The supernova SN1987A was observed to have a maximum apparent visual magnitude of m_v = 3. It is located in the Large Magellanic Cloud, at a distance of about 53000 pc from the Earth. What was the absolute visual magnitude of SN1987A at maximum luminosity? What luminosity in solar luminosities does this correspond to?
Make a scale sketch of our Milky Way galaxy with views from above the plane of the disk of the galaxy and edge-on. Label the coordinates of galactic longitude l and latitude b. Label the prominent features such as the central bulge, nucleus, disk, halo, and some spiral arms. Draw in the Sun's location and add a few globular clusters (try and make them the right scale size). Also draw in the Large Magellanic Cloud, a small neighbor galaxy about 7 kpc in diameter, which is located about 53 kpc from the Sun at galactic longitude l = 280 degrees and galactic latitude b = -33 degrees. You will probably want to draw these sketches on a separate (possibly larger) piece of paper than the other problems, and be neat and legible! (Note: some spiral arms near the Sun are the Perseus Arm at 10.5 kpc from the galactic center, the Orion Arm at 8.8 kpc from the center, and the Sagittarius Arm at 7.5 kpc from the center. See Fig 12-18 in Seeds. Assume the Sun is at 8.5 kpc. Remember a kiloparsec is 1 kpc = 1000 pc.)
Assume the Sun is 8.5 kpc from the center of the galaxy (the true number is still uncertain, and is between 7 to 10 kpc). Doppler shifts of distant stars and nearby galaxies are combined, we find that the orbital velocity of the Sun around the galactic nucleus is around 220 km/s. How long does it take for the Sun to make one orbit of the galaxy? How many orbits has it made in its life so far (the age of the Sun is about 4.5 x 10^9 years)?
You can use Kepler's Law to find the mass of the galaxy interior to the Sun's orbit! Using the period and radius of the orbit (remember to convert to AU), find the mass of inner part the Milky Way in units of solar masses. (You can also use Newton's Law for centripetal force and velocity.)
The Hubble Space Telescope measured the distance to the galaxy M100 (in the Virgo Cluster) to be 17.1 Mpc (million parsecs) using Cepheid variable stars. How many light-years is this? (This is how long the light took to reach us from M100!) Spectra of galaxies in the Virgo cluster show Doppler shifts that indicate an average Hubble recession velocity for this cluster of 1404 km/s. What value does this imply for the Hubble Constant H (see Box 13-1 in Seeds p.290) in km/s/Mpc?
Using the distance to M100, find the apparent visual magnitude m_v for a supernova of the same absolute visual magnitude as SN1987A (Problem 1). Supernovae have been seen in galaxies like M100, and have been used to find the distance assuming a given absolute magnitude for them. Finding distances using brightnesses of known objects is called using standard candles as distance indicators.
Assume globular clusters have an average diameter of 25 pc. What would be the angular diameter of a globular cluster in M100? (I shouldn't have to remind you to use the small angle formula.) Is this large enough to be resolved by optical telescopes? This method for finding distances has also been used for galaxies in the Virgo cluster, though it isn't very accurate since globular clusters don't come all the same size! Finding distances using objects of known size is called using standard yardsticks as distance indicators.
Be sure to visit the DRL rooftop Student's Observatory on a clear Monday or Thursday night, or the Flower & Cook observatory during one of the bi-weekly Wednesday field trips.
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Steven T. Myers - Last revised 05Apr96