Kilonova r-process Nucleosynthesis 2D: Reaction-Network Flow

Neutron Irradiation

Neutron flux 60

Ejecta temperature 1.2 GK

Simulation speed 1.0×

Seed Nucleus

Wave 1 · neutron capture in progress

Live Readouts

Elapsed ejecta time

0 ms

Mean mass number ⟨A⟩

56.0

Neutron-to-seed ratio

120.0

How it works

This is the 2D counterpart to the 3D kilonova r-process simulation — not a flattened version of its scene. The 3D model samples the process with a small population of discrete Monte-Carlo walkers hopping around the nuclide chart. This 2D model instead numerically solves a genuine reaction-network flow equation for a continuous abundance density Y(Z,A,t) directly on a (proton number Z, mass number A) grid, evolved every frame by explicit conservative finite differences:

dY(Z,A)/dt =  −Y(Z,A)·[λ_capture(Z,A) + λ_β(Z,A)]
             + Y(Z,A−1)·λ_capture(Z,A−1)   (neutron capture in)
             + Y(Z−1,A)·λ_β(Z−1,A)         (beta decay in)

Neutron capture moves abundance from A to A+1 at fixed Z (n,γ); beta decay moves it from Z to Z+1 at fixed A (A is exactly conserved, matching real β⁻ decay). Every transition is mirrored exactly between the losing and gaining cell, so the total abundance in the grid never changes by construction — the same mass-conservation guarantee real Bateman decay-chain equations have. The capture rate turns off smoothly as A approaches the local (n,γ)⇆(γ,n) equilibrium set by N_eq(Z,T9), and the beta-decay rate is suppressed by a shell-closure factor that is smallest exactly at the closed neutron shells N = 50, 82, 126 — the real waiting points, where nuclei must sit far longer before they can advance in Z.

Neutron flux — sets the capture rate and how large the initial neutron budget is; higher flux drives the equilibrium curve to higher N before neutrons run out.
Ejecta temperature — higher T9 strengthens photodissociation, pulling the (n,γ)⇆(γ,n) equilibrium back toward lower N.
Seed nucleus — the iron-group starting point for each irradiation wave; the flow re-injects a fresh pulse of abundance there once the previous wave has fully frozen out, while the displayed dwell-time heatmap and abundance histogram keep accumulating across waves.
Neutron-to-seed ratio — free neutrons remaining for the active wave, per unit of seed abundance; once it hits zero, capture halts and freeze-out beta decay takes over, driving each nucleus toward its stable Z(A).

The lower chart accumulates ∫Y(Z,A,t)·dt over every wave — the total abundance-time spent at each mass number — which is exactly the quantity that piles up at a waiting point even after the flow has since drained past it, and it builds the same three real r-process peaks (near A ≈ 80, 130 and 195) that forged essentially all of the universe's gold, platinum and uranium, confirmed observationally in the kilonova AT2017gfo following GW170817.

FREEZE-OUT: neutrons exhausted

Active flow Y(Z,A) — this wave Dwell-time heatmap (nuclide chart) Abundance vs mass number A