<p>AY C10/L&S C70U Fall 2006 Nicholas McConnell, GSI</p><p>A Long Time Ago, In A Galaxy Far, Far Away. . .</p><p>A popular bumper sticker (at least, um, among astronomers) has red letters that read: </p><p>If this sticker is blue, you are driving too fast.</p><p>Similarly, we can imagine a giant beacon that changes apparent color due to cosmological redshift. Unlike the bumper sticker (which assumes you are approaching the witty astronomer’s car), this beacon will be receding because of the expansion of the universe.</p><p>Suppose that we know the beacon is green (= 5000 Å), but when we observe it in outer space, it appears yellow (= 5500 Å)!</p><p>1a. Redshift z is defined by: z =  Use this and the non-relativistic approximation z ≈ v / c to estimate the speed of the beacon. Recall that c = 3 x 105 km/s.</p><p>1b. Use Hubble’s law to determine the distance to the beacon. Take H0 = 70 km/s / Mpc. How old is the light we currently see from the beacon? Recall that 1 parsec ≈ 3 light- years.</p><p>1c. The non-relativistic approximation works fairly well for z < 0.2. Does the beacon meet this limit?</p><p>1d. Now suppose we observe the beacon glowing at an infrared wavelength,  = 25,000 Å. What is z now? If we used the non-relativistic formula, what speed would that give? Is that acceptable? 2. Suddenly, the beacon gets magnificently brighter! It remains at the new brightness level for 15 minutes, then quickly decreases back to its original brightness. What is the maximum distance from the front of the beacon to the back? Why can’t it be any bigger?</p><p>(For the distance, first use the intuitive unit of light-minutes. Then try to recall how that compares to the distances between solar system objects.)</p><p>3. From your observations, you conclude that the beacon is actually created by matter heating up and glowing as it spirals into a massive black hole (realistically, this phenomenon wouldn’t give a single intrinsic color—I just made that part up). Draw a picture of this. What features do we sometimes see in quasars?</p><p>4. And now for something completely different. . . (sort of)</p><p>-1 We have noted that the inverse of the Hubble constant, H0 , corresponds to the age of the universe, so long as we assume that the universe has always expanded at the same rate. The oldest globular clusters have been dated to be at least 12 billion years old. If we assume a constant rate of expansion, does this observation place any limits on the value of H0? Try to compute the minimum or maximum value (you get to determine which it is) of H0 set by this observation. </p><p>7 -1 (Use 1 yr ≈ 3 x 10 s to figure out H0 in seconds based on the age of globular clusters. 19 Then use 1 Mpc ≈ 3 x 10 km to get H0 in km/s / Mpc.) </p>