Element diffusion in the solar interior

Abstract

We study the diffusion of helium and other heavy elements in the solar interior by solving exactly the set of flow equations developed by Burgers for a multi-component fluid, including the residual heat-flow terms. No approximation is made concerning the relative concentrations and no restriction is placed on the number of elements considered. We give improved diffusion velocities for hydrogen, helium, oxygen and iron, in the analytic form derived previously by Bahcall and Loeb. These expressions for the diffusion velocities are simple to program in stellar evolution codes and are expected to be accurate to ∼ 15%. We find that the inclusion of the residual heat flow terms leads to an increase in the hydrogen diffusion velocity. We compare our numerical results with those obtained analytically by Bahcall and Loeb using a simplified treatment, as well as with those derived numerically by Michaud and Proffitt. We find that for conditions characteristic of the sun, the results of Bahcall and Loeb for the hydrogen diffusion velocity are smaller than our more accurate numerical results by ∼ 30%, except very near the center where the error becomes larger. The Michaud and Proffitt results differ from the numerical results derived here by < ∼ 15%. Our complete treatment of element diffusion can be directly incorporated in a standard stellar evolution code by means of an exportable subroutine, but, for convenience, we also give simple analytical fits to our numerical results.

A seismic and gravitationally bound double star observed byKepler

“…OPAL05: Rogers & Nayfonov (2002). TBL94: Thoul et al (1994); MP93: Michaud & Proffitt (1993). CG68: Cox & Giuli (1968); BV58: Böhm-Vitense (1958); CGM96: Canuto et al (1996); H65: Henyey et al (1965).…”

The frequency separations of stellar p-modes

“…The newest OPAL EOS-2005 1 (Rogers & Nayfonov 2002), OPAL opacity (Iglesias & Rogers 1996), and the Alexander & Ferguson (1994) opacity for low temperature are used. Element diffusion is incorporated for helium and metals (Thoul et al 1994). The parameters of the models calculated are listed in Table 1.…”

Element Settling in the Solar Interior

“…The second method is that of Burgers (1969), in which separate ow and heat equations for each component of a multicomponent mixture are solved simultaneously. Descriptions of this method may be found for example in Cox, Guzik and Kidman (1989), Pro tt and VandenBerg (1991), Richer and Michaud (1993), Thoul, Bahcall and Loeb (1994) . 9809354.tex; 9/10/1998; 10:37; no v.; p.2 ELEMENT SETTLING IN THE SUN 3 In the formalism of RVCD, which has been used for the results given below, the local abundances of the elements are given in terms of their concentrations, solutions of equations of the following type : with :…”

“…Many authors have computed the gravitational and thermal di usion of helium and heavier elements in the Sun with various approximations : see, for example, Michaud and Vauclair (1991) and references therein; Cox, Guzik and Kidman (1989); Bahcall and Pinsonneault (1992); Pro tt (1994); Thoul, Bahcall and Loeb (1994); Christensen-Dalsgaard, Pro tt and Thompson (1993); RVCD. In all cases the radiative accelerations were neglected.…”