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Astron. Astrophys. 340, L35-L38 (1998)

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5. Conclusions

Among the two methods presented in this paper to represent the pdf of the distance determined from the parallax [FORMULA] has two disavantages.

  • The distribution is strongly asymmetrical and can be used only numerically in later computations.

  • In deriving the rms from the variances, the unprobable large values of x play a major role, increasing the rms in a way that can be considered as unrealistic.

The Gaussian representation [FORMULA] of [FORMULA] has the advantage of being usable as such in further evaluations of uncertainties of quantities depending among others on the observed parallaxes. One may remark from Table 2 that the quality of fit worsens rather quickly when k increases. For this reason, our suggestion is to use the solution with k=2.5 which encompasses 98.64% of the probability distributions and formulae (13) and (15). One may remark also that with this Gaussian pdf, the position of the maximum correspond closely to the mean between the maximum given by [FORMULA] and [FORMULA]. It is however to be noted that its derivation used the true rather than the observed value of the parallax. This may introduce an additional uncertainty, particularly for large [FORMULA].

Finally, the tables presented show that the solutions degrade for large values of [FORMULA]. It is not reasonnable to use any pdf for [FORMULA]. Then, the determination of the distance from parallaxes looses its physical significance, and photometric determinations are definitely better. In any case, cutting a sample at some value of [FORMULA] may introduce a bias, so that users are invited to ascertain that the sample satisfies the conditions of applicability of the method.

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998
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