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Chandrashekhar Limit

  1. Aug 21, 2005 #1
    HI friends,
    What is Chandrashekhar limit? HOw is it calculated? Does it remain same for every star? What are its dimensions?
    Any suggestions are welcome.
     
  2. jcsd
  3. Aug 21, 2005 #2

    turbo

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    Here is a reference:

    http://scienceworld.wolfram.com/physics/ChandrasekharLimit.html

    For the mechanics: the Pauli exclusion principle says that no two similar Fermions (like electrons, protons, neutrons) can occupy the same quantum state. They expert a pressure resisting being forced into the same quantum state with a similar particle. It is the Fermionic repulsion between electrons that keeps a white dwarf from further gravitational collapse. The Chandrasekhar limit is a calculated limit (based on solar mass equivalents). If a white dwarf has a mass any greater than about 1.4 solar masses, the fermionic repulsion between electrons will not be able to prevent further collapse. The electrons and protons will merge to become neutrons, making a neutron star - severely degenerate matter indeed. If the mass of the neutron star exceeds about 4 solar masses or so, the Fermionic behavior of the neutrons will be unable to prevent further collapse, and the neutron star will collapse further and become a black hole.
     
  4. Aug 21, 2005 #3

    ek

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    Something the linked reference doesn't mention...

    Though the Chandrasekhar limit is 1.4Mo, that is not to say a star 40% more massive than the Sun will become a neutron star. Throughout a star's lifetime and primarily during its death a star loses a lot of its mass through various processes. So while the Chandrasekhar limit is 1.4Mo, the corresponding mass for main sequence stars is actually approximately 5-7Mo. So a star would have to be considerably larger than the Sun to become a neutron star, not slightly more massive as indicated on the surface by the Chandrasekhar Limit.

    This same stipulation goes for the Oppenheimer-Volkov limit, which is ~2.0Mo.

    So basically what this means is a star with a dying mass of under 1.4Mo becomes a white dwarf, a star of dying mass of between 1.4 and 2.0Mo becomes a degenerate neutron star, and a star of dying mass larger than 2.0Mo becomes a black hole.

    Edit: Dying mass is not a technical term. It's just a term I use to differentiate from a star's main sequence mass.
     
    Last edited: Aug 22, 2005
  5. Aug 22, 2005 #4

    Labguy

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    True, a lot of people think of a star's initial mass and should be thinking of the mass remaining after all the mass ejections, usually as a Red Giant. It is always the remaing mass (usually a "core") that should be considered. The Chandrasekhar Limit is well known as 1.44 Ms for most star remaining material (C, N. O, Si, etc,), but he also calculated another for a remaining iron core. This number is 1.39 Ms.

    The Oppenheimer-Volkov limit is actually ~3.2 Ms.
     
  6. Aug 22, 2005 #5

    ek

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    I learned it as ~2, but googling it it seems there are lots of numbers between 2 and 3. It also says it has been calculated only very roughly, which is obviously understandable.

    Can you shed some light on this ambiguity? Is this akin to the Hubble constant in terms of accuracy?
     
  7. Aug 22, 2005 #6
    The "Chandrasekhar mass",is the mass of a star beyond which electron degeneracy pressure cannot hold a star up from gravity. Hence gravity becomes stronger than the counter-acting electron pressure and the star implodes. This mass is around 1.4 times the mass of the sun. Once it's passed (thus, during the implosion), the electrons and protons undergo inverse beta decay and form neutrons. This leads to a star that is instead held up by neutron degeneracy pressure, called a neutron star. There is also a mass beyond which neutron degeneracy pressure will fail and the object will collapse to a black hole.

    regards
    marlon
     
  8. Aug 22, 2005 #7

    SpaceTiger

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    Even worse, I would say. The condition of matter (and, thus, the equation of state) in neutron stars is very poorly understood. There are theories that give a variety of numbers, but as far as I know, the observations don't rule out anything much above the Chandrasekhar limit. If anyone knows of some reliable observations of more massive neutron stars, I'd be curious to see the paper.
     
  9. Aug 22, 2005 #8

    Labguy

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    A "minimum mass" for a black hole is not a direct correlation to the maximum mass of a neutron star, but I found the 3.2 Ms # in several books I have. Also it is interesting to note that ~4.25 is the smallest BH detected that I have heard of.

    From: http://casswww.ucsd.edu/dawn.html :
    And the chart at: http://hoku.as.utexas.edu/~gebhardt/blackhole.html has interesting BH masses, but since it is mainly about AGN's, one would expect large masses.

    So, if a white dwarf collapses to a neutron star if mass exceeds (accretion?) 1.44 Ms, and anything above ~3.2 Ms will become a black hole, what objects between 1.44 and 3.2 Ms are there?? (legit question)
     
  10. Aug 22, 2005 #9

    SpaceTiger

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    That's true; in fact, I don't know of any minimum mass for a black hole (perhaps the Planck mass). Everything I've read has referred to the Oppenheimer-Volkov limit as the maximum mass for a neutron star, not the minimum for a black hole.


    I don't doubt that there are such theoretical predictions, but I would not call any of them reliable without observations to back them up. Observations of black holes aren't necessarily reliable for this purpose because black holes can form by other methods and they can grow by accretion/mergers. The only way to put definitive observational constrains on the OV limit would be to find massive neutrons stars.
     
  11. Aug 23, 2005 #10
    uhh?
    they'll be stars, and eventually neutron stars.
     
  12. Aug 24, 2005 #11

    ek

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    White dwarfs.

    Or am I reading your post wrong? Hmmm...

    The question is "what objects are there between 1.4 and 3 solar masses?"

    There are stars. And there are neutron stars. But a star that was in this range when it was on the main sequence will not be in this range when it dies. A main sequence star in this range will become a white dwarf, not a neutron star.

    And to the guy who asked the question, remember that while a neutron star is very small radius wise, it is still approximately the same mass as the dying star.
     
    Last edited: Aug 24, 2005
  13. Aug 24, 2005 #12

    SpaceTiger

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    If, by approximately, you mean within a factor of a few. Neutron stars and white dwarfs are what remains of the star's core, the rest having been expelled either by supernova or stellar winds.
     
  14. Aug 24, 2005 #13

    Labguy

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    Yes, of course. And as to the 2 posts above I was referring only to masses of remaining cores (matter) at the end of a star's life, as was the subject of this thread. Main sequence stars were not considered in my posts... :zzz:
     
  15. Aug 24, 2005 #14

    LURCH

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    Isn't this the range of mass in which stellar remnants are expected to form "Quark stars"?
     
  16. Aug 24, 2005 #15

    Labguy

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    If meaning the range of 1.44 to 3.2 Ms, this is where I would expect to find neutron stars even though none have yet been detected near the 3.0 level. That doesn't rule out their existence though. Actually, since it is now known that neutron stars are not composed of only neutrons, have a small "atmosphere" and Nickle/Iron surfaces, I expect that several new types will be found in this mass range such as the "quark" star:
    http://spaceflightnow.com/news/n0204/11newmatter/
    http://www.arxiv.org/PS_cache/astro-ph/pdf/0405/0405262.pdf
     
  17. Aug 24, 2005 #16

    ek

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    I thought it was a little less than a factor of a few...like maybe a factor of 2. But you know more than me so I'll believe what you say!

    But by approximately I meant that it wasn't all of a sudden the mass of a brown dwarf or something.
     
  18. Aug 24, 2005 #17

    SpaceTiger

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    It varies along the main sequence, I just wanted to make sure you weren't suggesting that there was no mass loss.
     
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