# How do interstellar hydrogen atoms form stars?

I would like to learn the basics about how interstellar matter contracts into stars under the influence of gravity.

Some of my questions:

Let's assume an ideal and infinite large cloud of equally distributed hydrogen atoms of zero K temperature. Will it collapse into a star if there is a small inhomogenity anywhere, for example a single dust grain, or a single cubic meter of space having more than the average number of hydrogen atoms?

What is the effect of the temperature? Obviously if the interstellar matter is hot, the individual hydrogen atoms have a high speed so it would need much more gravity to condense into a star.

What is the effect of ionization, or what happens if I consider molecules instead of single atoms, or even larger objects such as dust grains.

I would appreciate it if you can point me to relevant physics textbooks or online courses.

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I'm not sure how useful it is to talk about an infinite dust cloud as you couldn't say that I would collapse to a star if there were some small inhomogeneity as it is infinite in extent. Also since 0K cant be achieved, the dust particles will have some kinetic energy so you get random fluctuations in density as the move around, interact and collide, eventually there will be less and less homogeneity and eventually stars I guess. –  Dmist Apr 17 '13 at 14:01
The reality is of course much more complex, but I was thinking of the simplest possible model to get started. –  nn4l Apr 17 '13 at 18:48

Carroll and Ostlie, and Shu are both excellent introductory texts which have good discussions of star formation. The former is a little more quantitative, the latter qualitative. Also the online notes of Mark Krumholz are fantastic if you have some background in physics. The wikipedia page is also not bad for concepts.

## Star Formation

The most basic treatment of star formation is generally 'Jeans Collapse' (or 'Instability'). You start with a large extent of gas, and estimate at what mass and radius (the "Jean's Mass" and "Jean's Radius") the 'cloud' will collapse and start forming stars. The initial material has to have a non-zero temperature, because 1) reaching 0 Kelvin is impossible, 2) the thermal motion and pressure is what keeps the gas from having already collapsed.

As you suggest, any initial density perturbations (which there are always plenty of) can be seeds for initial collapse. If you imagine a perfectly uniform distribution of cold matter, any increase in density is unstable - and will trigger gravitational collapse. Collapse is generally thought to be 'hierarchical' --- a large cloud or 'clump' (1,000s - 10,000s of solar masses) will start to collapse, then smaller 'cores' (100's of solar masses) will collapse within it, then finally protostars within cores.

If gas is hot, it won't collapse because the thermal pressure resists gravity. Thus star formation requires cooling (the details of which are a very active area of research). To form stars, gas needs to reach about 10 Kelvin (very cold!). At such low temperatures, hydrogen is neutral (ions exist at higher temperatures), and eventually combined into 'molecular hydrogen' ($H_2$).

Dust (molecules heavier than $H_2$ in astro-parlance) helps cooling, and thus is associated with enhanced star formation. Dust and molecular gas are the main things you see in active star formation regions, like the Carina Nebula

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If you took what you have described literally, so infinite in extent (so no net force on each point) and at 0K so each particle doesn't move, the neglecting other mess from 0K, then you may well have just a static dust cloud, but as this isn't physical look instead at a finite cloud at some temperature close to 0K. Then as described above you wold end up with stars as a result of first of all a net force towards some centre, and also local regions of greater density which would collect matter eventually as well. Increasing the temperature means each particle can sit higher in the gravitational potential well of the system so probably would slow the whole star forming down a bit. As stars start to form, the particles would naturally gain more kinetic energy and the temperature would increase so there would be some outward pressure resisting the collapse, but overall gravity would win if we are talking about a sizable dust cloud. If we are talking about close to absolute zero then there wouldn't be any ionisation unless the density is very very low and the probability of a positive and negative ion coming together is very low. Looking at molecules and bigger, anything that increases the non-homogeneity would result in quicker collapsing I think.

Not sure how wonderful that is and exactly how correct some bits are but I'm sure others will correct where necessary, try looking into Newtonian gravity specifically the potential well inside a spherically symmetrical body with constant density. I think that would be quite instructive.

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