Astron. Astrophys. 359, 743-754 (2000)

2. 3D model atmospheres and spectral line calculations

The procedure for calculating the spectral line transfer is the same as in Paper I and therefore only a short summary will be given here. For additional information on the details of the convection simulations and the 3D spectral synthesis, the reader is referred to Paper I.

Realistic ab-initio numerical hydrodynamical simulations of the solar surface convection have been performed and used as 3D, time-dependent, inhomogeneous model atmospheres with a self-consistent description of the convective flow and temperature structure in the photosphere. A state-of-the-art equation-of-state (Mihalas et al. 1988) has been used together with the 3D equation of radiative transfer which included the effects of line-blanketing (Nordlund 1982) with up-to-date continuous (Gustafsson et al. 1975 with subsequent updates) and line opacities (Kurucz 1993). The original simulation has a resolution of 200 x 200 x 82, which was interpolated to a grid with dimension 50 x 50 x 82 to ease the computational burden in the spectral line calculations. Simultaneously the vertical resolution was improved by only extending down to depths of about 700 km compared with the initial 2.9 Mm. Various test ensured that this procedure had no effect on the resulting profiles. The convection simulation used for the spectral synthesis here and in Paper I covered about 50 min on the Sun. For the present purposes the time coverage is sufficient to obtain properly spatially and temporally averaged line profiles, as verified by test calculations; even intervals as short as 10 min result in abundances within 0.02 dex of the estimates using the whole time-sequence. The resulting effective temperature is very close to the nominal solar value, K, while the adopted surface gravity was log [cgs]. For the computation of background continuous opacities and equation-of-state, a standard solar chemical composition was used (Grevesse & Sauval 1998). In particular the assumed He abundance (10.93) was consistent with the helioseismological evidence (e.g Basu 1998; Grevesse & Sauval 1998) though the exact value is of no practical importance for the present investigation.

In the present investigation only intensity spectra at solar disk center () were considered, which have been calculated for every column of the snapshots, before spatial and temporal averaging and normalization. The assumption of LTE in the ionization and excitation balances and for the source function () have been made throughout in the line transfer calculations. The line profiles were computed for 141 velocities around the laboratory wavelength with a interval of 0.2 (weak and intermediate strong lines) or 1.5-2.0 km s^-1 (strong lines); one additional point was computed without consideration of the line to estimate the continuum intensity necessary for the normalization. All lines were calculated with three different abundances (, 7.50 and 7.70) from which the final profile with the correct line strength was interpolated from a -analysis of the whole profile in a similar fashion to the study of Nissen et al. (2000); test calculations ensured that the abundance step was sufficiently small not to introduce any significant errors in the derived abundances ( dex).

© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000
helpdesk@link.springer.de