The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be divided into separate two-body orbits with distinct time and length scales, such that one orbit is only mildly affected by the gravitation of the other bodies. Previous work has mapped the stability of such systems at varying resolutions over a limited range of parameters, and attempts have been made to derive analytic and semi-analytic stability boundary fits to explain the observed phenomena. Certain regimes are understood relatively well. However, there are large regions of the parameter space which remain unmapped, and for which the stability boundary is poorly understood. We present a comprehensive numerical study of the stability boundary of hierarchical triples over a range of initial parameters. Specifically, we consider the mass ratio of the inner binary to the outer third body ( $q_\mathrm{out}$ ), mutual inclination (i), initial mean anomaly and eccentricity of both the inner and outer binaries ( $e_\mathrm{in}$ and $e_\mathrm{out}$ respectively). We fit the dependence of the stability boundary on $q_\mathrm{ out}$ as a threshold on the ratio of the inner binary’s semi-major axis to the outer binary’s pericentre separation $a_\mathrm{in}/R_\mathrm{p, out} \leq 10^{-0.6 + 0.04q_\mathrm{out}}q_\mathrm{out}^{0.32+0.1q_\mathrm{out}}$ for coplanar prograde systems. We develop an additional factor to account for mutual inclination. The resulting fit predicts the stability of $10^4$ orbits randomly initialised close to the stability boundary with $87.7\%$ accuracy.

The research of James Croll on the nature of Ice Ages led him into a detailed investigation of ocean currents. By the early 1870s he had calculated from first principles the quantities of heat delivered by ocean currents to high latitude areas and he understood how this heat supply may have altered drastically during ice ages. The publication of his many papers on ocean currents as well as his book, Climate and Time, coincided with Challenger expedition that, in 1872, embarked on a 4-year voyage of scientific exploration of the world's oceans. The expedition was crucially important for Croll since it enabled him to test his theories of ocean circulation using real data. His novel theories of ocean circulation based on this information conflicted with the established views popularly advocated by William Carpenter but they ultimately prevailed. In the many writings of Croll on ocean currents, we encounter, as with other areas of his research, numerous remarkable ideas many decades ahead their time.

While predominantly dipolar, large-scale magnetic fields are usually assumed in most studies involving neutron stars, there are multiple observational, theoretical hints and numerical simulations highlightening the importance of non-dipolar components. I review here the most important observational facts and numerical studies pointing towards the existence of magnetospheric currents and internal small-scale structures, arising from multipoles of poloidal and toroidal fields. This holds for all neutron star stages: at birth, during their lifetime and after a merger.

We summarize a series of numerical experiments of collisional dynamics in dense stellar systems such as globular clusters (GCs) and in weakly collisional plasmas using a novel simulation technique, the so-calledMulti-particle collision (MPC) method, alternative to Fokker-Planck and Monte Carlo approaches. MPC is related to particle-mesh approaches for the computation of self consistent long-range fields, ensuring that simulation time scales with N log N in the number of particles, as opposed to N2 for direct N-body. The collisional relaxation effects are modelled by computing particle interactions based on a collision operator approach that ensures rigorous conservation of energy and momenta and depends only on particles velocities and cell-based integrated quantities.

The Laser Interferometer Space Antenna (LISA) mission will observe from space gravitational waves emitted by neutron stars and white dwarfs within galactic binaries. These compact stars can have intense magnetic fields. Therefore, the impact of the magnetic fields on the orbital and the spins evolution of binary systems can potentially be detected by LISA through the GW’s strain. Within the magnetic dipole-dipole approximation, we found that magnetism generates a secular drift of the mean longitude which, in turn, shifts all the frequencies contained in the GW signal. For a quasi-circular orbit, the signal is mainly monochromatic and the magnetic shift is proportional to the product of the magnetic moments and is inversely proportional to the 7/2 power of the semi-major axis. Hence, for a highly magnetic binary system in compact orbit, a non-negligible amount of the frequency measured by LISA might have a magnetic origin.

In recent years, an increasing amount of attention is being paid to the gravitational few-body problem and its applications to astrophysical scenarios. Among the main reasons for this renewed interest there is large number of newly discovered exoplanets and the detection of gravitational waves. Here, we present two numerical codes to model three- and few-body systems, called tsunami and okinami. The tsunami code is a direct few-body code with algorithmic regularization, tidal forces and post-Newtonian corrections. okinami is a secular, double-averaged code for stable hierarchical triples. We describe the main methods implemented in our codes, and review our recent results and applications to gravitational-wave astronomy, planetary science and statistical escape theories.

Upcoming VLBI observations will resolve nearby supermassive black holes, most notably Sagittarius A* and M87, on event horizon-scales. Recent observations of Sagittarius A* with the Event Horizon Telescope have revealed horizon-scale structure. Accordingly, the detection and measurement of the back hole “shadow” is expected to enable the existence of astrophysical black holes to be verified directly. Although the theoretical description of the shadow is straightforward, its observational appearance is largely determined by the properties of the surrounding accretion flow, which is highly turbulent. We introduce a new polarised general-relativistic radiative transfer code, BHOSS, which accurately solves the equations of polarised radiative transfer in arbitrary strong-gravity environments, providing physically-realistic images of astrophysical black holes on event horizon-scales, as well as also providing insight into the fundamental properties and nature of the surrounding accretion flow environment.

The Square Kilometre Array (SKA) is a planned large radio interferometer designed to operate over a wide range of frequencies, and with an order of magnitude greater sensitivity and survey speed than any current radio telescope. The SKA will address many important topics in astronomy, ranging from planet formation to distant galaxies. However, in this work, we consider the perspective of the SKA as a facility for studying physics. We review four areas in which the SKA is expected to make major contributions to our understanding of fundamental physics: cosmic dawn and reionisation; gravity and gravitational radiation; cosmology and dark energy; and dark matter and astroparticle physics. These discussions demonstrate that the SKA will be a spectacular physics machine, which will provide many new breakthroughs and novel insights on matter, energy, and spacetime.

Stars ejected from the Galactic Center can be used to place important constraints on the Milky Way potential. We have used Hills stars to constrain models for the Galactic potential, demonstrating that meaningful constraint can be obtained if we have samples of around 50 nearby Hills stars.

We review some of our recent results about the Radial Acceleration Relation (RAR) and its interpretation as either a fundamental or an emergent law. The former interpretation is in agreement with a class of modified gravity theories that dismiss the need for dark matter in galaxies (MOND in particular). Our most recent analysis, which includes refinements on the priors and the Bayesian test for compatibility between the posteriors, confirms that the hypothesis of a fundamental RAR is rejected at more than 5σ from the very same data that was used to infer the RAR.

General Relativity has been successfully tested on small scales. However, precise tests on galactic and larger scales have only recently begun. Moreover, the majority of these tests on large scales are based on the measurements of Hubble constant (H0), which is currently under discussion. Collett et al. (2018) implemented a novel test combining lensing and dynamical mass measurements of a galaxy, which are connected by a γ parameter, and found γ=0.97±0.09, which is consistent with unity, as predicted by GR. We are carrying out this same technique with a second galaxy, SDP.81 at z=0.299, and present here our preliminary results.

We developed a numerical method[-70pt] to compute the gravitational field of an infinitely-thin axisymmetric disc with an arbitrary surface mass density profile. We evaluate the gravitational potential by a split quadrature using the double exponential rule and obtain the acceleration vector by numerically differentiating the potential by Ridders’ algorithm. By using the new method, we show the rotation curves of some non-trivial discs: (i) truncated power-law discs, (ii) discs with a non-negligible center hole, (iii) truncated Mestel discs with edge-softening, (iv) double power-law discs, (v) exponentially-damped power-law discs, and (vi) an exponential disc with a sinusoidal modulation of the density profile. Also, we present a couple of model fittings to the observed rotation curve of M33: (i) the standard deconvolution by assuming a spherical distributin of the dark matter and (ii) a direct fit of infinitely-thin disc mass with a double power-law distribution of the surface mass density.

We present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of massive particles and distorts light rays due to gravitational lensing. Efficient numerical methods are required for solving the equations of motion and compute i) the black hole shadow obtained by tracing light rays from the object to a distant observer, and ii) obtain information on the dynamics of the plasma at the microscopic scale. Here, we present generalized algorithms capable of simulating ensembles of photons or massive particles in any spacetime, with the option of including external forces. The coupling of these tools with GRMHD simulations is the key point for obtaining insight on the complex dynamics of accretion disks and jets and for comparing simulations with upcoming observational results from the Event Horizon Telescope.

The Square Kilometre Array (SKA) will be sensitive enough to discover all of the pulsars in the Milky Way that are beamed towards Earth. Already in the initial deployment, SKA Phase 1, it will make significant advances in pulsar science. In these proceedings I briefly overview what the SKA is, and describe its pulsar search and timing capabilities.

The millisecond pulsar PSR J0337+1715 is in a mildly relativistic hierarchical triple system with two white dwarfs. This offers the possibility of testing the universality of free fall: does the neutron star fall with the same acceleration as the inner white dwarf in the gravity of the outer white dwarf? We have carried out an intensive pulsar timing campaign, yielding some 27000 pulse time-of-arrival (TOA) measurements with a median uncertainty of 1.2 μs. Here we describe our analysis procedure and timing model.

PSR J0337+1715 is a millisecond radio pulsar in a hierarchical stellar triple system with two white dwarfs. This system is a unique and excellent laboratory in which to test the strong equivalence principle (SEP) of general relativity. An initial SEP-violation test was performed using direct 3-body numerical integration of the orbit in order to model the more than 25000 pulse times of arrival (TOAs) from three radio telescopes: Arecibo, Green Bank and Westerbork. In this work I present our efforts to quantify the effects of systematics in the TOAs and timing residuals, which limit the precision of an SEP test. In particular, we apply Fourier-based techniques to the timing residuals in order to isolate the effects of systematics that can masquerade as an SEP violation.