{'fraction_non_alphanumeric': 0.01581395348837209, 'fraction_numerical': 0.0013953488372093023, 'mean_word_length': 5.042134831460674, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Effects of Heavy Elements and Excited States in the Equation of State of the Solar Interior

Although 98% of the solar material consists of hydrogen and helium, the remaining chemical elements contribute in a discernible way to the thermodynamic quantities. An adequate treatment of the heavy elements and their excited states is important for solar models that are subject to the stringent requirements of helioseismology. The contribution of various heavy elements in a set of thermodynamic quantities has been examined. Characteristic features that can trace individual heavy elements in the adiabatic exponent γ1 = (∂ ln p/∂ ln ϱ)s (s being specific entropy), and hence in the adiabatic sound speed, were searched. It has emerged that prominent signatures of individual elements exist and that these effects are greatest in the ionization zones, typically located near the bottom of the convection zone. The main result is that part of the features found here depend strongly on both the given species (atom or ion) and its detailed internal partition function, whereas other features only depend on the presence of the species itself, not on details such as the internal partition function. The latter features are obviously well suited for a helioseismic abundance determination, while the former features present a unique opportunity to use the Sun as a laboratory to test the validity of physical theories of partial ionization in a relatively dense and hot plasma. This domain of plasma physics has so far no competition from terrestrial laboratories. Another, quite general, finding of this work is that the inclusion of a relatively large number of heavy elements has a tendency to smear out individual features. This affects both the features that determine the abundance of elements and the ones that identify physical effects. This property alleviates the task of solar modelers because it helps to construct a good working equation of state that is relatively free of the uncertainties from basic physics. By the same token, it makes more difficult the reverse task, which is constraining physical theories with the help of solar data.