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Astron. Astrophys. 330, 619-625 (1998)

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5. Discussion

The obvious conclusion from the foregoing examination of both the MK and the Garrison-Gray standards is that we have to reconsider one of the byproducts of the MK system - namely the link between luminosity class and absolute magnitude. The luminosity class itself is a summary of the description of certain spectral features. The luminosity - as expressed by the absolute magnitude - refers to the whole star and not just to its superficial layers where the spectrum is produced. As remarked above, the implicit assumption up to now has been that the luminosity class translates directly into the absolute magnitude, in a unique way. The preceding discussion shows that this is not so, because the order of luminosity classes is not always the same as the order in absolute magnitude. One is thus led either to conclude that a) the relation is only a statistical one or that b) there exist one or more other parameters which influence the relation.

As remarked before, there exists an overall agreement of luminosity classes with absolute magnitude, in the sense that giants are on the average brighter than dwarfs, so it seems that the relation is a statistical one. With the accuracy of the individual Hipparcos parallaxes one can be sure that the scatter does not come from the absolute magnitudes.

To examine this possibility in more detail, we have plotted in Figs. 6 and 7 the spectral-type absolute magnitude relations for subgiants and giants respectively (for class V see Fig. 1). One can then draw average curves through the points or segments of straight lines, to establish the scatter around the mean relations. For dwarfs we have fitted two straight lines, one through the B-type stars and the other through the A and F-type stars. The dispersion of the points around these straight lines is of the order of 0.7 mag. For giants we have adopted one straight line. Leaving aside two very deviating points, the dispersion is again of 0.7 mag. Such large dispersions explain easily the occasional misplacement of giants below dwarfs, or of dwarfs above giants. For subgiants the dispersion is also of the order of 0.7 mag.

[FIGURE] Fig. 6. Absolute magnitude as a function of spectral type for luminosity class IV MK standards. The straight line represents the average relation adopted.

[FIGURE] Fig. 7. Absolute magnitude as a function of spectral type for luminosity class III MK standards. The straight line represents the average relation adopted.

As remarked above the large dispersion is not due to the absolute magnitudes, because they have very small errors - the cause must lie with the luminosity classes. In principle this is understandable, because absolute magnitude and its correlated spectroscopic characteristics are continuous variables, whereas luminosity classes are discrete variables. On top of this, luminosity classes are estimated by eye, not measured. It is therefore hard to imagine that classifiers have chosen always as standards those stars which fall just in the middle of the range of the continuous variable which correlates strongly with absolute magnitude. This fact alone may be responsible for the scatter. Obviously it will be desirable that stars which deviate very much from the average should be eliminated, and this implies a critical revision of the list of standards.

If one accepts the opposite point of view, namely that the relation is strict, the cause of the deviations has to be sougth in other factors. One of the possible explanations - rotation - seems not the cause, as we have shown in the discussion of the Gray-Garrison standards. A second possibility is (undetected) binarity. The fact that some standards are close binaries (spectroscopic or interferometric) can not be excluded, even it is not very plausible, because the standards belong to the group of the most observed stars. However the number of "problem" stars seems too large to be explained this way.

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© European Southern Observatory (ESO) 1998

Online publication: January 16, 1998