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LD715: Determine on the mass of the most
massive neutron star that can be stable against collapse to a black hole (the Chandrasekhar limit).
Determine the ratios with which neutrons, protons, and electrons are present. Nucleons can convert to hyperons through weak interactions that involve the emission of pions. Determine the modified equilibrium conditions and the extent to which a more massive star can be stabilized by the conversion of nucleons to hyperons.
Are the stable conditions such that the Schwarxschild radius associated with the mass enclosed at any radius R is less than R, 2GM/c2 < R? You may
assume that the star is cold with T < 107 K and may neglect interactions among the constituent particles.
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LD721: Show that the slowing of the rotation rate of the Crab pulsar is
consistent with radiative energy loss from a rotating off-axis magnetic
dipole with a strength consistent with that obtained in the collapse
of an ordinary massive star with a typical magnetic field. (Hint: how
does the field change in the collapse?) The rotation period P of the Crab
pulsar is 33 ms and its mass is about 1.4 times the mass of the sun.
dP/dt = -4.2 × 10-13.
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LD722: The LEP electron-positron collider operated with a residual gas pressure of 10-10 Torr in the beam pipe. High energy photons were produced as bremsstrahlung in collisions of beam electrons with gas atoms (mainly N) and by inverse Compton scattering of electrons with the thermal radiation on the beam pipe. The number of up-scattered black body photons below 10 GeV was roughly three times the number of bremsstrahlung photons for a 50 GeV beam. Calculate the energy spectra of the scattered black body and bremsstrahlung photons as seen in the laboratory, and use the results to estimate the average temperature in the LEP beam pipe. |