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Astron. Astrophys. 329, 721-724 (1998)

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4. Application

The sensitivity indicators can be used for temperature diagnostics in the photospheric layers. So, for example, if we want to know the temperature variations [FORMULA] in the region of the perturbed photosphere, we should find a line with high sensitivity to temperature and with low sensitivity to pressure and velocity. For this purpose, we shall use graphic dependencies of the sensitivity indicators to temperature, pressure, and velocity (Figs. 1, 2). We should take into account the real limits in the probable values of the atmospheric parameters fluctuations. Further, for the line chosen we measure a relative difference between observed central depths in the perturbed region and in the quiet region, [FORMULA]. In the table, we find the temperature sensitivity indicator ([FORMULA]). Finally, we calculate the relative change of temperature [FORMULA] with the help of a simple ratio [FORMULA] The height where this temperature variation occurs in the photosphere corresponds to the height ([FORMULA]), where the effective response of the central line depression to this variation takes place. The heights [FORMULA] are shown in Figs. 3 and 4 and Tables 1 and 2.

However, the described application of sensitivity indicators for the temperature diagnostics of the photosphere is not possible in all cases. The accuracy of evaluations of changes of atmospheric parameters in the perturbed photosphere depends on the assumptions accepted when solving equations to obtain the response functions (Caccin et al. 1977). The main assumptions are: 1) LTE, and 2) that the perturbations of atmospheric parameters should be small, [FORMULA] [FORMULA] 1. According to our results (Sheminova 1993), the applications of the sensitivity indicators for the temperature diagnostics of the photosphere are possible when the observed variation in the central line depth [FORMULA] does not exceed [FORMULA], and the disturbance magnitude ([FORMULA]) is no more than 8 [FORMULA] ([FORMULA] 400 K).

It must be noted that the sensitivity indicators are less suitable for pressure and microturbulence diagnostics. The sensitivity to the microturbulent velocity is connected with the saturation of strong lines. In this case, the excitation temperature and NLTE effects may influence the accuracy of the estimates of the sensitivity of line profiles to microturbulence. In addition, gradients of temperature fluctuations which are not taken into account in calculations may introduce additional errors, because the temperature sensitivity of lines far exceeds the other ones. Nonetheless, approximate estimates of pressure and microturbulence fluctuations may be obtained when it is considered that the effective widths of the formation regions of central depths of Fe lines used are not too large (75-115 km).

The sensitivity indicators can also be applied to the evaluation of possible errors due to low accuracy of the model atmospheric parameters. So, for example, when determining the abundances of chemical elements, the error in the temperature adopted will cause errors considerably larger than NLTE effects or errors of the velocity and the damping constant. Such evaluations are of great practical importance for the determinations of the abundances of chemical elements in stellar atmospheres, which models are less accurate.

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© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997