Abstract
Abstract. Numerical 3-D radiative hydrodynamical simulations are the main tool for the analysis of the interface between the solar convection zone and the photosphere. The equation of state is one of the necessary ingredients of these simulations. We compare two equations of state that are commonly used, one ideal and one nonideal, and quantify their differences. Using a numerical code we explore how these differences propagate with time in a 2-D convection simulation. We show that the runs with different equations of state (EOSs) and everything else identical relax to statistically steady states in which the mean temperature (in the range of the continuum optical depths typical for the solar photosphere) differs by less than 0.2%. For most applications this difference may be considered insignificant.
Highlights
Realistic time-dependent 3-D numerical simulations (Nordlund, 1982; Stein and Nordlund, 1998, 2000) radically improved our knowledge of the near-surface convection and the solar photosphere
Two types of equations of state (EOSs) are used in the codes for the solar convection simulations: (1) the nonideal EOS including the effects of the pressure ionisation, Coulomb interaction and electron degeneracy and (2) the ideal EOS for a mixture including the partial ionisation effects
The relative differences between the quantities in the region of the T –p plane usually considered in the realistic nearsurface convection simulations are below 1 %, except for the electron density at the low temperatures, where the values of the OPAL tables are not reliable
Summary
Realistic time-dependent 3-D numerical simulations (Nordlund, 1982; Stein and Nordlund, 1998, 2000) radically improved our knowledge of the near-surface convection and the solar photosphere In these simulations the equations of magnetohydrodynamics, the equation of state (EOS) and the radiative transfer equation (RTE) are solved ab initio with only few free parameters. Tanner et al (2013) employed the radiative hydrodynamics (RHD) code to study the variation in the simulated stellar convection with varying input metallicity. They concluded that the variation in the superadiabacity and the convection dynamics in their simulation remains relatively small for a large range of metallicities (0.01 ≤ Z ≤ 0.40).
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