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If we plot graph between accumulate of forming mass (y-axis) and mass (x-axis), where is the maximum ?

There is a story how I get this question. It start when I think about question "Is our sun is big or small ?".

https://www.quora.com/What-is-the-average-mass-of-a-star

The average mass ends up being around 0.5 solar masses.

But very high mass stars have very short life span so there are more O-type main sequence stars ever form more than O-type main sequence stars we see today.

I think it would be better to measure our sun by using average mass of forming stars than average mass of stars we see.

So, what is average mass of forming stars ?

Then I think a litle bit more. There is no exact boundry between large brown dwarf and small red dwarf stars. So, if we include them too, what is the most mass that matter likely to form ?

If it is inverse-square law, so graph between accumulate mass (y-axis) and mass (x-axis) will be y=c/x where c is constant.

And make the maximum is zero or mean that most of matter aren't form star. At this point, I think I should limit the minimum mass of forming object at some point. But is it inverse-square law for all type of forming object?

If most of matter aren't form star, will be gas cloud. So we don't count them (both molecular gas and mono-atomic gas but dust is still count because it is solid not molecular or mono-atomic object), what is the most mass that matter likely to form?

Please help me or tell me what should read to answer or give keyword to me.

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    $\begingroup$ Very interesting question indeed. As I have a strong belief that the mass distribution of forming stars is going to vary during the age of universe, are you looking for a cumulative distribution up till now, or about the stars that are “alive” (ie main sequence or so) right now, or the stars that are currently forming? $\endgroup$ – tuomas May 2 at 12:13
  • $\begingroup$ @tuomas Thank you. If it is vary, for the question "most mass that matter likely to form", I want to see graph between most mass that matter likely to form and age of universe. For the question "what is average mass of forming stars ?", I want to see the graph too, but I really want to know average mass of forming stars when our sun was born. $\endgroup$ – uesdto signin May 2 at 12:24
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    $\begingroup$ Most of the matter in the universe hasn't condensed into stars (or planets, moons, asteroids, etc). It's still dispersed in gas clouds. $\endgroup$ – PM 2Ring May 2 at 12:28
  • $\begingroup$ @PM 2Ring Thank you. So, if we don't count gas cloud, what is the most mass that matter likely to form ? $\endgroup$ – uesdto signin May 2 at 12:37
  • $\begingroup$ At a guess, the vast majority of star mass is in red dwarfs. But it's hard to be exact, since it's not easy to see red dwarfs, and isolated brown dwarfs are virtually undetectable. $\endgroup$ – PM 2Ring May 2 at 12:49

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