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Astron. Astrophys. 353, 666-690 (2000)

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5. Sensitivity to the atmospheric parameters

As summarized in Sect. 2, the sensitivity of the Ca II infrared triplet lines to changes in the basic stellar atmospheric parameters has already been investigated in a number of papers. Several of them refer to integrated widths which are not fully descriptive and easy to interpret in the context of high resolution profile studies. None of the papers based on a theoretical approach take the effect of Paschen lines absorption into account, which becomes an important factor at higher temperatures or lower luminosities. In the following pages, an attempt is made to illustrate the response of the profile of the strongest [FORMULA] line to changes in the atmospheric parameters. To this end I have computed synthetic profiles of that line for a set of model atmospheres extracted from a homogeneous grid. For mid-F to K stars, such a homogeneous grid of model stellar photospheres is provided by the GBEN grid (Gustafsson et al. 1975, Bell et al. 1976, Eriksson et al. 1979). The discussion in Sect. 4 has shown that it was possible to obtain a good fit of the observed wing profiles of the Ca II IRT in the solar flux spectrum by LTE computations carried out with adequate empirical model solar photospheres. This tends to indicate that our physical description of the conditions of formation of these lines is essentially correct. Thus, even though the fit obtained with the solar model of the GBEN grid is not perfect, we expect that the differential variations of the computed profiles with changes in the basic model parameters will be adequately described, at least to first order, if we use model photospheres interpolated in the homogeneous GBEN grid.

The computations were carried out in exactly the same conditions as in the solar case. The emergent theoretical profiles were broadened by a gaussian profile with a width of [FORMULA] to mimic a typical stellar profile observed with a standard high resolution coudé spectrograph. The Paschen lines absorption was taken explicitely into account in all cases.

Subsequently, the response of the computed line profiles will be illustrated by figures showing how the full profile changes when only one of the three basic atmospheric parameters (effective temperature, gravity or metallicity) is changed at a time. It will be apparent that the development of the LTE part of the profiles can be characterized by changes in the depression at the wavelengths [FORMULA] and [FORMULA] Å which fall in regions which, at the same time, are well described in the LTE approximation and are not affected by telluric absorption features. At [FORMULA] Å the depression is little affected by the Paschen lines, whereas the perturbation is nearly maximal at [FORMULA] Å.

5.1. Contribution of the Paschen lines

Table 3 shows the relative contribution of the Paschen lines in the region of formation of the observed intensity at the center of the disk (unit total optical depth) in the red wing of the Ca II [FORMULA] line. For the formation of the flux (at [FORMULA]) the contribution is, on average, 80% of that given in Table 3. What is most striking in this table is the very strong positive luminosity effect on the contribution of the hydrogen lines. As can be anticipated, there is also a metallicity effect, although much weaker, in the sense of metal-poor stars showing a larger hydrogen contribution than more metal-rich stars. The assumptions on which the calculations are based (LTE and plane-parallel geometry) may loose their validity for the most luminous stars, but these clear trends will still prevail.

5.2. Sensitivity to the effective temperature

Fig. 9 shows predicted profiles for solar composition dwarf stars with effective temperatures ranging from 5000 to 6500 K. The LTE wing profile of [FORMULA] appears remarkably insensitive to the effective temperature in the interval [FORMULA] [FORMULA] [FORMULA].

[FIGURE] Fig. 9. Computed profiles of the Ca II [FORMULA] line for dwarf stars with solar chemical composition and different effective temperatures. Upper panel: dot-dashed line [FORMULA] = 5000; dashed, 5250; dotted, 5500; solid, 5750. Lower panel: solid [FORMULA] = 5750; dotted, 6000; dashed, 6250; dot-dashed 6500.

This property is further illustrated in Fig. 10a which shows the depression in the line at [FORMULA] Å for dwarf models of different effective temperatures, with different metallicities. A similar diagram giving the depth at [FORMULA] Å shows exactly the same behaviour. However, in Fig. 10 as well as in Fig. 11, we see that this insensitivity to [FORMULA] disappears progressively for non-solar metallicities or gravities.

[FIGURE] Fig. 10a and b. Sensitivity of the line depression at [FORMULA] to a effective temperature and to b metallicity, as computed from dwarf stars model atmospheres.

[FIGURE] Fig. 11. Sensitivity of computed line depressions at [FORMULA] and at [FORMULA] Å to gravity. The solid line corresponds to models with [FORMULA] = 6000 K, the dashed line to [FORMULA] = 5500 K and the dotted line to [FORMULA] = 5000 K. All the models have a solar chemical composition.

5.3. Sensitivity to gravity

The variations of the predicted profiles of the [FORMULA] line with gravity is shown in Fig. 12 for solar chemical composition models with effective temperatures of 6000, 5500 and 5000 K. At first sight the sensitivity to gravity appears quite large. For the two hotter models, the strong luminosity effect of the perturbation by the Paschen P15 line shows up quite conspicuously, in such a way that the behaviours of the blue wing and of the red wing turn out to be somewhat different. These properties are also well illustrated in Fig. 11 showing the variations of the line depression at [FORMULA] Å (blue wing) and at [FORMULA] Å (red wing). The variation at [FORMULA] is made more regular by the hydrogen line contribution. At [FORMULA], the effect of hydrogen is much less effective and we see the pure effect of gravity on the Ca II line: this effect is complicated and the observation of the line depression at this wavelength will not allow the sorting of stars by their different gravities. We further see that the sensitivity of the wings to gravity is only really significant for gravities [FORMULA]. For dwarfs and subgiants the sensitivity to gravity is very weak and almost non-existent. For giants, assuming that the temperature and metallicity have already been determined independently, our computations show that the gravity could be derived from observed profiles of Ca II [FORMULA] having a signal-to-noise ratio of 100 with an uncertainty between 0.10 and 0.15 in log g if [FORMULA] [FORMULA]. When 5000 [FORMULA] [FORMULA] [FORMULA] 5300 K the uncertainty can reach [FORMULA] in log g. The Ca II IRT lines have often been advocated as a powerful luminosity indicator. These computations confirm that this statement needs to be qualified. The Ca II wings are only effective for cool giants and a reasonable accuracy can only be reached if the effects of temperature and metallicity are considered as well as those of gravity. An example of the use of the IRT lines for the determination of the gravity of Hyades giants is provided by Smith & Ruck (1997).

[FIGURE] Fig. 12. Computed profiles of the Ca II [FORMULA] line for solar composition stars with effective temperatures [FORMULA] = 6000, 5500 and 5000 K, for different values of gravity. Solid line for log g = 4.5, dotted for log g = 3.75, dashed for 3.0, dot-dashed for 2.25 and long dash - short dash for log g = 1.5.

5.4. Sensitivity to metallicity

Fig. 13 shows the general behaviour of the Ca II [FORMULA] line wing profile with changes in the global metallicity of dwarf stars model atmospheres. It is further illustrated in Fig. 10b which shows the variations of the line depression at [FORMULA] Å; an equivalent diagram for the depression at 8545 Å is completely similar. These variations are seen to be quite regular, contrary to the variations with gravity. The sensitivity to metallicity is higher for the hotter models. Therefore, the depression in the observed wings of [FORMULA] may look like a good metallicity indicator provided that the stellar gravity has been determined beforehand with enough accuracy. Quantitatively, we can see that for a dwarf star (log g = 4.5) with [FORMULA] = 6000 K, the amplitude of the noise in an observation with a signal-to-noise ratio S/N = 100 is equivalent to the change in the depression at [FORMULA] = 8539 or at [FORMULA] = 8542 Å produced by a change in metallicity [FORMULA]. At [FORMULA] = 5500 K the noise amplitude corresponds to [FORMULA] and at [FORMULA] = 5000 K to [FORMULA]. We thus see that if we want to obtain a competitive accuracy on [M/H], say of [FORMULA], we have to use observations with S/N ratios higher than 200 for [FORMULA] = 6000 K and higher than 350 for [FORMULA] = 5000 K. The uncertainties induced by the errors on the model temperature and gravity are not taken into account by these figures. For Pop I dwarfs and subdwarfs the accuracy of the model parameters does not need to be very high, but for giants or metal-poor dwarfs the uncertainties on the temperature and gravity may be of much larger consequences.

[FIGURE] Fig. 13. Computed profiles of Ca II [FORMULA] with dwarf models for the effective temperatures [FORMULA] = 6000, 5500 and 5000 K and different metallicities. Solid line for [M/H] = 0., dotted for -0.25, dashed for -0.50 and dot-dashed for [M/H] = -1.00.

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Online publication: December 17, 1999
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