NATA: A Chemical-picture Equation of State for Stellar Merger Hydrodynamics

Abstract We present Nearly Always Truthful Approximations (NATA), a self-contained chemical-picture equation of state (EOS) for hydrogen-helium-carbon-oxygen mixtures, developed for hydrodynamics calculations of stellar mergers and common envelope evolution. NATA carries bound species explicitly in ionization and dissociation equilibrium and evaluates pressure, internal energy, and entropy from one continuous, single-physics chemical-picture solve built on analytic and semianalytic component physics, rather than by stitching together component EOS tables. The result is smooth thermodynamics across ionization, dissociation, and degeneracy fronts, with monotonic internal energy and no artificial energy steps at EOS seams, so the EOS inverts cleanly for codes that advance internal energy. We benchmark NATA against the blended MESA EOS, ab initio hydrogen-helium tables, and reference-independent analytic limits. NATA reproduces clean analytic limits and selected fully ionized benchmarks at the subpercent level, while most remaining percent-level residuals are confined to partial ionization and dissociation fronts; these residuals are traced to identifiable picture choices, front placements, and reference table seams or extrapolations. NATA therefore provides a well-behaved fallback in cool, low-density regimes where blended EOS tables may be stretched beyond their intended use and become physically unreliable.