Question

Answer all of the following questions:

A core-collapse supernova located near the Galactic Center ejects the outer 10 Msun of the envelope of its star star at a speed of 5000 km s-1. a. Estimate the kinetic energy of the expanding ejecta. b. The remnant core is a neutron star with a mass of 1.6 Msun and a radius of 11 km. Estimate the 5. gravitational binding energy of this neutron star. You may assume it is uniform density. What percentage of the binding energy liberated by the formation of the neutron star was converted into kinetic energy? Estimate the number of neutrinos emitted during the core bounce (Hint: you get 1 neutrino for reach new neutron made and the pre-bounce core was essentially 100% 56Fe) The IceCube Neutrino Observatory at the South Pole has an effective collecting area of about 1 square kilometer. How many neutrinos from this supernova will pass through IceCube? Bonus Points (2): IceCube, as the name suggests, is a cube 1 km on a side, and the cross- section for neutrino absorption is o 104* m2. Estimate how many of the neutrinos in part e c. d. e. f. would be detected.

Answer 1

To solve this problem the details calculations are given below
a . Kinectic energy g_n E_U = 1/2 mv^2 we have, m = 10 m_sun = 10 times 1.98 times 10^30 kg velocity, v = 500 times 10^3 m/s therefore E_u = 1/2 times 10 times 1.9891 times 10^30 times (500 times 10^3)^2 = 2.486375 times 10^42 J b) neutron stern mass, m = 1.6 m_sun = 1.6 times 1.9893 times 10^-30 kh radius, R = 11 km = 11 times 10^3 m therefore gravitational energy, w = -3/5 Gm^2/R = -3/5 times 1.67 times 10^-11 times (1.6 times 1.9891 times 10^30)^2/11 times 10^3 = -9.2263141 times 10^45 J (-ve sign of energy means required) \r\n c) what percentage of binding energy liberated by the formation of the neutron straw was = E_u/w = 2.986375 times 10^429.2263141 times 10^45 = 2.69487 times 10^-4 % = 2.19987 times 10^-2 % = 0.289487 % d) number of neutron emitted during the come bounnoe for