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

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• anyman
In summary, according to the information provided, a star the mass of our sun would require 9e35 cubic kilometers of space in the interstellar medium to form. This seems to be based on estimates of the number of atoms in a star, and the assumption that the interstellar medium is uniformly dense. However, as the number of stars that have been formed is unknown, and the details of how stars are formed are still unknown, this information is not completely reliable.
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.

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.

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.

rootone said:
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.

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.

Spinnor
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...

Nik_2213
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.

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Spinnor
anyman said:
..., 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.

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## What is interstellar space?

Interstellar space is the vast expanse of space between stars in a galaxy. It is mostly empty, consisting of gas, dust, and cosmic rays.

## How do stars form in interstellar space?

Stars form through the gravitational collapse of a dense region within interstellar space, called a molecular cloud. As the cloud collapses, it becomes denser and hotter, eventually forming a protostar.

## What factors determine the volume of interstellar space needed to form a star?

The volume of interstellar space needed to form a star depends on the density and mass of the molecular cloud, as well as the initial conditions of the cloud, such as temperature and turbulence.

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

The volume of interstellar space needed to form a star varies greatly and can range from a few light-years to several hundreds of light-years, depending on the factors mentioned above.

## Why is the volume of interstellar space important for star formation?

The volume of interstellar space is important for star formation because it determines the amount of matter available for a star to form and the conditions under which it forms. If the volume is too small, the cloud may not have enough mass to collapse and form a star. If the volume is too large, the cloud may not have enough density to trigger the collapse. Therefore, the volume plays a crucial role in the formation of stars in interstellar space.

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