Last update: 06.2022

This document contains a list of possible thesis projects in the fields of gravitational waves, numerical relativity and computational physics for the MSc in theoretical physics.

Students will be involved in the activities of the group, that include seminars, journal club, and outreach.

For more information you can contact Sebastiano Bernuzzi via email or telephone [+49 (0)3641 9 47111].

**Projects list**

- Deep neural networks for gravitational-wave astronomy
- Apparent horizon for parallel numerical relativity simulations
- Gravitational waveforms from black hole neutron star binaries
- Final black hole produced by the collision of a black hole and a neutron star
- Binary black holes with large mass-ratio
- Black hole formation via the collapsar scenario
- Neutrino annihilation above binary merger remnants
- Systematics of neutrino driven winds from binary mergers
- Parametric study of the properties of matter ejected by neutrinos in binary mergers
- Dual foliation implementation of the wave equation on hyperboloidal slices
- YinYang grids for numerical relativity

Gravitational-wave observations of events like black holes or neutron star mergers and supernova explosions are a new and invaluable tools to investigate fundamental (astro) physics in extreme regimes. A key challenge posed by these observations is the efficient analysis of a large data stream and the identification/extraction of physical information from the noise. For example, LIGO-Virgo experiments in science mode produce about a TB/day for several months, part of which is scanned with matched filtering technique to detect signal from mergers of black holes and neutron star.

Deep learning is a set of computational techniques used to automatically inform ("train") a computer ("machine") for feature detection or classification from raw data. Successful implementations of deep learning include image processing, voice recognition, medical diagnosis, and gene expression classification. These methods can be very efficient in identifying a signal/pattern, especially if combined with implementation on graphics-processing-unit hardware.

The use of deep learning techniques in gravitational-wave astronomy is subject of intense research, albeit still limited. Deep learning techniques appear to very promising for noise and glitch classification and also for the detection of signals. This project's focus is on the exploration of deep learning techniques for the detection of gravitational-wave transient from neutron star mergers.

References

- "Matching matched filtering with deep networks in gravitational-wave astronomy" H.Gabbard, M.Williams, F.Hayes, C.Messenger Phys. Rev. Lett. 120, 141103 (2018)
- "Machine Learning Gravitational Waves from Binary Black Hole Mergers" S. Schmidt et al Phys. Rev. D 103, 043020 (2021)

Black holes spacetimes are characterized by the presence of an even horizon. The event horizon is a causal boundary and a global property of the spacetime. Different, quasi-local (i.e. defined on a time-slice of the spacetime) definitions of horizons, have played an important role in understanding the role of singularities and black hole in general relativity (Penrose, Hawking, Ashtekar and others). For example, a marginally outer trapped surface (MOTS) in a time-slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion. An apparent horizon is defined as a MOTS not contained in any other MOTS.

Computing the event horizon from numerically generated spacetimes require to first calculate the four dimensional spacetime and then to separately post-process all the data. In contrast, an apparent horizon can be calculated during the simulation and is a key diagnostic in numerical relativity. Apparent horizon finders are algorithms that solve a nonlinear elliptic partial differential equation for the surface shape, using the metric of spatial hypersurfaces. The goal of this project is to implement an efficient AHF for parallel simulations employing adaptive-mesh-refinement.

References

- "Event and Apparent Horizon Finders for 3+1 Numerical Relativity" J. Thornburg Living Reviews in Relativity volume 10, Article number: 3 (2007)

Gravitational waves observations by LIGO/Virgo might probe the existence of a class of compact binaries composed of a black hole and a neutron star. Such "mixed binaries" are candidates for gamma-ray-burst and kilonova events engines. Waveforms models are necessary to estimate masses and spins of the objects from the LIGO/Virgo observations.

An analytical model for the gravitational waveform emitted by neutron star binaries has been proposed in [1]. The model can, in principle, also describe mixed binaries. The goal of this project is to test the model's performances against a set of numerical relativity simulations, [2].

References

- "Modeling the dynamics of tidally-interacting binary neutron stars up to merger", S. Bernuzzi, A. Nagar, T. Dietrich, T. Damour Phys. Rev. Lett. 114, 161103 (2015)
- "Gravitational waves from spinning black hole-neutron star binaries: dependence on black hole spins and on neutron stars' equations of state" K. Kyutoku, H. Okawa, M. Shibata, K. Taniguchi Phys. Rev. D84, 064018, (2011)

Gravitational waves observations by LIGO/Virgo might probe the existance of a class of compact binaries composed of a black hole and a neutron star. Such "mixed binaries" are candidates for gamma-ray-burst and kilonova events engines. Waveforms models are necessary to estimate masses and spins of the objects from the LIGO/Virgo observations.

An open problem in the modeling of mixed binaries is the prediction of the properties of the final black hole resulting from the collision [1,2]. The goal of this project is develop such a predictive formula using data from numerical relativity simulations [2,3].

References

- "The Black Hole Remnant of Black Hole-Neutron Star Coalescing Binaries", F. Pannarale Phys. Rev. D 88, 104025 (2013)
- "Hierarchical data-driven approach to fitting numerical relativity data for nonprecessing binary black holes with an application to final spin and radiated energy" Xisco Jiménez-Forteza et al Phys. Rev. D 95, 064024 (2017)
- "Gravitational waves from spinning black hole-neutron star binaries: dependence on black hole spins and on neutron star equations of state" K. Kyutoku, H. Okawa, M. Shibata, K. Taniguchi Phys. Rev. D84, 064018, (2011)

The merger of two stellar-mass black hole (BH) has been identified as the source of the first gravitational wave measured on Earth on September 2015. The interpretation (and observation) of the LIGO event was possible thank to the theoretical knowledge of the dynamics and radiation as predicted by first principle calculations in general relativity. A worldwide effort is ongoing to push these calculations to the whole binary black hole parameter space, which is composed of all the possible values of BH masses and spins, and to produce detailed waveforms and remnant predictions.

Binary black hole configurations with large mass ratio, q=M1/M2>~100, cannot be simulated in numerical relativity due to the enormous computation cost of those simulations. As an alternative approach one can employ black hole perturbation theory.

This project explores the dynamics of such large-mass ratio black hole binaries using an approximate approach that combines time-domain simulations in black hole perturbation theory with analytical methods [1]. Different directions are possible: development of an analytical radiation reaction guided by perturbative simulations [2,3], study of the final black hole and its quasi normal mode excitation, and a study of the radiation fluxes absorbed by the black hole.

References

- "Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis" S.Bernuzzi & A.Nagar Phys. Rev. D81 084056 (2010)
- "Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform" S.Bernuzzi, A.Nagar, A.Zenginoglu Phys. Rev. D83 064010 (2011)
- "Spinning test-body orbiting around Schwarzschild black hole: circular dynamics and gravitational-wave fluxes" E.Harms et al Phys. Rev. D 94, 104010 (2016)
- "The most powerful astrophysical events: gravitational-wave peak luminosity of binary black holes as predicted by numerical relativity" D.Keitel, et al Phys.Rev. D96 no.2, 024006 (2017)
- "Periastron Advance in Black-Hole Binaries"A.Le Tiec, A.H.Mroué, L.Barack, A.Buonanno, H.P.Pfeiffer, N.Sago, A.Taracchini Phys.Rev.Lett.107:141101, (2011)

The cores of a large fraction of the most massive stars (i.e., stars starting their life with more than ~15 Msun) are expected to collapse at the end of their life and to form a black hole (BH). Beside giving rise to a population of stellar BH (which is now partially accessible via GW observations of compact binary mergers), this process is expected to play a significant role in the so-called collapsar model for failed supernovae and gamma-ray bursts. The quantitative modelling of the BH formation and its subsequent growth due to the accretion of the stellar envelope is numerically challenging.

In this project, we will study the BH formation process and the accretion of matter inside the horizon in the context of general relativistic hydrodynamics, including realistic and detailed models of stellar collapse.

Co-advisor: Albino Perego (Trento U).

References

- "Very Low Energy Supernovae from Neutrino Mass Loss" Lovegrove E., Woosley S.E., Astrophys. J., 769, 2, 109 (2013)
- "Black Hole Formation in Failing Core-Collapse Supernovae" O'Connor E.P., Ott C.D., Astrophys. J., 730, 2, 70 (2011)

The annihilation of neutrino-antineutrino pairs is considered one of the viable mechanisms powering gamma-ray burst and a relevant process in the evolution of binary neutron star merger remnants. Calculations of the annihilation rates are computationally expensive and require large computational resources.

In this project, we would like to perform a detailed study of the properties of neutrino pair annihilation based on the outcome of full GR binary NS merger simulations. We will use advanced computational methods to compute the annihilation rates and to study their variability with respect to the properties of the merging system and of the remnant.

Co-advisor: Albino Perego (Trento U).

References

- "Neutrino pair annihilation above merger remnants: implications of a long-lived massive neutron star" A.Perego, H.Yasin, A.Arcones Journal of Physics G (2017)

The interaction between neutrinos and matter in the remnant of binary neutron star mergers drives the ejection of matter from the remnant inside the so-called neutrino-driven winds. The amount of ejected matter and its properties make this ejection channel unique and peculiar.

Up to now, neutrino-driven wind studies focused on a limited set of models. In this project, we would like to extend the present analysis to several different models, differing mainly by the mass of the merging neutron stars. This study will allow to explore how the properties of the wind correlates with the properties of the emitted neutrino radiation and, ultimately, with the properties of the merging system.

Co-advisor: Albino Perego (Trento U).

References

- "Neutrino-driven winds from neutron star merger remnants" A.Perego et al MNRAS, Volume 443, Issue 4, p.3134-315 (2015)
- "Neutrino-driven Winds in the Aftermath of a Neutron Star Merger: Nucleosynthesis and Electromagnetic Transients", D.Martin et el. Astrophys. J. Volume 813, Issue 1, article id. 2, 14 pp. (2015)

The interaction between neutrinos and matter in the remnant of binary neutron star mergers drives the ejection of matter from the remnant inside the so-called neutrino-driven winds. The amount of matter ejected and its properties makes this ejection channel unique and peculiar. Detailed hydrodynamical models allows to study the evolution of fluid elements inside the wind. However, large uncertainties in the neutrino and nuclear physics are still present and deserve a deeper analysis. This information is crucial to predict the properties of the ejecta and their impact on the electromagnetic counter parts of binary NS mergers.

In this project, we would like to perform parametric studies of the properties of the ejecta, starting from results of the detailed simulations. More specifically, we would like to study the sensitivity of the fluid element evolution with respect to the neutrino fluxes, to the neutrino interactions and to a more detailed treatment of the formation of nuclei.

Co-advisor: Albino Perego (Trento U).

References

- "Neutrino-driven winds from neutron star merger remnants" A.Perego et al MNRAS, Volume 443, Issue 4, p.3134-315 (2015)
- "Neutrino-driven Winds in the Aftermath of a Neutron Star Merger: Nucleosynthesis and Electromagnetic Transients", D.Martin et el. Astrophys. J. Volume 813, Issue 1, article id. 2, 14 pp. (2015)
- "Detectability of compact binary merger macronovae" Rosswog, et al CQG, Volume 34, Issue 10, 104001 (2017)

An open problem in numerical relativity is the implementation of a 3+1 decomposition of Einstein's equations on hyperboloidal slices. Hyperboloidal foliations allow one to incorporate null-infinity in the simulation domain, with two main advantages: the treatment of the outer boundary becomes trivial and the radiation fields can be computed accurately and unambiguously. A possible approach to hyperboloidal evolutions is the dual foliation formulation of general relativity, which relates the geometries of two foliations of the spacetime [1]. The dual foliation formalism, however, can be applied to first order formulations of Einstein equation [2], but not yet to second order ones like for example the popular BSSN or Z4c. The goal of the project is to investigate an implementation of the second-order wave equation on hyperboloidal slices using the dual foliation formalism.

Co-advisor: David Hilditch (CENTRA, Lisbon).

References

- "Dual Foliation Formulations of General Relativity" D.Hilditch, https://arxiv.org/abs/1509.02071
- "The evolution of hyperboloidal data with the dual foliation formalism: Mathematical analysis and wave equation tests" D.Hilditch et al. https://arxiv.org/abs/1609.08949

Spherical coordinates are ideal for many astrophysical problems, including isolated stars and black holes, accretion disks and supernovae explosions. However, the coordinate singularities at the poles and the convergence of the spherical grid lines near the poles pose serious problems for the use of these coordinate in numerical applications. An approach that retains such coordinates but allows one efficient computations, is the use of multiple patches (hence grids) to cover the sphere. The Yin-Yang grid design, in particular, has several interesting features: it uses the minimum number of patches (two); the two component grids are the same size and shape; the component grid is nothing but a low latitude part of the usual spherical polar coordinate (latitude-longitude) grid, which is orthogonal and has the well-known simple metric. This project aims at exploring the use of Yin-Yang grids for their use in numerical general relativity.

References

- "'Yin-Yang grid': An overset grid in spherical geometry", A.Kageyama, T.Sato, Geochemistry Geophysics Geosystems, 2004, Vol 5, Number 9.
- "YinZhong grid: An overset grid system for a sphere", H. Hayashi and A. Kageyama Journal of Computational Physics, 305, 2016
- "An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows", A.Wongwathanarat, N.J.Hammer, E.Müller Astron.and Astrophys., 2010, 514.
- http://www.research.kobe-u.ac.jp/csi-viz/members/kageyama/yin_yang_grid/index.html