# Sun from SuperNova

I have read that our sun was created from older star(s) which had exploded in a supernova. If all the matter is travelling away from the central point of explosion, how does it coalesce back into a nebula and then form a sun? Wouldn't all the matter just keep moving further and further apart? Wouldn't gravity be far too weak to bring it all back together into one place?

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I guess it's just that the time scales are incomprehensible. The forces due to gravity would be tiny. I can't get my head around the idea that tiny variations in a tiny force would generate something so huge as a star from particles travelling away from one another at tens of thousands of meters per second. – John C May 10 '14 at 8:07
The nebula slowed down due to gravity. It is even possible that the cloud collapsed due to a shock wave from a nearby supernova. See this for more. – Yashbhatt May 10 '14 at 8:07

Actually yes, gravity is too weak to do the job by itself. But as you mention, another force is acting on the system too, in a very strong way: it is the pressure that pushes outwards. In fact, the energy released by the explosion of the supernova, helps to compress the layers of released material (gas and clouds). You have shocks between the expelled gas (fast) and the ISM (slooow). Also, you need cold gas to produce a collapse event, and the ejected material from an explosion is not cold at all!

So, you need an efficient mechanism to induce collapse of the gas cloud, and this mechanism is furnished by compression instabilities.

You start from the Virial theorem: $2K + U = 0$

with K kinetic energy and U potential energy. What you want here, for your collapse is that the gravitational potential energy is larger than the kinetic energy (otherwise particles energy will overcome the gravity and avoid collapse - not exactly true, but you can think as if high energy particles pushes outward).

Then you can rewrite the Virial theorem as:

$$3 N K T = \frac{3}{5}\frac{G M^2}{R}$$

where K boltzmann constant, N atoms number, M mass of the cloud, R its size.

In our case (collapse case) the left term must be less than the right one.

Then you can transform $N = M/m$, with m mass of the single particles, and $R = \frac{3 M}{4\pi\rho}$, with $\rho$ cloud density (assumed constant).

Than you can calculate the Jean mass as:

$$M_J = (\frac{5KT}{Gm})^{3/2}(\frac{3}{4\pi\rho})^{1/2}$$

This is the limit after which your cloud can collapse. Look at the dependence on the temperature, and the inverse dependence on the density.

Just to give an idea of the typical values encountered, we can still rewrite the critical mass as:

$$M_J = 2M_{sun}(\frac{n}{10^5 cm^{-3}})^{-1/2}(\frac{T}{10 K})^{3/2}$$

Source: this lesson

PS: a similar mechanism is triggered by the rotating arms of spiral galaxies.

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Wow. So it's effectively the faster shock waves banging into the slower ones that compresses the matter. Does that mean that the first generation of stars were much larger, and the next generation after ours will be smaller again? – John C May 12 '14 at 11:25
This is indeed theorized, that the first population of stars (so-called Pop III), was much more massive than the current populations (I and II), but as far as I know, the theory was based on the amount of metals. Probably, also "unshocked" universe is playing a role there. But I dont know so much about that. I guess a smaller universe was pro-collapse. I think this is an on-going work, since Pop III stars have never been observed yet, and their mass properties are still debated. – Py-ser May 13 '14 at 3:35