Speaker
Description
Gaia and MUSE provide amazing data for both the Milky Way and external
galaxies. The data reflect huge selection effects and to overcome these we
need sophisticated chemo-dynamical models that can be `observed' with the
same biases. It's vain to suppose we can infer how galaxies formed and how they
work as machines until we have constructed credible chemo-dynamical models.
A chemodynamical model comprises a library of orbits with assignments of
stars or dark matter to each orbit such that the orbits' potential is jointly
generated by the stars and DM. The model doesn't need to be in equilibrium, but
equilibrium models are natural starting points - disequilibrium effects can
be modelled by perturbation theory.
Modelling requires a scheme for labelling orbits. Most current work follows
Schwarzschild in labelling orbits with initial conditons. This scheme is
highly non-unique and obscures the sampling density. The scheme is adapted to
the use of one pre-determined potential rather than a potential that emerges
from the modelling proces.
Orbits have natural labels - actions', which are constants of motion J(x,v)
that can be embeded asmomenta' in a canonical coordinate system. The
canonically conjugate variables are `angles' w. An equilibrium model
comprises the DFs f_A(J) of various species A of star or DM. The model is
completely specified by the set {f_A} because the potential Phi(x) can be
computed from {f_A}.
The key to this approach is computing the mapping (x,v) <-> (w,J). The
Staeckel Fudge is a widely used map (x,v) -> (w,J). Torus mapping provides
the inverse map (x,v) <- (w,J) and recently we have shown that torus mapping
can also map in the direction (x,v) -> (w,J).
In a galaxy as in the solar system, resonant trapping and chaos are ignored
at a first pass but are crucial for secular evolution. We use perturbation
theory to understand these processes, and a key capability of torus mapping is
the provision of an intgrable Hamiltonian H(J) to which p-theory can be
applied.
