Spectroscopic Determination of Atmospheric Parameters of Solar-Type Stars: Description of the Method and Application to the Sun

Abstract

A computer program has been developed for determining the fundamental model atmosphere parameters ($T_\mathrm{eff}$, $\log g$, $v_\mathrm{t}$, $[\mathrm{Fe/H}]$) of solar-type stars, which is based on the equivalent widths for a well-chosen set of Fe i and Fe ii lines. The basic principle of this method is to find the solution in the $(T_\mathrm{eff}$, $\log g$, $v_\mathrm{t})$ space, which minimizes the sum of the dispersion of the Fe i abundances and the square of the Fe i–Fe ii abundance difference. An application of this code to the observed solar equivalent widths turned out to yield satisfactory results, which are more or less consistent with the actual parameters of the Sun. The numerical performance of this approach as well as the errors involved in the resulting solutions are discussed.

The Penn State-Toruń Centre for Astronomy Planet Search stars

“…The iron EWs were analyzed with the TGVIT (Takeda et al 2002a(Takeda et al , 2005a, which is a part of the SPTOOL 5 package. This numerical algorithm is a modified version of an earlier code and is based on the atmospheric models computed by Kurucz (1993a,b).…”

“…This numerical algorithm is a modified version of an earlier code and is based on the atmospheric models computed by Kurucz (1993a,b). The TGVIT uses an iterative procedure to achieve more cohesive parameter fits, and the version available to us was more suitable for lower effective temperatures (T eff ≥ 4250 K) than the original version (Takeda et al 2002a). As a result, we could apply it to the late-type stars in our sample.…”

“…As a result, we could apply it to the late-type stars in our sample. More details concerning the iteration procedures, data calculations, and formulation of the numerical problems are presented in Takeda et al (2002aTakeda et al ( ,b, 2005a. This purely spectroscopic method is based on an analysis of Fe I and Fe II lines and fulfills three conditions resulting from the assumption of the local thermodynamical equilibrium (LTE):…”

“…The Fe abundance depends on both T eff and log g. The coupling is so strong that in the iterative approach of Takeda et al (2002a) T eff and log g are actually simultaneously fitted and treated as "one variable" (v t being the other). This coupling may, in principle, lead to degeneracy of purely spectroscopic parameters because higher effective temperatures may be compensated by gravitational acceleration.…”

“…However, in our sample, which is composed of stars with effective temperatures similar or lower to the Sun, we do not expect this effect to cause significant uncertainties. We refer the reader to Takeda et al (2002a) for a detailed discussion of this problem and for an extensive discussion on the behavior of the D 2 function, along with its related components, around the converged solutions.…”