I haven't done the math myself, but it used to be commonly taught that Boyle's Law would prevent a gas cloud in the vacuum of space from gravitationally collapsing and forming a star. Stars were said to form when a shock wave from a nearby supernova explosion disturbed the cloud(s) enough that a high-density area could form and start the process of stellar formation.
Obviously the first generation stars would have no supernova explosions to get them started, so new ideas have been advanced to get around the problem. Some require very high temperatures, and others go the opposite way and use very low temperatures. Some seem to use both simultaneously, but I must be mistaken about that - who wouldn't spot such an inconsistency?
I haven't seen dark matter invoked yet in star formation scenarios, but it's only a matter of time. Such a handy tool cannot be neglected forever.
These calculations assume the "typical stellar cloud" has the same mass as our sun, occupying a spherical space "about .1 LY across". Perhaps this is why your results are the first I've seen that indicate gravity is sufficient to form stars from these clouds.
I think the alternative approach would be to take a given amount of gas and calculate it's volume at various temperatures, or take the volume and calculate the mass.
I could be wrong. I don't have a lot of experience with this kind of thing. But there must be some explanation for your unique results.
I'm sorry if I misread your post. I was somewhat surprised at the conclusion, since to the best of my knowledge the supernova shockwave scenario has been the front-runner for quite some time.
Thus I took a closer look to see just exactly what your math was modeling. If you were to take the mass of the sun, translate it to gas, and calculate the volume it prefers to occupy at a given temperature, I think your results would probably match most models. If the gas is sufficiently "pre-condensed" at the start of the calculation, gravity alone should suffice; but then how does one account for the "pre-condensed" state?
Gases in space aren't easy to deal with. I'd prefer to leave it to persons more capable than myself. For example, they can turn to liquid if they decompress rapidly. Also, the ideal gas theory is said to only approximate many real-world gases. So I try to leave the nitty-gritty arguments to others.
There is some controversy between Big Bang advocates and Young-Earthers, but I don't think this thread was started for the purpose of arguing it. I see it as informational in nature. I think it would be more appropriate to explain the popular model. The difficulties it faces must be fairly minor, or they would already have applied dark matter to the model long ago.
Can't help you there. Strictly speaking, I probably could go look up some things and study for a few days or weeks, but it's not that important.
It easy to see the history of the models. Way back when, they used to say gravity pulled the clouds in until stars formed. Then they discovered gravity wasn't enough, so they used shockwaves from supernova explosions.
Could be somebody made a mistake - maybe gravity is enough all by itself. Last I knew, it was pretty well agreed that it isn't; but I haven't done all the calculations and I don't intend to. They don't appear to be very easy. I always get confused about how pressure emulates temperature, and I'll bet that's a factor somewhere in the mess.
If people want to believe clouds can condense into stars without supernovas, I don't have a problem with it. I've tried to pitch in, and I may even be wrong about which model is now "preferred". If your model is newer, that's fine. If it's older but still correct, that's fine too.
Now if it's always been common knowledge that gravity alone could get the job done, why was the supernova model even invented? I hardly think any YEC would invent such a thing. And I'm a tad curious just how many gas clouds should be present if it's a "done deal" and they're all busily condensing into new stars.
There may be someone who would like to argue about this and mix numbers with you, but that would be someone other than myself. If it wasn't a very close thing, dark matter would've come into play long ago. Since it is a very close thing, and the math is complex, I see no point in arguing it. I cannot say at what point a gas reaches equilibrium and the pressure matches up with the gravity. Perhaps your gas wasn't condensed enough for that to happen yet. Maybe it never will... (at least maybe not prior to ignition!)
Again, your model might be good. It might be the best. But it comes to a conclusion that is the opposite of what was commonly believed not long ago. I'm not going to argue. One way or another, under Big Bang cosmology the gas clouds become stars. I understood they needed something to jump-start the process, but I really don't care very much either way. I am not infallible, and neither are those who performed similar calculations in the past.
My criticism of your model may have been erroneous. If it was, I am sorry. I was merely attempting to account for the discrepancy.
If anything, I'm feeling overexposed these days. There's only so much I can take of stuff that's obviously untrue. Fortunately this isn't a case of obvious untruth. The more I look at it, the more complex it grows.
Here's some more links I dug up. I know there's better somewhere, but how to find it!? Anyhow, here's a couple from a fairly pro-banger forum. You'll need to find the "flat" button to view the whole threads. Then "find" words from my quotes below if you care enough.
"Star formation is usually thought to require a fairly good sized and energetic event such as a supernova, which can compress a gas cloud and begin the process of gravitational collapse."
Then from the other:
"The cloud started out spinning. This spin was very slow, in fact the same rate of rotation as the Galaxy as a whole. However, as the cloud collapses, it spins faster. The centrifugal force created by the spin counters gravity and this should prevent the cloud from collapsing, since it increases faster than gravitational force.
This is called the 'angular momentum problem' and it was a vexing puzzle to astronomers throughout the 19th Century and into the earliest part of the 20th Century. In our solar system, the enormous Sun has over 98% of the mass of the system, and yet the planets orbiting around the sun have over 90% of the angular momentum (the spin). What mechanism could have carried away the spin?"
As if we didn't have enough to deal with, they throw angular momentum into the mix. Oh, and the first guy's pretty much saying what I've was saying earlier. These guys probably aren't experts, but I'd say they represent pretty well what's taught in the mainstream.
But here's a nice find for you! Ever hear of a fellow named James Hopwood Jeans? He worked out some relatively simple formulas about gas clouds collapsing.
The physics of molecular clouds are poorly understood and much debated. Their internal motions are governed by turbulence in a cold, magnetized gas, for which the turbulent motions are highly supersonic but comparable to the speeds of magnetic disturbances. This state is thought to lose energy rapidly, requiring either an overall collapse or a steady reinjection of energy. At the same time, the clouds are known to be disrupted by some processâ€”most likely the effects of massive starsâ€”before a significant fraction of their mass has become stars.
Which is why I'll save my energy for something else. There just aren't too many areas where the big official brains so obviously don't know what's going on. I mean no insult by that. It's very much to their credit that they don't make more of an effort to hide it.
I mean just after what little research I've done for my posts on this thread it's my opinion that anyone who just up and says "yes it will" or "no it won't" is probably not taking everything into consideration. At this point I would not be confident betting on either side, myself. Times are changing, and I don't consider you "wrong".
Here's another bone: if some YEC wants to say you need the supernovas, just whip out a little magnetism & electricity on 'im. There are other not-so-obvious factors. You don't have to fall back on dark matter, not for a long time. But be prepared for some surprises the other way too, if he's sharp & up-to-date.
Goodness! It's been a while since I learned so much about something I care so little about. But it was more fun than watching any Hollywood awards show.
Good Luck, TD. I look forward to clashing with you on an issue I do care about sometime.