FreeEOS-1.3.0 has been released on 2005-02-21 just one day after the release of FreeEOS-1.2.0. The purpose of this quick release is to distinguish a change in free-energy model implementation using new Fermi-Dirac integral approximations that were developed in Paper I. A further quick release of FreeEOS-1.4.0 is planned which will include Coulomb fit improvements to be described in the forthcoming Paper III in the series of papers that document the FreeEOS implementation. Download FreeEOS-1.3.0 from here. The ChangeLog for 1.3.0 shows few code changes from 1.2.0 because that release already included all the infrastructure to support the new Fermi-Dirac integral approximations.

This figure shows the effect of the improved Fermi-Dirac integral approximations for FreeEOS-1.3.0. The 1.2.0 and 1.3.0 calculations being compared have been done using the EOS1 option suite and solar metallicity. Both calculations agree well at low densities for both low temperature (low ionization) and high temperature (large radiation pressure) because the electron pressure is just not an important component of the total pressure under those conditions. The Fermi-Dirac integral approximations used for FreeEOS-1.2.0 are based on the fitting coefficients in Table 4 of EFF (1973, A&A, 23, 325). The errors are similar to those in Figure 3 of Paper I for the fit labelled "P_e Errors (Original EFF: k_{NR} = 0; M,N =3)" in terms of being widespread for all physical conditions, but the errors are about an order of magnitude less because FreeEOS-1.2.0 uses the M,N=5 case rather than the illustrated M,N=3 case. FreeEOS-1.3.0 uses the fit labelled "P_e Errors (This work: k_{NR} = 1; M,N =3)". This lower order saves computer time. Furthermore, the approximation errors for the largely non-relativistic conditions illustrated in the present figure are much less than the FreeEOS-1.2.0 case because the new Fermi-Dirac fit uses an approximation form that gives much more accurate results than the original EFF approximation for non-relativistic conditions (see Figure 3 and the accompanying discussion in Paper I). Thus, I conclude that the residuals between the FreeEOS-1.2.0 and FreeEOS-1.3.0 results illustrated in the present figure are largely dominated by errors in the Fermi-Dirac approximations used for FreeEOS-1.2.0.

The effect of the improved Fermi-Dirac integral approximations is roughly 0.1 per cent in the worst case that occurs near log T = 4.5 and log rho = 2.5 (in SI units) at the calculational limit of FreeEOS. These extreme conditions correspond to the envelope of a 0.1 solar-mass star where FreeEOS results (and in fact all EOS results) are uncertain in any case. The relative residuals decrease for lower densities and become small enough for solar conditions that the outstanding agreement between FreeEOS and OPAL solar results that has been demonstrated in Figures 6 and 7 of Paper II is essentially unaffected by this improved Fermi-Dirac integral approximations.

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