A validity check of LTE on Hyades G dwarfs

As mentioned above, it is almost certain that the assumption of LTE cannot be applied to K dwarfs with Teff lower than ~5,000 K, at least for comparatively young stars. This, however, would not cause a very serious problem from the viewpoint of chemical-abundance studies, since spectra of K dwarfs are anyhow unsuitable for such a purpose because of their numerous mutually blended lines with strong damping wings. On the other hand, we should care about G-type stars more earnestly, since their spectra are commonly used in abundance determinations. In this respect, the results of Yong et al. (2004) and Schuler et al. (2006b) are not necessarily consistent with each other; i.e. the departure between A(Fe i) and A(Fe ii) over the range of ~5,000-6,000 K is not appreciably Teff-dependent in the former whereas it becomes progressively larger in the latter, though the average difference amounts to up to ~0.2 dex for both cases.

Figure 32.6. (a) Plots of Fe abundances versus TeS for Hyades G dwarfs, which we obtained by using the model atmospheres of [de Bruijne] parameters. Abundances from neutral [A(Fe i)] and ionized [A(Fe ii)] lines are indicated by filled and open circles, respectively. (b) Differences A(Fe i) - A(Fe ii) (shown in panel (a)) plotted against Teff.

Figure 32.6. (a) Plots of Fe abundances versus TeS for Hyades G dwarfs, which we obtained by using the model atmospheres of [de Bruijne] parameters. Abundances from neutral [A(Fe i)] and ionized [A(Fe ii)] lines are indicated by filled and open circles, respectively. (b) Differences A(Fe i) - A(Fe ii) (shown in panel (a)) plotted against Teff.

In order to check on this situation, our Japanese group carried out a systematic study of atmospheric parameters and Fe abundances for 37 Hyades G-type dwarfs at 5,000K < Teff < 6,000K, using the equivalent widths of Fe lines measured from the high-dispersion spectra (R ~ 70,000, signal-to-noise ratio ~ 100-200, 6,000-7,200 A) obtained with the 188-cm reflector and the HIDES spectrograph at Okayama Astrophysical Observatory. Two independent approaches were adopted, as described below.

First, the Fe abundances were determined separately from the lines of neutral and singly ionized species by using model atmospheres constructed with "actual" Tff and log g derived by de Bruijne et al. (2001) that are based on Hipparcos parallaxes, colors, and evolutionary tracks. Then the behaviors of A(Fe i) and A(Fe ii) were investigated in terms of their Tef dependences or mutual discrepancies. Regarding the model atmospheres, we used Kurucz's (1993) ATLAS9 models with convec-tive overshooting (our test calculations revealed that the differences caused by use of "non-overshooting" models were insignificant). The microturbulence was computed with the help of the empirical formula derived from the linear-regression analysis of Takeda et al. 's (2005) vt results:

vt (km s-1) = 9.9 x 10-4Teff (K) - 0.41 log g (cm s-2) - 2.92 (Teff < 5,800K) = 5.6 x 10-4Teff (K) - 0.31 log g (cm s-2) - 0.79 (Teff > 5,800K).

We denote these adopted parameters and the derived abundances by using a notation/suffix of "[de Bruijne]." The results are shown in Figure 32.6, from which we can conclude the following.

- Qualitatively, there is surely a tendency of A(Fe i) < A(Fe ii) as reported by Yong et al. (2004) and Schuler et al. (2006b).

400 200 0

400 200 0

5,000 5,500 6,000 Teff [de Bruijne]

5,500 6,00 Teff [de Bruijne]

Figure 32.7. In (a)-(c) A values, defined as the"[Fe i/ii] - [de Bruijne]" differences for Teff, log g, and A(Fe), are plotted against the [de Bruijne] parameters. (d) The mutual correlation between ATeff and Alog g.

5,500 6,00 Teff [de Bruijne]

-300 -200-100100 300 300 ATeff [Fe i/ii - de Bruijne]

Figure 32.7. In (a)-(c) A values, defined as the"[Fe i/ii] - [de Bruijne]" differences for Teff, log g, and A(Fe), are plotted against the [de Bruijne] parameters. (d) The mutual correlation between ATeff and Alog g.

- However, the typical difference is only <~0.1 dex and not very significant.

- Also, we cannot observe any clear trend of progressively increasing Fe i-Fe ii discrepancy toward lower Teff such as was derived by Schuler et al. (2006b) (Figure 32.5).

Next, all atmospheric parameters (Teff, log g, vt, [Fe/H]) were determined spec-troscopically in the same way as was done by Takeda et al. (2005). We denote such derived parameters by using a notation/suffix of "[Fe i/ii]." In this case, A(Fe i) = A(Fe ii) naturally holds, since it is one of the requirements to be satisfied. From the resulting solutions, the "[Fe i/ii] - [de Bruijne]" differences (A) of the parameters or of the Fe abundance (Fe abundances from neutral and ionized lines were averaged in the [de Bruijne] case) are plotted in Figure 32.7. The following trends between the "true" [de Bruijne] and "spectroscopic" [Fe i/ii] parameters can be seen from this figure.

• Teff(spec) tends to be higher than Teff(true) by ~ 100 (±100) K.

• There are no clear systematic differences between log g(spec) and log g(true), which scatter around zero with a dispersion of ~0.2 dex. Note that this result appears to disagree with what Melendez & Ramirez (2005) recently reported; namely, they concluded that there is a systematic underestimation of log g(spec) by ~0.2 dex.

• However, there is a positive correlation between ATeff and Alog g.

• The resulting Fe abundances for the two cases are consistent within <~0.1 dex.

From what has been described above, we would tentatively conclude as follows in response to the question of whether or not the hypothesis of LTE is safely applicable to the determination of Fe abundance and spectroscopic parameters in G-type dwarfs. Though a sign of slight NLTE overionization for Fe is detectable, its effect on the spectroscopic determination of atmospheric parameters appears marginal; e.g. the difference between A(true) and A(spec) is <~0.1 dex. If one is content with this precision, why not invoke LTE?

Literature [Fe/H] values of Hyades dwarfs

LL OT

Literature [Fe/H] values of |-Leo

Figure 32.8. Published [Fe/H] values taken from the literature: (a) Hyades (dwarfs) and (b) Leo. (The original references are cited here.)

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