Funding & Acknowledgements

4D-STAR is funded by European Research Council (ERC) under the Horizon Europe programme (Synergy Grant agreement No. 101071505: 4D-STAR)

Work for this project is funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council.

© 2025 4D-STAR Collaboration.

An Interactive Guide to Quasi-Equilibrium

Exploring the Approximations that Power Astrophysical Nucleosynthesis

The Equilibrium Ladder

The assumption of equilibrium is not a monolithic concept; rather, it is a hierarchy of approximations. A robust network must distinguish between these levels to apply the most efficient and physically appropriate model. Hover over each level to explore its role.

Level 5: Nuclear Statistical Equilibrium (NSE)

The highest level of equilibrium. All strong/EM reactions are balanced. Composition is set by T, ρ, and \(Y_e\).

5

Level 4: Global QSE

A single large group of heavy nuclei is in equilibrium, but the total number of heavy nuclei (\\(Y_h\\)) is kinetically controlled. Classic case: alpha-rich freeze-out.

4

Level 3: QSE Clusters

Distinct groups (e.g., Si-group, Fe-group) are internally equilibrated, but not with each other. Governed by slow reactions linking the clusters.

3

Level 2: Partial Equilibrium

A single species with a very short lifetime is assumed to be in equilibrium with its production and destruction channels. Classic example: Deuterium (H-2).

2

Level 1: Full Kinetic Network

The most general state where no equilibrium is assumed. The full system of ODEs is solved, which is always valid but computationally expensive.

1

Select a Level

Hover over a level on the ladder to learn more about its role in nuclear reaction networks.

QSE Criteria Dashboard

Translating the physical framework of QSE into a functional algorithm requires a set of practical, implementable rules. Here, we investigate the primary criteria used to establish and break equilibrium.

Astrophysical Scenarios

The general principles of QSE must be adapted to the unique physical conditions of different stellar environments. A number of complicating factors prevent a one-size-fits-all approach.

GridFire: Current State & Validation

A robust QSE network requires more than just physical rules; it needs careful numerical implementation. The following checklist summarizes the key features of a reliable code, many of which are targets for the GridFire project.