This work has been published in Physical Review D. A nature extension of this work is to include the dissipative spin effects and I am currently working with researchers at Institut des Hautes Études Scientifiques in Paris, France, the University of Sheffield, UK and University College Dublin to calculate these effects.

Accelerated motion in Schwarzschild spacetime - This work forms part of a longer term goal to accurately compute so-called self-consistent inspirals. Self-consistent inspirals differ from previous inspiral models in that the self-force at each instance is computed from the past inspiraling worldline (whereas previous models have used the self-force along a tangent geodesic). This inspiraling worldline is accelerated with respect to the background spacetime geometry of the massive black hole. Thus to perform accurate self-force calculations we need to incorporate the effects of this acceleration into our models. This project has been undertaken with another Marie Curie IOF Fellow (based as UCD but currently working at the University of Florida) and researchers at Louisiana State University and University College Dublin. This work will be submitted for publication in the next week.

Improvements to calculations in Kerr spacetime - This ongoing work with Prof. Marc Casals at Centro Brasileiro de Pesquisas Físicas, Brazil and the University College Dublin group is providing more efficient algorithms to compute perturbations in Kerr spacetime using the Teukolsky formalism. This work is in the process of being written up for publication.

The Black Hole Perturbation Toolkit - This is an initiative setup by the Fellow between University College Dublin, the Massachusetts Institute of Technology and the University of North Carolina at Chapel Hill. The goal of the project is to make common tools that many research groups around the world have independently developed, available freely to all. This way more researcher time can be spent doing physics, and less time reinventing and coding the wheel. Some initial tools are already available at: https://blackholeperturbationtoolkit.github.io/.

Further information about the Fellow and his work can be found at his personal website: http://www.nielswarburton.net

Modeling of small mass-ratio systems is tackled via black hole perturbation theory. The AWE project developed this approach in a number of interesting directions. At the end of the fellowship number of the work packages, as outlined in the Grant Agreement, have been computed and a total of 7 papers have been published in high-impact journals, with more in preparation for publication.

During the outgoing stage, hosted at the Massachusetts Institute of Technology (MIT), the research covered topics such as improved evolutions schemes for highly eccentric orbits; progress assessing the leading inspiral approximation scheme against the most accurate evolutions performed to date; progress extending black hole perturbation theory to second-order-in-the-mass-ratio; and the discovery of a new gravitational wave signature for the inspiral of a compact object into a rapidly rotating black hole. Let us address each of these areas now by describing the work performed and the main results achieved.

During the reintegration phase at University College Dublin (UCD) the project concentrated on adding additional physics to leading inspiral models, extending perturbation theory beyond linear order in the mass-ratio, accelerated motion in Schwarzschild spacetime, improvements to calculating perturbations in Kerr spacetime and the Black Hole Perturbation Toolkit, an open repository of software and results for black hole perturbation theory. Let us address each of these areas now by describing the work performed and the main results achieved.

Highly eccentric inspirals - Astrophysical EMRIs are expected to highly eccentric as the enter the detector band of LISA. Prior work modelling small mass-ratio systems, which the Fellow led during his PhD, had only reached eccentricities up to 0.2. This new work, in collaboration with Prof. Charles Evan's group at the University of North Carolina at Chapel Hill, extended the earlier work of the Fellow to cover the full astrophysical range of eccentricities from 0 up to 0.8.

Assessing the leading inspiral approximation scheme - A leading evolution scheme for EMRIs uses the self-force (which arises from the interaction of the body with its own metric perturbation and causes the smalled body to inspiral) to approximate the inspiral by a sequence of geodesics. It is know that this approximation introduces and error at order unity in the phase evolution of the systems, which could be problematic for accurate gravitational wave astrophysics if the coefficient of that error is not small. Working with Dr. Peter Diener of Louisiana State University and Dr. Barry Wardell at University College Dublin (UCD) has shown the coefficient is small for a scalar-field toy model, but unexpected technical hurdles have had to be overcome in order to make a code accurate enough to precisely quantify the unknown coefficient. This work is now almost complete and we expect to have interesting results in the coming months. After those results are published, we plan to turn to our attention the gravitational case.

Second-order perturbation theory - It is known that in order to model the phase evolution of a small mass-ratio binary to within one radian (a requirement to track the binary over its entire lifespan in the LISA band) we must push black hole perturbation theory beyond linear order. The necessary foundations for this advancement have been laid in the last few years and the Fellow has been part of the lead collaboration aiming to make the first practical calculation within this framework. Making calculations at second-order has required the development of new calculation techniques and the Fellow has published (along with Dr. Wardell) a paper on a aspect of the calculation for the gravitational case. Further collaboration with researchers at the University of Southampton has now brought us close to the first second-order result and there are plans for further work once this is complete. The current work is focused on the case where the massive black hole is not rotating.

The final topic is one that was not included in the original proposal. Working at MIT allowed the researcher to interact with other researchers in the Boston area and in particular the Fellow worked with researchers from Harvard Univesity. Together we explored the gravitational-wave emission from the inspiral of a compact object into an extremely rapidly rotating black hole. This work neatly brought together the numerical skills of the Fellow with the analytic skills of his collaborators Dr Sam Gralla and Achilleas Porfyriadis. The first work from that collaboration was published as Phys. Rev. D 92, 064029 (2015). A later follow up work identified a unique signature of the gravitational radiation from inspirals into rapidly rotating black holes. That work was undertaken by the Fellow and Dr Gralla and Prof. Scott Hughes and was published recently as Class. Quant. Grav. 33:155002 (2016). The Fellow presented this work to science journalists at the American Physical Society April meeting in Salt Lake City which lead to the publication of two popular science articles (http://www.space.com/32723-colliding-black-holes-sing-different-songs.html and https://www.sciencenews.org/article/how-make-gravitational-waves-sing). The Fellow also wrote an article for the Classical and Quantum Gravity blog (https://cqgplus.com/2016/08/23/inspiral-into-gargantua-where-science-meets-science-fiction/).

Evolution of an inspiral with a spinning secondary - This work extends the work undertaken during the first two years of the project to include the effect of the spin of the secondary on the inspiral phase. In particular, working with Prof. Charles Evan's group at the University of North Carolina at Chapel Hill, we extended the previous work of the collaboration to include conservative spin effects. Our calculation also covered binaries where the spin of the secondary was not aligned with the orbital angular momentum. This gave rise to the first calculation of an inspiral in Schwarzschild that was not confined to the equatorial plane of the black hole. This work has been published in Physical Review D. A nature extension of this work is to include the dissipative spin effects and I am currently working with researchers at Institut des Hautes Études Scientifiques in Paris, France, the University of Sheffield, UK and University College Dublin to calculate these effects.

Accelerated motion in Schwarzschild spacetime - This work forms part of a longer term goal to accurately compute so-called self-consistent inspirals. Self-consistent inspirals differ from previous inspiral models in that the self-force at each instance is computed from the past inspiraling worldline (whereas previous models have used the self-force along a tangent geodesic). This inspiraling worldline is accelerated with respect to the background spacetime geometry of the massive black hole. Thus to perform accurate self-force calculations we need to incorporate the effects of this acceleration into our models. This project has been undertaken with another Marie Curie IOF Fellow (based as UCD but currently working at the University of Florida) and researchers at Louisiana State University and University College Dublin. This work will be submitted for publication in the next week.

Improvements to calculations in Kerr spacetime - This ongoing work with Prof. Marc Casals at Centro Brasileiro de Pesquisas Físicas, Brazil and the University College Dublin group is providing more efficient algorithms to compute perturbations in Kerr spacetime using the Teukolsky formalism. This work is in the process of being written up for publication.

The Black Hole Perturbation Toolkit - This is an initiative setup by the Fellow between University College Dublin, the Massachusetts Institute of Technology and the University of North Carolina at Chapel Hill. The goal of the project is to make common tools that many research groups around the world have independently developed, available freely to all. This way more researcher time can be spent doing physics, and less time reinventing and coding the wheel. Some initial tools are already available at: https://blackholeperturbationtoolkit.github.io/.

Further information about the Fellow and his work can be found at his personal website: http://www.nielswarburton.net