A (VERY) BRIEF HISTORY OF COSMOLOGY

... By Dr. Kevin Marshall

The Cloud who wanted to be a Star

(A story to help in understanding the Jeans criterion and used at a recent Open University tutorial)

Once upon a time there was an interstellar cloud who wanted to be a star.
So he went along to the office and said, "Can I be a star please?".

"Can I just check your parameters, sir?" said the girl at the desk.

"Temperature?" "100K"

"Density?" "I’m afraid I don’t know."
So she weighed him - only 13 solar masses, not very big - and she measured his diameter - 10pc; so she could calculate his density.
"What sort of hydrogen are you? - neutral atomic? OK, so you’re about two million atoms per cubic metre; that seems reasonable. Any rotation? - no. Any significant magnetic fields? - no, good," she said.

So she put all the figures into her spread-sheet, and she said, "I’m sorry, sir - for your temperature and density, the Jeans mass is about 2500 solar masses, so at 13 solar masses you’re nowhere near massive enough to start contracting and become a star."

"Isn’t there anything can I do about it?" he asked.
"You could try lowering your temperature a bit," she suggested, and she showed him a diagram of how the Jeans mass depends on temperature and number density. (This is just a rough version.)

So he went away, and he came back a bit later, saying, "I’m a lot cooler now!"
She measured his temperature: it had dropped from 100K to only 1K. She was impressed [not surprisingly! - it's almost certainly impossible to get below 3K in interstellar space; but what the heck, this is only a story]. She changed the temperature in the spreadsheet: the Jeans mass was now only 2.5 solar masses.
"And you’re 13 solar masses, so yes," she said, "you can become a star! - assuming all your other parameters are still the same?"
"Well, I have expanded a bit...." he admitted.

She checked: he’d expanded from 10pc diameter to 100pc.
"Well, that changes your density," she said.
So she put in the new diameter, and his density was down to only about 2000 atoms per cubic metre; and the Jeans mass went up again, to 85 solar masses - not as high as it was before, but still well out of his reach.

"So I can’t be a star?" he said. "I mean, I can’t get any colder!"
"No," she said, "but perhaps you could go back to the way you were, and instead of worrying about your temperature, see if you can get your density up instead. Try to contract a bit."
So off he went, and he came back saying, "I must be really dense now - look how small I’ve got!"
He’d shrunk from 10pc to only 0.1pc.
"Wow - that should make a difference," she said, and she worked out his number density as 2x10¹² atoms per cubic metre.
"Great, your Jeans mass is now just 2.5 solar masses again, and you’re 13 solar masses, so yes, you can become a star! - assuming all your other parameters are still the same?"
"Well, I have heated up a bit...." he admitted.

She checked, and his temperature had shot way up - from a hundred K to a million K!
"Oh dear," she said, and she ran the calculations again - the Jeans mass was now 2½ million solar masses.
"Just a minute," she said suddenly, "You said you were neutral hydrogen, but I don’t think you can be now, can you? - not at that temperature!"
"No, I think I’m totally ionised now. Hey, so I’ve got twice as many particles!"
"Yes," she said, "but it also reduces your average particle mass. Let me see. No, it makes matters worse."
The Jeans mass was now three times greater - even further out of his reach.

"So I can’t ever be a star," he said.
"Look," she said (she really did want to help him), "I tell you what your problem is: you’re adiabatic, that’s what you are. You expand, you cool down; you contract, you heat up. You just keep moving backwards and forwards on this same line.

"You can't ever be a star unless you can manage to cool down and contract at the same time."
"But how can I do that?"
"You need to start interacting with your environment a bit. Look, go back to the way you were, and start contracting, but this time, instead of letting yourself heat up, try radiating a bit - throw some of your heat away into space, no-one will notice. And that’ll bring your Jeans mass down - honest!"

So he tried it: he started to contract, and as soon as he began to get hot, he waited until he could radiate away the heat, and then he contracted some more. And it worked: he finally got his Jeans mass down below his actual mass, and he did become a star. And he lived happily - not for ever after, but for about 20 million years, which is not far off.