AST460: Assignment 3
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(Sep 20 2016)

(1) One of the main characteristics of any telescope is its resolving power or
angular resolution. This can be expressed as:

theta [radians] = lamba / D, where lambda is the
wavelength of observations and D is the telescope diameter.

1.1 If our Small Radio Telescope has a diameter of 2.3m, calculate its angular resolution
at a wavelength of 21cm.

1.2 The Andromeda galaxy has an angular size of about 200 arc minutes on the sky.
What telescope size we need to resolve the detailed internal structure of Andromeda at 21cm?


(2) Another essential characteristic of a radio telescope is its ability to detect faint radio signals.
The lowest signal strength a telescope can detect is given with the radiometer equation:

delta_T = Tsys/sqrt{delta_nu x delta_t}

where delta_T is the uncertainty in the measured signal in Kelvin,
Tsys is the system noise in Kelvin, delta_nu is the frequency resolution of the 
desired spectrum in Hz, and delta_t is the integration time in seconds.

For example, the Small Radio Telescope has Tsys~200 K.
If we use the frequency resolution of 7800 Hz, and integrate for 20 minutes, we would produce a 
spectrum which has uncertainty of 0.07 K.
If the expected signal from Andromeda is 0.1 K at its peak, can we detect Andromeda in 20 minutes of
integration time? If no, what strategies can we use to change our experiment to try to detect Andromeda?


(2) Use the SRT Simulator in the classroom to produce the following:

2.1 Point at the Sun and run the npoint function which 
performs a 5 by 5 map around the Sun.
Pick another obvious source in your field of view, e.g. PULSAR,
Cass, test, GNpole and repeat npoint.
Notice how only by looking at the Sun you get a very nice 2d plot
of telescope's response pattern. This is because we need both a very strong and a point-like
source for such measurements, therefore more extended and/or weak sources will 
not give suitable results. Provide a printout (screen shot) of your plots.

2.2 Set central frequency to that of the HI line and select
the highest frequency resolution observing mode.
Open a test data file to save your observations.
Then point the telescope in the Galactic anti-center direction (l,b) = (180,0).
(in case this position is not visible feel free to use (l,b) = (90,0))
Take and print a screen shot.

2.3 Use the highest frequency resolution mode, it has a total frequency coverage of
1.21875 MHz over 156 frequency bins.
Using the (non-relativistic) Doppler shift equation 
[(nu_rest - nu)/nu_rest = V/c], we can convert the frequency 
axis into the radial velocity along the line of sight therefore measuring how fast
are observed objects moving away/toward us.
What will be the velocity resolution of your spectrum after this conversion (or
how wide will be the velocity bins in your spectrum)?
If your spectrum is centered on the HI line, what velocity range will it cover?


To take a screen shot: hold simultaneously
command, shift, and number 4 keys on your iMac keyboard.
This will save a screen shot as a file on your Desktop.
Open this file (double click), and go under File --> Print and select
floor3 as your printer, then click print. This will send your printing job to
the printer called "floor3" located on the same floor around Room 3511.
Let me know if you have problems finding the printer or doing this.


Printouts should be included in your homework.
The assignment is due at the next class meeting.