Question

To first approximation, a neutron star may be treated as a non-interacting gas of neutrons (spin-1/2 fermions). (

a) Find an expression for the degeneracy (zero point) energy of the star as a function its mass M and radius R. (Don’t worry that our calculation for degenerate Fermi systems was done for particles in a cubical box, the same results apply to a sphere of the same volume.)

(b) Write down an expression for the gravitational potential energy of the star as a function of M and R.

(c) Find an expression for the radius R that minimizes the total energy for a fixed M.

(d) Compute the radius (in km) of a 2 solar mass neutron star, M = 2M. (e) The temperature of neutron star is about 107K. Is it reasonable approximation to treat a neutron star as a zero-temperature Fermi gas? Why?

Answer 1

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