29:106/186 RADIO ASTRONOMY
Eighth Homework Set...April 4, 2000
Due: April 12, 2000
(1) A radio source is describable by a circular Gaussian brightness distribution
with an angular size 
arcseconds. It is observed with an
interferometer having a baseline of 10 kilometers. The observing wavelength is
21 cm. What is the amplitude of the visibility function, termed the
correlated flux density?
(2) An interferometer is located on the equator, and is observing a source at a
declination of 0 degrees. The baseline is 5 kilometers, and is oriented in the
East-West direction. It is observing a point double source, in which each
component as a flux density of 2 Janskys, and the separation of the components
is 5 arcseconds. The double is oriented in the East-West direction. The interferometer
observes at a frequency of 5000 MHz. Write down the formula for the visibility as
a function of time, and sketch this function.
(3) Prove that 
.
(4) The visibility function of a radio source is given by
where 
and 
. What is the brightness distribution of the source?
Draw a rough sketch of its brightness distribution. What is the total flux density of
the source?
(5) A source consists of a double Gaussian. Each component has an angular diameter of
4 arcseconds and the separation between the centers is 10 arcseconds. The axis of the
double has a position angle (measured from North through East) of 135 
. The
northwestern component has a flux density of 2 Janskys, the southeastern a flux density
of 1 Jansky. Derive an expression for the visibility function of the source and plot it.
A somewhat accurate, hand-drawn plot is acceptable, or you can do the job exactly.