Notes. All are calibrated to reproduce the observed solar surface metallicity, radius and effective temperature within 1σ of the respective error (see also Table 1), and have standard (unmodified) opacity and diffusion coefficients. They are computed with our reference EoS, except for those based on pure Free EoS and pure OPAL EoS respectively. The first model is our reference model at standard gravity and standard input physics (opacity, diffusion, etc.), and is based on the ‘old’ metallicity mixture of Grevesse & Sauval (1998), which is in good agreement with helioseisimic observations. Model A09 uses the revised metallicity of Asplund et al. (2009), which is, however, in tension with helioseismic data (see Fig. 4). The latter model is not used for computations with the fifth force, but was computed for comparison with GS98. The models in the table computed with the fifth force turned on (𝒴 = ±0.01) are used for illustration purposes throughout the text. More details about our choice of input physics are provided in Sect. 3.