Astronomical Observations and Technology: Homework 1

1. You can find a text file with values for the transmission of the Earth's atmosphere as a function of wavelength in
   • modtran_maunakea.txt

   Make a graph which shows the transmission as a function of wavelength, over the range from 200 to 1000 nm. Label it appropriately. Indicate on the graph the range of human vision, and place labels to show roughly the location of the colors red, green, and blue.

2. There are two ways to determine the distance to a star. The right way is to use parallax, but it only works for stars which are relatively close to the Earth. The approximate way is to measure or estimate the absolute and apparent magnitudes of the star, and then compare them. Let's try both methods on one particular star -- HD 13379 -- and see if they yield the same result.

   First, the "right" way.

   1. Use the "Search" tool at the Gaia archive website http://gea.esac.esa.int/archive/ or the Gaia DR2 interface in Vizier, via SIMBAD (or another search engine of your choice) to look up the Gaia-based parallax of this star. What is the parallax in milli-arcseconds?
   2. Use this parallax to compute the distance D to the star in parsecs.

   Now, the "approximate" way. The star HD 13379 has spectral class A0V. Stars of this spectral class have on average an absolute magnitude of M_V = +0.80, and an intrinsic color (B-V) = 0.00.

   3. What is the (RA, Dec) position of this star?
   4. Use the SIMBAD database to look up the apparent magnitudes of this star, in the B and V passbands: m_B and m_V.
   5. What is the measured color (B-V) of this star?
   6. The difference between the measured (B-V) color and the intrinsic (B-V) color is written as E(B-V), and called the "color excess" or reddening of the star. What is E(B-V) for this star?
   7. Using the standard extinction law, based on this reddening, what should the V-band extinction be for this star? In other words, compute A_V using E(B-V).
   8. Compute a corrected version of the apparent V-band magnitude, by subtracting this extinction from the observed V-band apparent magnitude.
   9. Now that you know the (corrected) apparent magnitude m_V and the absolute magnitude M_V for this star, you can use the distance modulus (m-M) to compute the distance to the star.

      
                  (mV - MV) = 5*log(D) - 5
                 

   The second method is a lot more work, but it's the only way to estimate a distance if a star is too distant for the parallax to be measured.

   10. How similar are these two distances?
3. Lucky you! You are observing a galaxy with the Subaru Telescope, on top of Mauna Kea in Hawaii, on a night which is clear and dark. No clouds at all. Your target is a star-forming galaxy at redshift z = 0.10, and you are using a spectrograph to measure the oxygen [OIII] emission line at a REST wavelength of 5007 Angstroms.
   1. What is the OBSERVED wavelength of this emission line in your spectrum? (Not sure how to figure this out? Please ask)

   At midnight, this galaxy is DIRECTLY overhead. Awesome!

   2. What is the declination of this galaxy?
   3. What is the airmass of the galaxy at this moment?

   You take a 1-minute exposure, and measure the bright emission line to have 3000 photons. That's a nice, high signal.

   Two hours later, you decide to go back to the galaxy and take another 1-minute exposure with exactly the same instrument setup.

   4. What is the airmass of the galaxy now?
   5. How many photons will you measure in the spectrum now?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.