galaxy_collision.hpp File Reference

Two disc galaxies on a collision course: the project's headline scenario. More...

#include "orrery/core/particle_data.hpp"
#include "orrery/core/random.hpp"
#include "orrery/core/types.hpp"
#include "orrery/core/vec3.hpp"
#include "orrery/initial_conditions/disc_galaxy.hpp"

Go to the source code of this file.

Classes
struct	orrery::initial_conditions::GalaxyCollisionParameters
	An encounter between two disc galaxies. More...

Functions
core::ParticleData	orrery::initial_conditions::make_galaxy_collision (const GalaxyCollisionParameters &parameters, core::RandomSource &random)
	Sample both galaxies and place them on the encounter, in the combined centre-of-mass frame.
core::Vec3	orrery::initial_conditions::galaxy_collision_separation (const GalaxyCollisionParameters &parameters)
	The separation vector from the primary's centre to the secondary's.
core::Vec3	orrery::initial_conditions::galaxy_collision_relative_velocity (const GalaxyCollisionParameters &parameters)
	The relative velocity of the secondary with respect to the primary.
core::Real	orrery::initial_conditions::galaxy_collision_orbit_energy (const GalaxyCollisionParameters &parameters)
	The energy of the encounter, treating each galaxy as a point mass.

Detailed Description

Two disc galaxies on a collision course: the project's headline scenario.

Section 7 of the implementation plan names the galaxy collision as the demonstration Phase 12 exists to produce, and this is where it is defined rather than in the renderer that draws it. That separation is the point: the scenario is a configuration of point masses like any other, it can be integrated with any solver in the project, its energy is conserved to the same tolerance as anything else, and the renderer has no opinion about it. A demonstration that only existed inside the viewer would be an animation rather than a result.

The encounter

Each galaxy is placed at rest in its own centre-of-mass frame by disc_galaxy.hpp, and then the two are put on the two-body orbit their total masses would follow if each were a point. The separation vector runs along the x axis with the impact parameter offset along y, and the relative velocity is directed along the separation's own x component, so the encounter is planar in x-y whatever the discs are inclined to.

The relative speed is a multiple of the local escape speed, sqrt(2 G M / d), where M is the total mass of both galaxies and d the separation. That parametrisation is worth the small amount of arithmetic it costs, because the multiplier says what kind of encounter it is without any further calculation: below one the pair is bound and will merge, at one the orbit is exactly parabolic, and above one the galaxies pass once and separate for ever. The parabolic case is also an analytic check, since the two-body energy of the encounter is then exactly zero, and the tests use it as one.

A merger is the interesting case and the default. Real major mergers are bound encounters, tidal tails come from the first passage, and the second passage is what actually destroys the discs.

What is being approximated

The placement treats each galaxy as a point mass, which is exact only while the separation is large compared with the galaxies. At the default separation of twenty disc scale lengths the leading correction is the quadrupole of each disc, and it is small. It is not zero, so the encounter that actually happens is not precisely the Kepler orbit it was placed on, and nothing in the tests claims otherwise: what they check is the state at the moment it was built.

Function Documentation

make_galaxy_collision()

core::ParticleData orrery::initial_conditions::make_galaxy_collision ( const GalaxyCollisionParameters & parameters, core::RandomSource & random )

nodiscard

Sample both galaxies and place them on the encounter, in the combined centre-of-mass frame.

The primary's particles come first, then the secondary's, so a renderer can tint the two apart by index alone and the tests can measure either galaxy's centre of mass on its own. Both galaxies are drawn from the same random stream, in that order.

Throws std::invalid_argument for anything either galaxy refuses, and for a separation vector of zero length, which has no direction to approach along. A negative approach speed is refused rather than read as a receding pair: two galaxies moving apart is a configuration, but it is not a collision, and a caller that meant it can write it with a negative separation instead.

galaxy_collision_separation()

core::Vec3 orrery::initial_conditions::galaxy_collision_separation ( const GalaxyCollisionParameters & parameters )

nodiscard

The separation vector from the primary's centre to the secondary's.

(separation, impact_parameter, 0). Exposed so that a test can measure the sampled configuration against the vector it was built from rather than against a second spelling of it.

galaxy_collision_relative_velocity()

core::Vec3 orrery::initial_conditions::galaxy_collision_relative_velocity ( const GalaxyCollisionParameters & parameters )

nodiscard

The relative velocity of the secondary with respect to the primary.

Directed along the negative x axis, with magnitude approach_speed times sqrt(2 G M / d).

galaxy_collision_orbit_energy()

core::Real orrery::initial_conditions::galaxy_collision_orbit_energy ( const GalaxyCollisionParameters & parameters )

nodiscard

The energy of the encounter, treating each galaxy as a point mass.

mu v^2 / 2 - G M_1 M_2 / d. Negative for a bound pair, zero for the parabolic case and positive for a hyperbolic one, which is the statement the approach speed parameter makes and the one the tests check it against.