Is there some ranking / statistics that shows how common given type of celestial objects is? A table that would allow the answers to questions like: What type of star is most common per volume of our galaxy? Are white dwarfs more common than red giants? What percentage in the number of celestial objects located are the black holes? Pulsars? How many red giants have been catalogued?
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In general smaller stars are more common than larger, more massive stars. This is typically described by the Initial Mass Function which describes the number of stars of a given mass which form initially. Moreover, larger, more massive stars burn through hydrogen quickly and live shorter lives, making them even less common as time passes. Thus, to determine the distribution of objects of various types of equal masses, you need to start with an initial mass function, and then use a stellar evolution model to evolve the system to the time of interest.
More generally, a Universal Mass Function, is an attempt to answer the question you pose in terms of mass. That is, are more massive or less massive objects more common in the universe?
The Universal Mass Function provides a description the density of occurrence of objects of various masses per cubic parsec, shown in Figure 3 of Kroupa et al. 2011. As you can see, the more massive something is, the less common its occurrence. Thus, black holes which form from massive stars will be far less common that small low mass stars which become white dwarfs. There are still uncertainties the exact distribution, shown at least partially by the shaded portions of the figure, and it will vary from one region of space to the next.
For more info check out Kroupa et al. and Binggeli and Hascher. 2007. “Is There a Universal Mass Function?”.
Kroupa, Pavel, Carsten Weidner, Jan Pflamm-Altenburg, Ingo Thies, Joerg Dabringhausen, Michael Marks, and Thomas Maschberger. 2011. “The Stellar and Sub-Stellar IMF of Simple and Composite Populations”. ArXiv e-print 1112.3340.
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$\begingroup$ Thank you, that's a very nice answer covering a large part of the field, but it still only scratches the surface of the problem of popularity of types of stars/bodies of similar mass, so I'm going to leave this question open. $\endgroup$– SF.Commented Nov 20, 2013 at 15:04
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$\begingroup$ Nice answer indeed. Can you speculate, whether the slope in the figure you are showing can be derived from the first principles? $\endgroup$ Commented Nov 20, 2013 at 21:14
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$\begingroup$ @AB:Intuition suggests larger, more complicated things are more rare, but physics governing different sections of the figure varies -manifested in the variations in slope. The authors of the figure, Binggeli and Hascher speculate a few underlying processes, but point out, "that our primary goal is not to find a sort of cosmological principle that governs the mass distribution function of the universe, but to provide a valuable piece of cosmography. A good knowledge of the frequency distribution of things in the universe is an end in itself." Which addresses the original question. $\endgroup$ Commented Nov 27, 2013 at 4:00