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Mass-Radius relation of a Neutron star

  1. Feb 22, 2008 #1
    Hey all,

    I need a help to determine the Mass-Radius relationship for a neutron star. I've done it for a white dwarf, but for a neutron star I need to know the Neutron degeneracy pressure expression, can anyone please help me to solve it?

    I am thinking that if I have the n.deg.pressure expression then I can use the hydrostatic equilibrium, and assume the masses of proton and neutron to be exactly equal;

    I am not sure, but I might also need the density ratio? is it correct? for instance for a white dwarf, I have [ro_c]/[ro_mean] = 5.99, I don't know the value for a neutron star.

    please help me,
    thanks,
    T
     
  2. jcsd
  3. Oct 17, 2008 #2
    for non relativistic case the degeneracy pressure varies as:- p=k*(density)^(5/3). The 'k' here you can easily calculate my first calculating the total energy of degenerate neutron gas and then differentiating it w.r.t volume to get pressure.
     
  4. Oct 18, 2008 #3
    neutron star mass-radius relation...


    The neutron star mass-radius relation is dependent on a particular neutron star model, however the mass-radius relation for my model based upon the Proton charge radius and Tolman mass equation solution VII:

    [tex]m_n = 1.6749272928 \cdot 10^{-27} \; \text{kg}[/tex] - Neutron mass
    [tex]r_p = 0.8757 \cdot 10^{-15} \; \text{m}[/tex] - Proton charge radius

    Proton charge radius neutron density:
    [tex]\rho_n = \frac{3 m_n}{4 \pi r_p^3}[/tex]

    Neutron star core density equivalent to Proton charge radius neutron density:
    [tex]\rho_c = \rho_n[/tex]

    Total Tolman mass equation solution VII:
    [tex]M_0(R) = \frac{8 \pi \rho_c R^3}{15} = \frac{8 \pi R^3}{15} \left( \frac{3 m_n}{4 \pi r_p^3} \right) = \frac{2 m_n R^3}{5 r_p^3}[/tex]

    Total mass-radius equation for the Tolman solution VII:
    [tex]\boxed{M_0(R) = \frac{2 m_n R^3}{5 r_p^3}}[/tex]

    Mass of a 10 km radius Tolman VII neutron star:
    [tex]\boxed{M_0(10 \; \text{km}) = 9.976 \cdot 10^{29} \; \text{kg}}[/tex]

    Note that the lower limit for total radius R, is equivalent to the Schwarzschild radius and the upper limit for total mass M(R), is equivalent to the Tolman-Oppenheimer-Volkov mass limit.

    Reference:
    Neutron - Wikipedia
    TOV #39 - Orion1
    TOV #47 - Orion1
    Schwarzschild radius - Wikipedia
    Tolman-Oppenheimer-Volkoff mass limit - Wikipedia
     
    Last edited: Oct 18, 2008
  5. Oct 25, 2008 #4

    Tuugii, what is your mass-radius equation for a white dwarf?
     
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