Question 2: (a.) Find the radius of a 1.5 Mo neutron star relative to its Schwar

Question

Question 2: (a.) Find the radius of a 1.5 Mo neutron star relative to its Schwarzschild radius: RNs /Rs (b.) What neutron star mass is required to make its radius equal to its Schwarzschild radius? What do you think this is telling us is the (approximate) maximum mass a neutron star can have? Note: The actual calculation of the marimum mass of a neutron star is eztremely difficult - harder than the full relativistic quantum mechanical calculation Chandrasekhar did for white dwarfs and is still, in fact, something theorists still work on, but the above calculation gets us surprisingly close to values the theorists have come up with!

Explanation / Answer

a. densoty of neutron star, rho = 10^17 kg/m^3

Mass of sun. M. = 1.989*10^30 kg

hence, radius of 1.5M. neutron star = R

rho = M/V

10^17 = 1.5*1.989*10^30*3/4*pi*R^3

R = 19240.32827 m = 19.24032827 km

swarchild radius = rs = 2MG/c^2 = 2*1.5*1.989*10^30*6.67*10^-11/c^2

rs = 4422.21 m

hence

R/Rs = 4.35084002

b. mass of neutron star, for radius = rs is M

then

10^17 = M*3/4*pi*rs^3

M = 0.0362248 *10^30 kg

M = 0.01821259848 M.

where M. is mass of sun

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