Astronomy 5150
Homework Set 2: Due September 20
Learning goals: Practice applying the angular size-distance and redshift computations; become familiar with standard astronomical bandpasses; practice converting
astronomical fluxes to various systems of measurement in common use; summarize the
operation of a CCD.
1. For what ranges of redshifts does the [O II] λ3727 line fall in the J,H,K windows?
2. If a galaxy is 1 Mpc away and has a diameter of 30 kpc, how large is it in the sky?
3. If this same galaxy has a transverse speed of 500 km/s, what is its proper motion? How many
years would you have to wait to observe a detectable proper motion with a telescope of your
choice? Give your telescope of choice and justify why you chose that telescope to make the
best possible proper motion measurement.
4. You are observing on a 8 m diameter optical telescope with an f/3 prime focus or an f/12
Nasmyth focus. The typical seeing is 0.5 arcsec FWHM at this site. What physical size in
microns should your ccd pixels have in order to Nyquist sample a star image at Prime focus?
At Nasmyth? What is your resulting field of view in each case if the ccd has 20482 pix.
5. Show that an error of 3% in flux units is very nearly the same as an error of 0.03 magnitudes.
6. A star has a B magnitude of B=9.5. Convert this to erg s−1 cm−2 Angstrom−1 , photons s−1
cm−2 Angstrom−1 and Jy. Use the HST NICMOS unit conversion tool (linked on our class
web page) to check your results. Write out each step of the conversion in detail, showing
units, rather than simply adopting the handy conversions I have in the class notes.
7. A star has an AB magnitude of 20 at 5500Å. Convert this into standard Johnson V magnitude
and into photons s−1 cm−2 Angstrom−1 .
8. An astronomical source A has surface brightness of 1 MJy per steradian at 5500 Angstroms.
Convert this into erg s−1 cm−2 Hz−1 arcsec−2 , into erg s−1 cm−2 Angstrom−1 arcsec−2 , into
mag arcsec−2 , and into photons s−1 cm−2 Angstrom−1 arcsec−2 .
9. For the source A in the above problem, suppose that you are observing with a V filter with a
CCD camera on a 2.3 m diameter telescope like WIRO. How many photons will you collect
per second in a single ccd pixel assuming that the pixel equals 1 square arcsecond on the sky
and assuming you have a typical V filter bandpass width. Assume that the efficiency of the
camera, CCD, and all the optics is 100%.
10. If a galaxy at a distance of 10 Mpc has a monochromatic luminosity of 1038 erg s−1 Angstrom−1
over the optical part of the spectrum, how many photons per second do you expect to detect
with a 2.3 m telescope in the V filter, assuming your optics and CCD have a total efficiency
of 50%? Assume you observe your source at 2 airmsses.
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11. Write a 1 page description (use a figure if you like) of how a CCD works as if you were
educating a family member. Be sure to include the fundamental physics of the detection
process, and the process by which the ccd is read out.
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