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Astron. Astrophys. 343, 990-996 (1999)

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2. New solar models

We constructed a large number of solar models taking into account diffusion of helium and heavy elements following Thoul et al.(1994). In one model (Model 5), which we refer to in Sect. 5, diffusion was ignored. In all the models, we use OPAL equation-of-state (Rogers et al., 1996). For opacity we use the newest Livermore opacity table (OPAL96, Iglesias & Rogers, 1996) for Grevesse & Noels (1993) heavy element mixture. For comparison, we calculated one model using an earlier version of the Livermore opacities (OPAL92, Iglesias et al., 1992; Rogers & Iglesias, 1992). At low temperatures we used Alexander & Ferguson (1994) data on molecular and grain opacities. Nuclear reaction rates are calculated according to Bahcall & Pinsonneault (1995). We calculated one model (Model 4, see Sect. 5) with modified reaction rates, still within the range of uncertainties quoted by Bahcall & Pinsonneault.

We assumed the value of photospheric radius [FORMULA] = 696.3 Mm. This value is by 0.8 Mm higher than the most recent determination of Brown & Christensen-Dalsgaard (1998). The reason for our choice is a better agreement with the seismically inferred sound-speed in the lower convective zone. The small difference is inconsequential for the conclusions of this work. The model radii were fitted to the adopted value with the precision better than [FORMULA]. The luminosity was assumed to be [FORMULA] erg s-1 and models were fitted to precision better than [FORMULA].

We calculated a number of models for various values of the age, t, at the standard value of the metal-to-hydrogen ratio, [FORMULA], and at an enhanced value of 0.027. The parameters for selected models are listed in Table 1.


Table 1. Parameters of selected solar models

A comparison between Model 0 and Model 1 shows the effect of the age on main parameters of the solar models. The older sun ([FORMULA]) has produced a larger amount of helium in the core. Longer evolution means also more time for the gravitational settling i.e. a larger difference between the initial helium abundance, [FORMULA], and the present abundance in the outer layers, [FORMULA]. In order that the solar model accounts for the same luminosity, one has to reduce the initial helium abundance with respect to that of the SSM. With the exception of the energy production region, the helium abundance is reduced everywhere in the solar model and one can thus explain the following features:

  • i) The present photospheric helium abundance is lower.

  • ii) Matter is more opaque to radiation, so that convection starts deeper in the sun.

  • iii) Below the convective zone and above the energy production core the sound speed is higher, due to the reduced "mean molecular weight" µ.

  • iv) In the energy production core, the effect of helium accumulation should dominate, resulting in a larger µ and consequently a smaller sound speed.

Of course, the opposite occurs for a younger sun. In the next section we will discuss in greater detail the differences in the sound speed between various models.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999