Related papers: Torus mapper: a code for dynamical models of galax…
Galaxy modelling is greatly simplified by assuming the existence of a global system of angle-action coordinates. Unfortunately, global angle-action coordinates do not exist because some orbits become trapped by resonances, especially where…
Our Galaxy's bar makes the Galaxy's potential distinctly non-axisymmetric. All orbits are affected by non-axisymmetry, and significant numbers are qualitatively changed by being trapped at a resonance with the bar. Orbital tori are used to…
The vertical kinematics of stars near the Sun can be used to measure the total mass distribution near the Galactic disk and to study out-of-equilibrium dynamics. With contemporary stellar surveys, the tracers of vertical dynamics are so…
A phase-space distribution function of the steady state in galaxy models that admits regular orbits overall in the phase-space can be represented by a function of three action variables. This type of distribution function in Galactic models…
The maximally compact representation of a regular orbit is in terms of its action-angle variables. Computing the map between a trajectory's Cartesian coordinates and its action-angle variables is called torus construction. This article…
Many approaches to galaxy dynamics assume that the gravitational potential is simple and the distribution function is time-invariant. Under these assumptions there are traditional tools for inferring potential parameters given observations…
Understanding the lives and interior structures of stellar objects is a fundamental objective of astrophysics. Research in this domain often relies on the visualization of astrophysical data, for instance, the results of theoretical…
Under the assumption of a simple and time-invariant gravitational potential, many Galactic dynamics techniques infer the Milky Way's mass and dark matter distribution from stellar kinematic observations. These methods typically rely on…
Using the radiative transfer code Torus, we produce spectral-line cubes of the predicted HI profile from global SPH simulations of spiral galaxies. Torus grids the SPH galaxy using Adaptive Mesh Refinement, then applies a ray-tracing method…
Orbital Torus Imaging (OTI) is a dynamical inference method for determining the Milky Way's gravitational potential using stellar survey data. OTI uses gradients in stellar astrophysical quantities, such as element abundances, as functions…
We present a method for computing invariant tori of dimension greater than one. The method uses a single short trajectory of a dynamical system without any continuation or initial guesses. No preferred coordinate system is required, meaning…
The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic…
Torus mapping yields constants of motion for stars trapped at a resonance. Each such constant of motion yields a system of contours in velocity space at the Sun and neighbouring points. If Jeans' theorem applied to resonantly trapped…
Our understanding of the mechanisms governing the structure and secular evolution galaxies assume nearly integrable Hamiltonians with regular orbits; our perturbation theories are founded on the averaging theorem for isolated resonances. On…
We suggest to use the Hubble Space Telescople (HST) follow-up observations of the TESS targets for detecting possible plasma tori along the orbits of exoplanets orbiting M dwarfs. The source of the torus could be planetary volcanic activity…
I discuss the importance of dynamical models for exploiting survey data, focusing on the advantages of "torus" models. I summarize a number of applications of these models to the study of the Milky Way, including the determination of the…
We present a toolbox for the continuation of two-dimensional tori in autonomous dynamical systems and non-autonomous systems with periodic forcing. A torus is solved as the solution to a boundary-value problem. Truncated Fourier series and…
As a star orbits the center of its host galaxy, the trajectory is encompassed within a 3D toroid. The orbit probes all points in this toroid, unless its orbital frequencies exhibit integer ratios (commensurate frequencies), in which case a…
We introduce the Theoretical Astrophysical Observatory (TAO), an online virtual laboratory that houses mock observations of galaxy survey data. Such mocks have become an integral part of the modern analysis pipeline. However, building them…
Owing to the pioneering work of Contopoulos, a strongly barred galaxy is known to have irregular orbits in the vicinity of the bar. By definition, irregular orbits can not be represented by action-angle tori everywhere in phase space. This…