Status: Accepted
Date: 2026-08-11

Context

Every initial condition in the project before this one is either an exact solution or an equilibrium: the Kepler orbit is analytic, the Plummer sphere is a self-consistent solution of the collisionless Boltzmann equation, and the uniform sphere is a deliberate non-equilibrium whose departure from one is stated in closed form. That consistency is not an accident. It is what lets the validation suite hold a run to a number rather than to an earlier run.

Phase 12 needs a galaxy, and a reviewer who has read the other four generators will reasonably expect a fifth of the same kind.

Decision

The disc galaxy is a scenario. It is a Plummer bulge inside an exponential disc whose particles are placed on circular orbits, and it is not an equilibrium solution in three separate ways, each named in include/orrery/initial_conditions/disc_galaxy.hpp: the disc's own gravity is treated as spherical when the circular speed is computed, the bulge is drawn as though the disc were not there, and the disc is given no velocity dispersion at all.

It is validated against what it claims rather than against equilibrium: the particle count, equal masses, a centre of mass at rest at the origin, an angular momentum along the spin axis, an enclosed mass function that matches the mass actually sampled, and every disc particle on the circular orbit that function supports.

Alternatives considered

A self-consistent disc. The honest version of this model needs the distribution function of a three-component system, which has no closed form, so it is built either by iterating a distribution function to convergence or by integrating the Jeans equations for the velocity moments and drawing from a Gaussian approximation with an asymmetric drift correction. Both are real methods, both are a phase of work on their own, and neither would change what the demonstration shows. The literature's standard tools for this exist because building such a model well is a research task.

A warm disc, dispersion added without the correction. Two lines of code, and it would make the disc stable against its own self-gravity. It was rejected because it is worse than either of the other two options: a disc given random motions without the corresponding reduction in its mean rotation is out of balance in a way that is neither stated nor small, so it expands over the first dynamical time and the model would be wrong for a reason nothing in the code admits to. The cold disc is out of equilibrium in a way that is stated and understood.

Use the Plummer sphere for the demonstration. It is in equilibrium and it would look like a fuzzy ball. Nearly all of a galaxy's kinetic energy is in ordered rotation, and rotation is what produces the shape, the spiral structure and the tidal tails a collision draws out. A demonstration of two colliding Plummer spheres shows a slightly larger fuzzy ball.

Consequences

The disc is Toomre unstable, with a stability parameter of zero everywhere, so it develops spiral structure and a bar within a couple of rotations and, if the force law lets it, breaks into clumps. That is the behaviour the demonstration exists to show and it is also the model's largest artefact, so the demonstration configuration chooses its softening to confine the fragmentation to scales the model does not resolve anyway. examples/collision.orrery says so and gives the value.

Nothing in the validation suite treats a galaxy as a conservation reference. The Plummer sphere remains the equilibrium case and the uniform sphere the collapse case, and both are unaffected by this.

A future phase that wants an equilibrium disc has somewhere to put it: the parameters are already a structure, the sampler is one function, and a second generator beside this one would not disturb anything. This ADR would then be superseded rather than edited.

The model's softening is one of its parameters, which is unusual for an initial condition and follows directly from the decision. A disc placed on circular orbits has to be placed on the orbits the run's own force law supports, so the assembly passes solver.softening through. That is the only setting in the configuration format that crosses between sections.