Limitations

Morrigan is a statistical model of the giant-impact phase, not an N-body integrator. Its approximations are inherited from Kimura et al. (2025)¹ and from the choices of this implementation; the ones a user should hold in mind are listed here.

Dynamical approximations

• Semi-analytic timing. Instability times come from the Petit et al. (2020)³ crossing-time fit and calibrated interaction timescales, not from direct integration. Individual system histories are statistical realisations; only ensemble statistics are meaningful for comparison with N-body results.
• Perfect merging. Collisions always merge the pair. There is no fragmentation, no hit-and-run channel, and no debris, so a body only ever grows: the merged mass is the exact sum of the two, and mass leaves a system only when a body is ejected or falls into the star.
• Single impact angle. One configured impact angle applies to every collision of a run; the model does not draw a distribution of impact geometries.
• Linear secular theory. Eccentricities between events follow the Laplace-Lagrange solution, which is linear in eccentricity and excludes inclination; the model is two-dimensional, and radially overlapping neighbours are simply decoupled from the secular solution.
• No dissipation. There is no gas drag, no tidal damping, and no dynamical friction from a planetesimal population; excitation is removed only by mergers, ejections² (whether through an eccentricity driven past unity or a scattering that leaves an orbit hyperbolic), and the star-infall cutoff.

Atmospheres

• The model carries no atmosphere. Bodies are bare: a mass is a bulk mass, a radius follows from it at the configured bulk density, and no envelope is tracked or shed. A giant impact erodes a real atmosphere, and that erosion is applied downstream by the consumer rather than here; in a coupled PROTEUS run it comes from zephyrus.collision.mass_loss, evaluated from the impact geometry each record carries. The scaling law itself is Kegerreis et al. (2020)⁴.
• Bodies are bulk objects in the dynamics too: radii do not distinguish a rocky core from an envelope, so a body with a heavy envelope is represented by its bulk mass and radius alone.

Numerical conventions

• The gravitational constant is carried at three significant figures (6.67e-11), the au as 1.5e11 m (0.27 % from the defined value), and the year as 365 days; results agree with CODATA-constant implementations only to the corresponding relative level, which matters when cross-checking against other codes.
• All Monte Carlo draws share numpy's global random state, seeded per system. Library code must never reseed mid-run; a hidden reseed would silently correlate ensemble members.
• Ejections remove the body excited past unity eccentricity; its unbound orbit is not followed, and the survivor's orbit conserves the pair's orbital energy at the moment of the event.
• The excitation applied to a pair before a collision is drawn without an upper bound, and so is the fallback taken when no draw satisfies the overlap condition. A body can therefore enter the collision branch already past unity eccentricity, which the ejection branch treats as grounds for removing it: the two branches disagree about what an unbound orbit means. Such a body is removed on the same step by the perihelion cut, so it does not survive to be reported, and the impact histories run_system returns are unaffected. A caller reading the raw merger list rather than the returned histories can see an eccentricity at or above one and should check for it.

References