Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002sf2a.conf..557p&link_type=abstract
SF2A-2002: Semaine de l'Astrophysique Francaise, meeting held in Paris, France, June 24-29, 2002, Eds.: F. Combes and D. Barret,
Astronomy and Astrophysics
Astrophysics
Scientific paper
The modelling of stars with a stellar code, e.g. with CESAM, requires the determination of the value of some (so-called) parameters depending of the value of some (so-called) observations. This can be done with some usual techniques (for instance, in our case, using generalised least square adjustments with SVD decomposition) and, obviously, are not the subject of this contribution. Here, we define a "Model" of the Sun (for the actual work) as the union of the set of some given observations and the set of some chosen parameters. Hence, the "model" of the Sun with luminosity and surface temperature as observations is different from a "model" with luminosity and radius as observations. Again, with the same set of observations, we obtain different "models" if we consider the mixing length as the only parameter or if we consider as parameters the mixing length and (for example) the age of the Sun. The goal of this paper is to determine in a consistent way (and for various "models") the uncertainties of the (fitted) values of the parameters depending of the uncertainties of the (observed ! ) values of the observations. This can be done in inverting the "equation of propagation of errors" with a design matrix which is, in a certain manner, the square root of the matrix involved in the least square adjustments. As illustration, we present a very simple but not so trivial example. It is known that, in a case of a star, there is a relation between luminosity, surface temperature and radius and, hence, it is sufficient to give two values among the three ones. In the case of Sun, there are (really) independent determinations of the value of this three observations ; values that, of course, do not verify (as their level of accuracy) the above constraint. Depending of our choice of the two (independent) parameters, we can show which "model" is the more consistent.
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