High Energy Astrophysics
- Fall 2016
Homework #4 - due October 26
1. Find the Eddington luminosity and the orbital inner radius for a
10 solar mass black hole. Modeling the accretion disk as a
black body radiator with a radius equal to the inner disk radius,
estimate the temperature of the disk assuming the black hole is
accreting at the Eddington limit.
2. Using equation 14.52 in Longair and the Stefan-Boltzmann law,
find an expression for the temperature of an accretion disk as a
function of radius. Take beta = 1 and use the radius of the
innermost stable circular orbit for rI.
Note that the expression will differ from equation 14.54. With
your expression for the temperature, find an expression for the
maximum temperature. Numerically evaluate the maximum
temperature for a 10 solar mass black hole accreting at the
Eddington limit and compare with your answer for problem #1.
If you need to use an efficiency to calculate the mass accretion
rate, use 6%.
3. Using python, plot the temperature, energy dissipation
rate, and product of kinematic viscosity times surface density
versus radius for a disk surrounding a black hole. Be sure to
choose suitable dimensionless units for all four quantities.
Cover a radius range up to 100 times the inner radius of the disk.