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Astron. Astrophys. 322, 147-154 (1997)

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3. Propagated errors

Errors related to the atmospheric parameters depend heavily on the procedure used to calculate them. Torra et al. (1990) compared the atmospheric parameters obtained from photometry with the fundamental ones in order to evaluate the errors, which can be considered external errors. For Main Sequence A type stars they found a mean error of 270 K in [FORMULA], and 0.18 dex in [FORMULA]. In this section we take these last two values to study how these errors are propagated to the age and mass as a function of the position of the star in the HR diagram. The contribution to the final error of the uncertainties in metallicity was not considered in the present work since [FORMULA] -[Fe/H] relationship is defined only for stars later than A3 and the errors induced in the [Fe/H]-Z relationship remains somewhat uncertain (Strömgren, 1987).

In order to evaluate the effect of the uncertainties in effective temperature and surface gravities on the age and mass, we simulated a gaussian distribution of [FORMULA] points around the observed values (log  [FORMULA], [FORMULA]) of each star, adopting their corresponding individual errors as standard deviations. Applying our algorithm to these points we obtain a set of [FORMULA] ages and masses for each star; their dispersions are considered as the errors we finally assign to these variables. The dependence of these errors on the HR region where the star is placed is presented in Fig. 3. Errors in [FORMULA] have their maximum value near the ZAMS, where the age of stars is of the same order as its own error. The accuracy in the age determination drastically improves for stars slightly separated from the ZAMS. Except in the case of low temperatures, where the Main Sequence width is appreciably reduced, the most precise ages ([FORMULA] in age) are obtained around the position of the isochrone turnoff point; isochrones at these point are parallel to the [FORMULA] -axis, so the large error in [FORMULA] does not contribute significantly to the error in age. Another remarkable feature from Fig. 3 is that, as expected, the error in [FORMULA] increases when log  [FORMULA] decreases.

[FIGURE] Fig. 3. Error in [FORMULA] and relative error in M along a line of constant effective temperature log  [FORMULA]  = 3.8 (solid line), 4.0 (dotted line) and 4.2 dex (long dashed line). The horizontal dashed line in the upper graphic indicates an error in age of 100 % (SSMM models)

The fact that the real evolutionary phase of a star located in the Overlap Region is not known represents an additional uncertainty contributing to the final error for stars placed in this region. Thus, an estimation of this error ([FORMULA]) has been computed as:


where [FORMULA] is the dispersion of the three possible star ages ([FORMULA]) around the adopted value (see Sect. 2.1). The new error is easily seen in Fig. 3 as a discontinuity at the end of the Main Sequence.

The variation of the relative error in mass (Fig. 3) is much smaller than for [FORMULA] (less than [FORMULA]  15%), basically due to the fact that errors in mass depend heavily on the slope of the evolutionary tracks in a [FORMULA]   [FORMULA] - [FORMULA] diagram, and this slope does not change much in the Main Sequence and subsequent phases. As in the case of ages, [FORMULA] /M in the Overlap Region has been calculated with an expression analogous to (2) in order to consider the phase uncertainty.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998