Mass-Radius relation of a Neutron star

Tuugii

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.

thanks,
T

Related Astronomy and Astrophysics News on Phys.org

Tarunks

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.

Orion1

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:

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

$$\rho_n = \frac{3 m_n}{4 \pi r_p^3}$$

Neutron star core density equivalent to Proton charge radius neutron density:
$$\rho_c = \rho_n$$

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

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

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

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:
http://en.wikipedia.org/wiki/Neutron" [Broken]
https://www.physicsforums.com/showpost.php?p=1718805&postcount=39"
https://www.physicsforums.com/showpost.php?p=1792334&postcount=47"
http://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_limit" [Broken]

Last edited by a moderator:

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving