Pontential energies and potential-energy tensors for subsystems: general properties

TL;DR

This paper reviews the theory of potential energies and tensors in two-component systems, providing explicit expressions, physical interpretations, and examples to understand subsystem interactions and properties.

Contribution

It introduces explicit formulas for subsystem potential energies and tensors, along with conceptual experiments and guidance examples for physical interpretation.

Findings

Derived explicit expressions for subsystem potential energies.

Provided physical interpretation of subsystem potential-energy tensors.

Compared results with earlier studies to validate findings.

Abstract

With regard to generic two-component systems, the theory of first variations of global quantities is reviewed and explicit expressions are inferred for subsystem potential energies and potential-energy tensors. Performing a conceptual experiment, a physical interpretation of subsystem potential energies and potential-energy tensors is discussed. Subsystem tidal radii are defined by requiring an unbound component in absence of the other one. To this respect, a few guidance examples are presented as: (i) an embedding and an embedded homogeneous sphere; (ii) an embedding and an embedded truncated, singular isothermal sphere where related centres are sufficiently distant; (iii) a homogeneous sphere and a Roche system i.e. a mass point surrounded by a vanishing atmosphere. The results are discussed and compared with the findings of earlier investigations.