Mass-Radius relation of a Neutron star

[Tuugii]

Homework Statement

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

 

[BigJDubs]

eddyHomework Equations Neutron degeneracy pressure = p_deg = (2/5) h^2 n^5/m_n^4Hydrostatic equilibrium equation: P(r) = -Gm(r)/r^2The Attempt at a Solution The Neutron degeneracy pressure expression is given by: p_deg = (2/5) h^2 n^5/m_n^4, where h is the Planck's constant, n is the number density of neutrons and m_n is the neutron mass. The hydrostatic equilibrium equation can be used to determine the Mass-Radius relationship for a neutron star. The equation is given by: P(r) = -Gm(r)/r^2, where G is the gravitational constant and r is the radius of the neutron star. Assuming that the masses of protons and neutrons are equal, we can combine the two equations to obtain the Mass-Radius relationship for a neutron star. The expression for the Mass-Radius relationship is given by: M(r) = (5/2)(h^2/Gm_n^4)(n^5r^2). You do not need to know the density ratio for a neutron star, since this value is not relevant for the Mass-Radius relationship.