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Red dwarfs are more common than larger stars. Does this trend continue to smaller objects? If you take every "condensed object" from dust grains through asteroids, planets, and stars in the galaxy, do you see an approximate power-law relationship where more massive objects are rarer? If so, what is the exponent? Lets consider "condensed objects" to be objects with at least 50% of their mass in a region denser than then the average density of a large red supergiant. Does a power-law also hold true if you only count "rouge objects", which we count as objects that aren't orbiting a more massive condensed object? Does this power-law get steeper when you exceed ~1 solar mass and the lifetime of the star drops below that of the galaxy (significant mass is lost when stars die)?

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    $\begingroup$ It doesn't hold true for brown dwarfs versus red dwarfs; see astronomy.stackexchange.com/questions/44669/… $\endgroup$ Jan 5 at 9:49
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    $\begingroup$ Yes, power laws are ubiquitous in the Universe, not only for "condensed" object. But the power law index varies quite a lot from e.g. dust grains (~ –3.5 for size), to stars (~ –2.3 for mass), to galaxies (~ –2 to –1 for luminosities at the faint end, but a cut-off at the bright end). $\endgroup$
    – pela
    Jan 5 at 10:56

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