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1.17.0
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Orrery
A GPU-accelerated N-body gravitational simulator
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A rotating disc galaxy: the configuration the project's demonstration is built from. More...
#include "orrery/core/particle_data.hpp"#include "orrery/core/random.hpp"#include "orrery/core/types.hpp"#include "orrery/core/vec3.hpp"Go to the source code of this file.
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| struct | orrery::initial_conditions::DiscGalaxyParameters |
| A disc galaxy to sample. More... | |
Functions | |
| core::ParticleData | orrery::initial_conditions::make_disc_galaxy (const DiscGalaxyParameters ¶meters, core::RandomSource &random) |
| Sample the model, in its own centre-of-mass frame at the origin. | |
| core::Index | orrery::initial_conditions::disc_galaxy_disc_count (const DiscGalaxyParameters ¶meters) |
| How many of the sampled particles belong to the disc. | |
| core::Real | orrery::initial_conditions::disc_galaxy_particle_mass (const DiscGalaxyParameters ¶meters) |
| The mass every particle in the galaxy carries. | |
| core::Real | orrery::initial_conditions::disc_galaxy_total_mass (const DiscGalaxyParameters ¶meters) |
| The total mass the sample actually has, which is the particle mass times the count. | |
| core::Real | orrery::initial_conditions::disc_galaxy_enclosed_mass (const DiscGalaxyParameters ¶meters, core::Real radius) |
| The mass inside cylindrical radius radius, as the model computes it. | |
| core::Real | orrery::initial_conditions::disc_galaxy_circular_speed (const DiscGalaxyParameters ¶meters, core::Real radius) |
| The speed of a circular orbit at cylindrical radius radius, in the plane of the disc. | |
| core::Vec3 | orrery::initial_conditions::disc_galaxy_spin_axis (const DiscGalaxyParameters ¶meters) |
| The unit vector the galaxy spins about. | |
A rotating disc galaxy: the configuration the project's demonstration is built from.
Every configuration before this one is spherical and either in equilibrium or at rest, which is what a conservation test wants and what a picture does not. A galaxy is the opposite case: nearly all of its kinetic energy is in ordered rotation rather than in random motion, so it has a shape that persists, an axis that means something, and structure that develops as it turns. That is what makes it worth looking at, and Phase 12 of the implementation plan is the phase that needs something worth looking at.
The model is a Plummer bulge with an exponential disc around it, which is the standard two-component decomposition of a disc galaxy and the simplest one whose parts both have closed forms. The bulge is drawn by the sampler in plummer.hpp rather than by a second copy of it here. The disc is drawn from the surface density Sigma(R) = Sigma_0 exp(-R / R_d) with an exponential vertical profile, and every disc particle is placed on the circular orbit that the enclosed mass at its radius supports.
It is not an equilibrium solution. A Plummer sphere is: its density and its distribution of velocities solve the collisionless Boltzmann equation together, so a sample from it stays as it was drawn, and the conservation tests can hold it to that. This does not, in three separate ways, each of which is a deliberate simplification rather than an oversight.
The disc's own gravity is treated as spherical when the circular speed is computed. The true circular speed of a razor-thin exponential disc involves Bessel functions of the enclosed surface density and is about fifteen per cent higher near the peak of the rotation curve than the spherical approximation gives. Implementing it would add a special-function evaluation per particle to a setup routine and change nothing a viewer would notice, since the disc is not in equilibrium anyway.
The bulge is drawn as though the disc were not there. Its velocities come from the distribution function of an isolated Plummer sphere, so it is slightly sub-virial in the deeper combined potential and contracts a little over the first dynamical time.
The disc is cold. Particles get the circular speed exactly, with no velocity dispersion, so the Toomre stability parameter is zero everywhere and the disc is violently unstable to its own self-gravity. That is not a defect to be apologised for: it is why the model develops flocculent spiral arms and a bar within a few rotations, which is the behaviour the demonstration is there to show. A disc heated enough to be stable would be a smooth disc that stays a smooth disc.
A configuration that needs equilibrium should use the Plummer sphere, which has it and is validated against it. This one is a scenario, and what it is validated against is what it claims: the particle count, equal masses, a centre of mass at rest at the origin, an angular momentum along the spin axis, and every disc particle on the circular orbit the stated enclosed mass supports.
The circular speed follows from the acceleration a particle will actually feel, and that depends on the softening the solver runs with (ADR-0008). A disc built for point masses and then integrated with a softening length comparable to its scale height would start out rotating too fast for the forces acting on it and would expand. So the softening is one of the model's parameters, and the assembly in sim/assembly.cpp passes the solver's value through rather than letting the two disagree.
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Sample the model, in its own centre-of-mass frame at the origin.
The disc particles come first and the bulge particles follow. That ordering is part of the interface rather than an accident of the implementation: the tests check the disc's circular speeds and need to know which particles are disc, and a renderer that tints the two components differently needs the same thing. disc_galaxy_disc_count reports where the boundary is.
Throws std::invalid_argument if the disc mass is not positive, if the bulge mass is negative, if any of the three lengths is not positive, if the softening is negative, or if the cutoff is outside (0, 1). A zero bulge mass is accepted and produces a pure disc.
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How many of the sampled particles belong to the disc.
The split is by mass, rounded to the nearest particle, so that every particle in the galaxy carries the same mass. The realised component masses are therefore this count and its complement times the particle mass, which is what the circular speeds are computed from, rather than the requested masses. The difference is at most half a particle mass and matters only in that the model and the tests must agree about which it is.
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The mass every particle in the galaxy carries.
Zero for a galaxy of no particles, which is the one case where there is no answer and no caller that needs one.
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The total mass the sample actually has, which is the particle mass times the count.
This rather than disc_mass + bulge_mass is what an encounter between two galaxies has to be placed with, since it is the mass that will actually attract.
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The mass inside cylindrical radius radius, as the model computes it.
The bulge contributes its Plummer enclosed mass and the disc contributes the fraction of its own sampled mass inside that radius. Exposed because it is half of the circular speed below, and a test that recomputed it would be checking the code against itself.
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The speed of a circular orbit at cylindrical radius radius, in the plane of the disc.
v^2 = G M(R) R^2 / (R^2 + eps^2)^(3/2), which is the softened acceleration towards the centre times the radius. With no softening it reduces to the familiar G M(R) / R.
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The unit vector the galaxy spins about.
The z axis carried through the inclination and the position angle. The angular momentum of a sampled galaxy points along this, which is the sharpest statement of the orientation that a test can check.
1.17.0