29:106/186 RADIO ASTRONOMY
Tenth Homework Set...April 24, 2000
Due: May 1, 2000
(1) An electron moves perpendicular to a magnetic field B with nonrelativistic
velocity v. Give an expression for the radiation electric field as a function
of time.
(2) This is a radio source count problem. Throughout the universe, radio sources have the same luminosity function
where A has dimensions of #/cm 
/ergs/sec.
Derive an expression for the differential radio source count 
in such
a universe.
(3) The radio galaxy 3C79 has a flux density of 2.5 Janskys at 1.4 GHz, a spectral
index of -0.95 from 20 MHz to 10 GHz, and a redshift of 0.25. What is its luminosity
over this frequency range?
(4) Magnetic fields in extended extragalactic radio sources are estimated to be
of order 
G. What are the energies of electrons responsible for emission
at a frequency of 5 GHz?
(5) A radio source contains two populations of electrons. There are 100 electrons/cm
with an energy of 1 GeV, and 50 electrons /cm with 1.41 GeV. The magnetic field
is 
Gauss. Assume the pitch angle of all electrons is 
.
Calculate the synchrotron radiation volume emissivity as a function of frequency.