Exercises 1 for RÖ1 (6 Feb)



  1. Go to SIMBAD (follow the link on the "Astronomy Tools page") and find coordinates for the two cataclysmic variables VV Pup and AN UMa. Which are the best times during 2006 to observe these sources with the Nordic Optical Telescope on La Palma (Roque de Los Muchachos) if you want the longest possible continous observation with airmass less than 1.6 and a moon illumination of less than 0.25.
    Tools to plot source visibilities over the year and over the night from La Palma are available under "Visibility plots" on the NOT tools and resources for observers.page. Save the plots and include them in the report you hand in. (For gif images you have to right-click on the image and select save image. When saving you need to give individual file names for storage).

  2. What is the Julian date at the start of LAB1 (to one minute accuracy). Guidlines.

  3. The table below contain 4 measurements of the 3-10 keV photon flux obtained from observations of the Crab nebula with the X-ray monitor, JEM-X on the INTEGRAL satellite.
    The first 2 columns are time and length of observation in MJD(days)  and column 3 and 4 gives the flux in counts/s with the 1 sigma error.
    53654.099697 0.003762   109.7818   1.13
    53654.125143 0.020654   109.0764   0.60
    53654.166156 0.020359   109.3476   0.61 
    53654.203552 0.017037   108.4437   0.60 

    Compute the weighted mean first with all 4 measurements and then with only the 3 last. Which value should you use? Why?
  4. You observe a star with a telescope whose diameter is 3 meters. You collect 1346 photons in one second. How long do you need to observe to be sure that your error is less than 1%? How large a telescope would you need to able to make this measurement to an accuracy of 1% in one second? (Background is neglected).

  5. You are trying to detect a pulsar at gamma-ray energies.
    The pulsar light curve is known to be the one shown in the figure. The average count rate over the observation is expected to be 1 photon per second, half of which is due to the background. The pulsation period is 2 seconds, the pulse shape is rectangular and the pulsar radiation is only seen during 20% of the period.
    A) For how long total time do you need to observe the pulsar to make a 3 sigma detection (S/N = 3) assuming that the background has already been determined with high accuracy.
    B) Do the same assuming that the background has to be determined from the faint part of the light curve (where the pulsar signal is = 0).

    See pdf-file with notes for lecture 1 on the course web page for hints about error estimation!


  6. The observed flux for an object measured at four different times was found to be 7.8, 8.1, 4.2 and 3.5 counts per second. The error (1 sigma) was estimated to be +/- 0.1 counts per second in each case. You can test the assumption of a constant flux level by computing the Chi-square for that model. Do so and discuss the interpretation of the resulting Chi-square.

  7. A radio telescope operates at a frequency of 5.3x109 Hz.  It has a diameter of 20 meters. What is the smallest angle that it can resolve?