And while I was preparing the previous reply, which just barely made the maximum character cut (sorry it took a while: I've been busy with a paper), you posted this:
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Originally Posted by Ari Jokimaki
Well, it seems that Arp was prepared to this discussion, in his latest paper he suggests a new definition for quasar:
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Originally Posted by Arp & Carosati
A quasar is a compact (high surface brightness) object which shows appreciable non thermal radiation.
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So there. 
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That definition is pretty close to the standard definition, depending on what exactly is meant by "appreciable." After all, star-forming galaxies and planetary nebulae can have "appreciable" narrow emission lines (which are non thermal) due to hot gas, as I discussed above. And a supernova is an "appreciable" non-thermal point source, like the one that confused me (though it's only around for a short while)...