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What examples are there of fuzzy concepts in astronomy? In particular, how fuzzy are the boundaries between different types of stars?

As an example of a fuzzy concept I'm thinking of the planet/brown dwarf distinction:

The IAU decided to define the term "planet" (at least for the solar system) by giving specific conditions, but for exoplanets the distinction between brown dwarfs of 13 Jupiter masses (MJ) is observationally difficult, and scientifically dubious anyway for various reasons: the initial mass function of star clusters forming does not stop at 13 MJ but could go as low as 1 MJ; objects larger than 13 MJ could form in the same way as planets; and in any case the 13 MJ limit of deuterium burning is for objects of solar metallicity and otherwise doesn't apply - especially if the object has a rocky core, and "deuterium burning" is itself ambiguous - how much deuterium must burn before it qualifies?1 It seems that many objects would be of interest to planetologists and brown dwarf studiers. The Extrasolar Planets Encyclopaedia goes up to 25 MJ.

1) The Deuterium-Burning Mass Limit for Brown Dwarfs and Giant Planets

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Fuzziness is, in some respects, in the eye of the beholder, and it will always be impossible to answer this question definitively. That being said, there are certainly some fuzzy areas, in addition to the good examples mentioned already in the question. I think fuzziness occurs mainly where humans have imposed a discrete classification on objects that turn out to be part of a continuum, or different manifestations of the same object under different circumstances.

The boundaries between different classifications of galaxies in the Hubble Sequence are notoriously fuzzy.

The various ultra-high energy phenomena associated with active galactic nuclei may also be an example of fuzziness arising from artificial divisions introduced simply because a phenomenon looks quite different when viewed at different angles.

Neutron stars exhibiting different aspects of their behavioral repertoire are given lots of different names.

EDIT: PS, Stellar classification is less fuzzy in the eye of this beholder.

EDIT 2: The Shapley-Sawyer Globular Cluster Concentration Class system (Thanks Carson) is ridiculously fuzzy. See How can I judge a globular cluster on the Shapley & Sawyer scale?

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Some nice examples. Thanks. –  XOPs Jun 28 '11 at 21:37
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