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I Is there a point during star formation when gas is 1 atm?

  1. Aug 27, 2016 #1
    I have been reading about and contemplating the early stages of star formation lately. An interstellar cloud collapses under it's own gravity to form a star. There is much data about what could trigger it, and what happens when the gas heats up or starts fusing.

    However, i couldn't find anything that answers what would the collapse look like from the inside.

    Specifically, is there a point during it where the gas is at around atmospheric pressure?
    Logically, there should be such a point...

    Would that point last, and for how long? What sort of temperature would there be inside of it? The numbers i've seen list temperature of 2000 *C at much lower density.

    All in all, i imagined a place that is a gas cloud in interstellar space that is slowly collapsing, which someone stumbled upon while it had earth-like pressure at it's center, and wondered if something like that could actually exist.
     
  2. jcsd
  3. Aug 27, 2016 #2
    The density and pressure at the center of the collapsing nebula must continually increase and at some point be similar to the atmosphere at the surface on Earth.
    At some point it will also be similar to the surface atmosphere on Venus.
    There is nothing significant about that though, and the temperature will be nowhere remotely close to that needed for fusion reactions.
    It is not at this stage a star, but just a gradually contracting gas and dust cloud.
     
    Last edited: Aug 27, 2016
  4. Sep 3, 2016 #3
    But will the temperature be anywhere near survivable?
    The thought that piqued my curiosity was that there could be a longer-than-instant period where such survivable conditions could exist inside such a collapsing nebula.
     
  5. Sep 3, 2016 #4

    Ken G

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    That would depend on where you are in the star, but I don't think you'll ever get 1 atm and 300 K, and here's why. The surface pressure of the Sun is about 0.001 atm, so in the current Sun, you'd need to go well under the surface, and of course it would be way too hot. So you are wondering if a forming star, cooler than the Sun, might allow cosy temperatures at 1 atm. It turns out that the surface pressure is always proportional to the surface gravity divided by the opacity, so if the opacity does not change a huge amount (that might not be a great assumption), it means the surface pressure is always about 0.001 m/r2, where m is the stellar mass and r its radius, both in units relative to our Sun. So it doesn't sound like the stellar surface is promising. Let's try the opposite limit of the stellar core, and then you can use the virial theorem, which states that the temperature is about 107 m/r in Kelvin, where m and r are again in solar units. The pressure is then roughly 109 m2/r4 atm, given that the core pressure of the Sun is of the order of a billion atm. This all means that if you want T to be about 300 K in the core, you need m/r to be about 0.00003, very roughly, and so that means to get 1 atm in the core, you need m ~ .0003 or so. In short, stars with any kind of reasonable mass always have very high temperature by the time their cores reach 1 atm, temperatures of many tens of thousands Kelvin. It also means the stellar radius is red giant scale when the core reaches 1 atm. But by the time the star reaches red giant scale, it is a kind of star called a "Hayashi track" star, and such stars have their surface T regulated to be about 3000 K. So we can conclude that a star with a core P of 1 atm is always too hot everywhere, and to get any other place in the star up to 1 atm, it must only contract even more and get even hotter. I therefore do not think stars ever have a place in them that is at both 1 atm and about 300 K.
     
  6. Sep 4, 2016 #5
    Use that to derive the opacity and surface pressures of Jupiter, Saturn, Neptune and Uranus.
    Which is about the mass of Saturn...
    So where are stars before they reach Hayashi track?
     
  7. Sep 4, 2016 #6

    Ken G

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    Yes, you could look for places in gas giant planets that are 1 atm and 300 K, but not stars. Before stars are on the Hayashi track, they are very low pressure and very low temperature, so you can certainly get 300 K, but you can't get 1 atm.
     
  8. Sep 4, 2016 #7
    Are protostars subject to virial theorem? Such as, are they supported by pressure against gravity?
     
  9. Sep 4, 2016 #8

    Ken G

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    Yes, protostars are pretty much ideal gases in force balance with gravity and pressure, so they are ideal candidates for the virial theorem. But the virial theorem is even more general than that, it holds even if you have other interparticle forces than gravity, and even if you have degeneracy. But it gets harder to use when there are other forces than gravity, though simple Coulomb interactions end up not playing essentially any role so they are generally neglected. I suspect van der Waals forces would be trickier though. Interestingly, the normal form of the virial theorem still works great for degenerate systems like white dwarfs, but gas giants are likely hard to track that way because of the complex force interactions.
     
  10. Sep 5, 2016 #9
    Is there any point where the force balance breaks down, and gravity instead of being balanced causes inward acceleration on free fall timescale?
     
  11. Sep 5, 2016 #10

    mfb

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    If you want to survive, temperature is more relevant than atmospheric pressure. You'll need some oxygen supply anyway because stars mainly consist of hydrogen and helium, with a negligible fraction of oxygen (and even more negligible for elementary oxygen).
     
  12. Sep 5, 2016 #11

    Ken G

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    Yes, in the original "Jeans instability" that collapses the molecular cloud. There is a fragmenting phase where clumps of mass contract on free-fall times, and fragment into smaller and smaller clumps, but eventually you get down to stellar mass sizes and by then pressure kicks in and the contraction is much slower.
     
  13. Sep 5, 2016 #12
    Protostars are certainly not in thermal equilibrium, because some on them have negative absolute temperature. Otherwise they could not emit microwaves as masers.
     
  14. Sep 5, 2016 #13

    Ken G

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    Nothing is in global thermal equilibrium-- nothing. But it is a useful local approximation in all kinds of situations, including protostars.
     
  15. Sep 6, 2016 #14
    Note that protostars heat up by roughly 7 orders of magnitude. For a not yet compressed cloud, the temperature is similar to relic radiation - now around 3 K. For a main sequence star, the central temperature ranges from around 4 million degrees of red dwarfs through 15 millions of Sun-sized dwarfs to over 40 million degrees of massive dwarfs of Sun-like metallicity.
    So, a protostar with initial central temperature of 3 K and final temperature of 30 million K will be 30 K, 300 K, 3000 K, 30 000 K, 300 000 K and 3 million K somewhere along the path.
    What does a protostar with central temperature of 300 K look like?
     
  16. Sep 6, 2016 #15

    Ken G

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    Its pressure is everywhere much lower than 1 atm if it has reached force balance at that low T. My guess would be that it is in force balance by that point, but maybe not, that's still pretty cool.
     
  17. Sep 6, 2016 #16
    The molecular mass of snowflakes, dust, meteors, comets and asteroids is far bigger than that of dihydrogen.
    If protostars are balanced by gas pressure, would the solids sink to the centre once the gas is dense enough to stop them from orbiting by friction?
     
  18. Sep 6, 2016 #17

    Ken G

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    That's a good question, perhaps the same friction that would tend to pull them into the center of the protostar would also heat them up and destroy them. But it does seem like there might be a cool phase when stuff like that tends to get pulled in moreso than does the gas. It probably wouldn't leave much imprint on the final chemical composition, because the star will go fully convective as it heats up.
     
  19. Sep 7, 2016 #18
    A meteor falling to the centre of protostar cannot produce more energy per unit mass than a parcel of gas doing the same.
     
  20. Sep 7, 2016 #19

    Ken G

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    You have a point, it would be hard to get the meteor to a temperature hotter than virialized gas around it. So if the gas was already at 300 K, the meteor might not go much above that due to friction. Certainly a baseball moving at the speed of an air molecule, so having the same kinetic energy per gram, will heat up to a temperature much higher than air, but air is highly under-virialized, unlike the gas in a 300 K protostar. So maybe dust grains would tend to congregate near the center without being destroyed, though it doesn't sound like that would have any long-term impact.
     
    Last edited: Sep 7, 2016
  21. Sep 7, 2016 #20
    Also note that cooling is concentrated near unit optical depth. Clear gas above the visible surface of the cloud is unable to cool, because it is transparent and can neither absorb nor emit radiation; the dust and gas mixture near the centre is unable to cool because opaque dust prevents escape of radiation.
     
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