Most of the differences between observed p-mode frequencies and those calculated from evolutionary solar models are believed to reflect uncertainties in the ingredients of solar modelling. Much effort has consequently been applied to finding which aspects of the uncertain physical assumptions are responsible for the differences between observation and theory (e.g. Turck-Chièze & Lopes 1993). This has led, for example, to the use of the MHD equation of state (Mihalas et al. 1988), the improved calculation of opacity in the OPAL tables (Iglesias & Rogers 1991; Rogers & Iglesias 1992), the inclusion of the effects of helium settling and diffusion (Bahcall & Pinsonneault 1992b; Christensen-Dalsgaard et al. 1993), and finally the development of models with heavy element settling and diffusion (Proffitt 1994; Bahcall & Pinsonneault 1995).
Several components go into a typical recipe for solar evolution: these include a set of opacity tables, a set of equation of state tables, and a set of reaction rates and temperature dependences for each appropriate nuclear reaction. Additional assumptions concern the choice of convection theory used, the model of the solar atmosphere employed, and various input parameters, such as present-day solar age and luminosity. Given a certain set of choices for each of these ingredients, any evolution calculation should ideally give the same result to within the numerical accuracy of its integration scheme. Much progress has been made towards attaining this goal (e.g. Christensen-Dalsgaard 1991a) by eliminating the errors in complex evolution codes which previously caused them to disagree.
Given the accuracy with which p-mode frequencies are currently being measured by such instruments as SOI-MDI (Kosovichev et al. 1997) and GONG (Harvey et al. 1996), subtle aspects of the input physics are becoming subject to scrutiny. In order to facilitate such progress, not only should errors be eliminated in evolution codes, but also codes should be developed with very carefully controlled truncation errors, such as the CESAM code described by Berthomieu et al. (1993). With these considerations in mind, we have developed a new stellar evolution package named MoSEC, designed with minimization and control of truncation errors very much to the fore.
MoSEC is used to generate a series of seven evolutionary solar models with varying input physics. These are designed to investigate the effect of including settling and diffusion of helium and heavy elements, the effect of the choice of equation of state, the effect of ignoring the variation of the heavy-element abundance in the calculation of the equation of state (as has been done by various authors), and the effect of mixing below the base of the convection zone. The neutrino flux predictions are compared to measured solar values, while the sound-speed is compared to that of the sun using an inversion of the latest SOI-MDI p-mode frequencies. In the case of the equation of state, MHD-E is a new MHD-like calculation taking into account the relativistic correction to the electron pressure, a correction which was not included in either the OPAL or the original MHD equations of state. A solar model is calculated using MHD-E equation of state, and compared to two models, one calculated with OPAL, and the other also calculated with OPAL, but adding in the relativistic correction to the electron pressure. The last model enables us to evaluate what fraction of the difference between the OPAL and MHD-E models arises from the different treatment of the electron pressure.
© European Southern Observatory (ESO) 1998
Online publication: May 15, 1998