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Stellar Homework #5 Remember to show all your work and to put your final answer for each question in the form of a complete English sentence!
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1. Suppose a certain Cepheid variable star is discovered in a nearby galaxy with a period of 20 days. a) According to the graph on Figure 23.7, how does the average luminosity of this star compare to the luminosity of the Sun? HINT: I chose 20 days deliberately because it should lead to a nice, round number for the luminosity. Keep things simple! b) Given that the absolute magnitude of the Sun is +5, what is the average absolute magnitude of this star? HINT: In part a), you get a value for the luminosity ratio between the star and the sun. Now you must convert this into a difference in absolute magnitudes. For clues on how to do this, refer to the answers to problem 1 of Homework 4 and the second example in the distance modulus section of this site. Remember that the brighter star should have a smaller value for magnitude! c) Say that this star has an average apparent magnitude of 10. How far away is the galaxy in which this star lies, in parsecs? In light years? HINT: This is a straightforward application of the distance modulus technique. The first example is especially relevant.
2. a) A "typical" dwarf elliptical galaxy has a total absolute magnitude of -15. Our telescopes can detect dwarf ellipticals with apparent magnitudes as faint as +20. What is the distance of the farthest dwarf elliptical we can currently detect? How does this distance compare to the diameter of the Local Group? How does it compare to the distance to the Virgo cluster? HINT: This is yet another application of the distance modulus technique, but you're going to get a VERY large number for the distance. The distances that you need to compare these distances to are in the section of the textbook that deals with galaxy clusters. b) How would your answer be different if the absolute magnitude of the "typical" galaxy were -12 instead of -15? HINT: Just re-do the computation that you did for part a) and compare the two distances! No tricks here! The difference you get is a pretty typical error for a galaxy distance.
3. A quasar is found to have a redshift of z = (wavelength change)/(rest wavelength) = 2.45. This quasar has a redshift greater than 1, so we must use the Relativistic Doppler Effect Formula: a) Use the Relativistic Doppler Effect formula to determine the recession velocity of this galaxy. HINT: What a hideous equation! Take it in small steps. Divide the complex equation into simpler parts, then bring those parts together. First, calculate z + 1. Then do (z + 1)2, and so on, working your way outward from the parenthesis. You should get a velocity close to the velocity of light. Make sure you use the speed of light in kilometers / second! b) Assume a value for the Hubble constant of 75 km/sec/Mpc. What is the distance to this galaxy? How long has the light from this object been traveling to get to us? HINT: No tricks here, just a simple multiplication. Convert the Megaparsecs into light years for the last question. c) What is the absolute magnitude of this object if its apparent magnitude is +18? If the Sun's absolute magnitude is +5, how much brighter than the Sun is this quasar? HINT: In this problem we work the distance modulus technique backwards. Start with a distance and work you way back to a value for m-M. Then you can get the absolute magnitude M. The last part of the problem is what we've done many times over: transforming a magnitude difference ( Sun - Quasar ) to a luminosity ratio (Quasar / Sun).
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Updated 5/22/02
By James
E. Heath
Copyright Ó 2002 Austin Community College |