Chaotic Dynamics in N-body systems

Ever since Isaac Newton in 1687 posed the N-body problem, astronomers have been looking for its solutions in order to understand the evolution of dynamical systems, such as our own solar system, star clusters and galaxies. The main difficulty is that small errors grow exponentially, so that numerical solutions diverge easily from the mathematical solution. This thesis presents two new state of the art N-body algorithms, one of which is designed for high precision (Brutus) and the other for speed (Sakura). The assumption that N-body results are accurate in a statistical sense, is put to the test for three-body configurations. Finally, a new mathematical model is constructed that describes the origin of chaos in a dynamical systems, and explains the short Liapounov time of Comet Halley's orbit.Computational astrophysic

Relativistic Pythagorean three-body problem

Computational astrophysic

Stellar triples on the edge.: Comprehensive overview of the evolution of destabilised triples leading to stellar and binary exotica

Stars and planetary systemsInterstellar matter and star formatio

Chaos in self-gravitating many-body systems: Lyapunov time dependence of N and the influence of general relativity

Computational astrophysic

A MODEST review

We present an account of the state of the art in the fields explored by the research community invested in 'Modeling and Observing DEnse STellar systems'. For this purpose, we take as a basis the activities of the MODEST-17 conference, which was held at Charles University, Prague, in September 2017. Reviewed topics include recent advances in fundamental stellar dynamics, numerical methods for the solution of the gravitational N-body problem, formation and evolution of young and old star clusters and galactic nuclei, their elusive stellar populations, planetary systems, and exotic compact objects, with timely attention to black holes of different classes of mass and their role as sources of gravitational waves. Such a breadth of topics reflects the growing role played by collisional stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next decade, many revolutionary instruments will enable the derivation of positions and velocities of individual stars in the Milky Way and its satellites and will detect signals from a range of astrophysical sources in different portions of the electromagnetic and gravitational spectrum, with an unprecedented sensitivity. On the one hand, this wealth of data will allow us to address a number of long-standing open questions in star cluster studies; on the other hand, many unexpected properties of these systems will come to light, stimulating further progress of our understanding of their formation and evolution.Comment: 42 pages; accepted for publication in 'Computational Astrophysics and Cosmology'. We are much grateful to the organisers of the MODEST-17 conference (Charles University, Prague, September 2017). We acknowledge the input provided by all MODEST-17 participants, and, more generally, by the members of the MODEST communit

On the reliability of N-body simulations

Computational astrophysic

A triple star origin for T Pyx and other short-period recurrent novae

Recurrent novae are star systems in which a massive white dwarf accretes material at such a high rate that it undergoes thermonuclear runaways every 1-100 yr. They are the only class of novae in which the white dwarf can grow in mass, making some of these systems strong Type Ia supernova progenitor candidates. Almost all known recurrent novae are long-period (Porb ? 12h) binary systems in which the requisite mass supply rate can be provided by an evolved (sub-)giant donor star. However, at least two recurrent novae are short-period (Porb ? 3h) binaries in which mass transfer would normally be driven by gravitational radiation at rates three to four orders of magnitude smaller than required. Here, we show that the prototype of this class - T Pyxidis - has a distant proper motion companion and therefore likely evolved from a hierarchical triple star system. Triple evolution can naturally produce exotic compact binaries as a result of three-body dynamics, either by Kozai-Lidov eccentricity cycles in dynamically stable systems or via mass-loss-induced dynamical instabilities. By numerically evolving triple progenitors with physically reasonable parameters forward in time, we show explicitly that the inner binary can become so eccentric that mass transfer is triggered at periastron, driving the secondary out of thermal equilibrium. We suggest that short-period recurrent novae likely evolved via this extreme state, explaining their departure from standard binary evolution tracks.</p

Newton versus the machine: Solving the chaotic three-body problem using deep neural networks

Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system’s chaotic nature. We show that an ensemble of converged solutions for the planar chaotic three-body problem obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at a fixed computational cost and up to 100 million times faster than the numerical integrator. In addition, we demonstrate the importance of training an ANN using converged solutions from an arbitrary precise integrator, relative to solutions computed by a conventional fixed precision integrator, which can introduce errors in the training data, due to numerical round-off and time discretization, that are learned by the ANN. Our results provide evidence that, for computationally challenging regions of phase space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black hole binary systems or the origin of the core collapse in dense star clusters.Computational astrophysic