ASTR 3730 Problem Set #2 Reading: Chapters 4 and 5 of the text   1. In 1977 the German X-ray astronomer J. Trumper observed the neutron star Hercules X-1. He found two emission lines, one at 55keV and the other at 110keV. He interpreted these as cyclotron emission from charged particles near the surface of a magnetized neutron star. a) Derive the strength of the magnetic field at the surface of the neutron star. b) What is the velocity of the electrons assuming they have a temperature of 108K? What is the radius of their orbit? c) What is the timescale for the decay of the electron orbit on this neutron star? d) At what frequency would the protons be emitting their cyclotron lines? What is the corresponding wavelength? e)What is the relative amount of power radiated by protons compared to electrons? 2. The Crab Nebula is observed to emit x-rays having an energy of at least 100keV from an extended region. A) Assume we know that the magnetic field is 10-4 Gauss and that the radiation is synchrotron. Compute the energy, lifetime, and Larmor radius of the electrons producing this radiation. B) Next we will see how the magnetic field was derived by astrophysicists. The nonthermal spectrum of the Crab exhibits a downward turn above 1015 Hz. We assume this bend is due to lifetime losses. Use the known age of the Crab (supernova in 1054 AD) to estimate the magnetic field strength. 3. The great cluster of galaxies in Coma Berenices exhibits 5x1044 ergs/s of x-ray emission from 108 K gas trapped in the potential well of the cluster. It has a radius of 2x1024cm. Assuming a uniform distribution of gas, compute a) the electron density b) the mass of the x-ray emitting plasma c.) its thermal energy content d) its cooling time.