What volume of interstellar space is needed to form a star?

[anyman]

So, let me preface by saying I’m neither a scientist nor a mathematician, so am requesting some talented help here checking the accuracy of my source information and math.

Regarding star formation, I got curious about how much volume of space in the interstellar medium is actually required to form a star, and to determine that size based on something relatable conceptually. This has no doubt already been done ages ago, and if so please just pass the link on so I can check it out.

Nonetheless, for fun I’ve laid out what I think is a logical sequence and mathematical progression below based on what I hope is reliable information (as reliable as possible at least) that is generally accepted in the science community. So, for those with the expertise and are willing, would appreciate checking to see if my conclusion on the required volume of space to form a star is in the ballpark, though I could have easily messed things up anywhere along the progression. Thanks! I’ve tried to ere on the conservative side each step. Here it is:

1. "The density of the interstellar medium ranges from as high as 10 to the power of 6 atoms per cm3 in a molecular cloud”

https://www.quora.com/How-many-atoms-are-contained-in-1-liter-of-interstellar-space

So, though it seems the norm is much much less, I took 1,000,000 atoms per cubic cm as a baseline density for a molecular cloud that’s going to gravitationally collapse to form a star.2. Next, how many atoms are in a star? It has been estimated that there are ~9.1 x 10^56 atoms in the sun (I’m using 9 x 10^56 for simplicity).

https://www.quora.com/How-many-atoms-fit-in-the-sun

Now, that’s the number of today’s atoms. Seems the number would have been significantly higher when the sun was initially formed, but will go with that estimate.

9e56 / 1,000,000 = 9e50

So, based on 1,000,000 atoms per cubic cm, using the number of atoms estimated to compose the sun, it would take 9e50 cubic cm of volume in space to form one star roughly the mass of our sun.3. There are 1,000,000,000,000,000 cubic cm in a cubic kilometer, so 9e50 divided by that number is a volume of 9e35 cubic kilometers of interstellar space required to form a star the mass of our sun.
4. The volume of the sun in cubic kilometers is estimated to be 1.4e18 (https://brainly.com/question/72396). So, an estimate of how many suns it would take to fill the interstellar space volume required to form a star is: 9e35 / 1.4e18 = 642857142857142857.

So it would roughly take the volume in space of 642857142857142857 suns to create one star.
5. "We can fit 278.8 billion Suns in the Solar System in a 3D plane.”

https://www.quora.com/How-many-suns-would-theoretically-fill-up-our-solar-system

642857142857142857 / 279,000,000,000 = 2304147

So, based on this (perhaps highly suspect) math, it would take the volume of over 2 million of our solar systems to form one star. Now, sun’s aren’t square, so step 4 isn’t completely accurate, so I’ll shave 33% off the total to account for this. 2304147 - 33% = 1,543,778

Again, please check my logic and math and let me know what’s what, but according to the above, the amount of interstellar space (at its densest) that it would take to form one star is an estimated 1.5 MILLION of our solar systems.

 

[rootone]

I think it would depend on the composition of the material involved.
While most of interstellar space has only small amounts of Hydrogen and Helium in it,
this can be modified locally by emissions of heavier elements originating from Supernovea.
These and the effects of shockwaves are enough to cause a nearby region (in astronomical terms),
to reach a density high enough so that gravitational collapse occurs.

 

[mfb]

9e35 km³ is a cube with a side length of about 1 trillion km or 0.1 light years. As comparison: The nearest star is 4 light years away. Doesn't look too far off.

 

[anyman]

I think it would depend on the composition of the material involved.
While most of interstellar space has only small amounts of Hydrogen and Helium in it,
this can be modified locally by emissions of heavier elements originating from Supernovea.
These and the effects of shockwaves are enough to cause a nearby region (in astronomical terms),
to reach a density high enough so that gravitational collapse occurs.

Interesting point, but are you saying that every star that’s been formed needs shockwaves and emissions of heavier elements to form? From what I’ve read about star formation, this should not be required, and the norm is that stars are formed from “normal” interstellar dust clouds. Also, what exactly are the measurements of what you’re calling a “region”, and what exact density from the shockwave and emissions of heavier elements would result within that region? Without defining those two things, there’s no way to verify what you’re suggesting mathematically.

 

[Janus]

Star are formed in molecular clouds which have a much higher density than the general interstellar medium does. They also contain a fair amount of molecular hydrogen in contrast to the general interstellar medium which is is mostly ionized particles.

 

[alantheastronomer]

You might be interested in looking up what's called the "Jean's mass" and "Jean's length" on Wikipedia, the mass and length needed for a given part of a molecular cloud to begin contracting under it's own gravity to form a star...

 

[Chronos]

For a sun like star, the molecular cloud fragment from which the protostar forms is probably starts out about 10¹⁷meters in diameter, and shrinks to about 10¹¹ meters upon reaching the protostar phase. It needs about a million years before it then stabilizes at solar size [`10⁹ meters.

 

[rootone]

..., this should not be required,.

It isn't required, but usually is the case with Population III stars. (the ones we can see).
The earliest stars (in theory) would have been very massive and short lived, and almost entirely hydrogen.