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A Neutron star mass-radius relation plot

  1. Jul 8, 2017 #1
    Hi there...

    I have a question about the tipical mass-radius relation plot for a neutron star, something that looks like this for different equations of state:

    My question is, what is exactly happening at the ends of the EOS lines? I know that after passing the maximum mass the curve starts to spiral if you would go further, and on the other end we have something with big radius and very few mass? I am not sure I understand the plot. Also, do we expect that all NSs have the same radius? Regardless of their mass? What is the EOS actually representing? Shouldn't then each NS that we measure lie on the EOS line in M-R diagram? Well, hope to et some clarifications :-/
  2. jcsd
  3. Jul 8, 2017 #2


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    Staff: Mentor

    If you try to increase the mass beyond the end of the lines, the object collapses to a black hole (or at least this particular model breaks down).
    If the object is too light, it cannot be a neutron star, and you get a white dwarf - low mass, extremely large radius (on this scale).
    That would correspond to an exactly vertical line, and none of the models has that.
    At least approximately. Mass, temperature and spin should be the only things that differ notably between neutron stars in the universe, and mass should have the largest impact on the size.
  4. Jul 8, 2017 #3
    The WD comment I don't understand, you do have large radius, but from this plot they should have masses that are very low (and they can have masses that are up to 8 solar masses?) Is it valid to say that the lower right part of the panel is not physically valid since these objects can not exist cause of the rotation constraint?

    So, how is it possible that a NS of same radius can have different masses? Would that mean that the central density of the star is higher, if the mass is higher?

    Also, could you clarify me some of the constraints on the plot? As much as I know, GR is constraint from general relativity, which means that for the masses that high you would have a black hole. Causality should be limit for compactness of the star? Or the fact that the velocity can not be higher then c? What is P< infinity? The rotation I know that comes from the fact that the NS would be teared apart if its spin frequency would be above some value. Usually there are also these lines of "constant radiation radius? R_inf?

    And why do strange quark model stars start from the left side? :P Many questions xD Tnx for you answer!
  5. Jul 8, 2017 #4


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    They are the low-mass extension of the mass/radius relationship, yes. The models in the plot don't include white dwarfs, they are not designed to model them.
    They cannot. You are probably thinking about the original star mass, not the mass of the stellar remnant.
    The rotation constraints only applies to very fast rotating neutron stars. There are objects to the right of this. Every star for example.

    The source of the plot should have explanations of the different features in it.

    Models starting from the lower left have a high density even at small overall masses.
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