The Virial Theorem as Pe = 1/2: A Universal Bound-State Law from Hydrogen to Binary Stars

Key Points

• The aim is to demonstrate a universal relationship between kinetic and binding energy across various systems influenced by 1/r² forces.
• Derived the Péclet number formulation of the virial theorem.
• Analyzed systems bound by 1/r² forces including hydrogen and binary stars.
• Utilized the Saha equation for empirical validation across nine atomic species.
• Applied the Jeans mass criterion to support findings.
• Establishes that the equilibrium ratio of kinetic to binding energy is Pe = 1/2 for the relevant systems.
• Identifies Pe = 1 as the ionization or escape threshold.
• Unifies concepts such as hydrogen ionization and binary star evaporation under a single framework.