A Stairway to Heaven: The Cosmic Distance Ladder		Figure 19.19 from the textbook How do we know how far away galaxies are? We figure out distances, step by step, using different methods--each step of known distance helps us calibrate our method for figuring out distances at the next step. This is sometimes called the Cosmic Distance Ladder, although your textbook calls it the distance chain. Once we have solar system distances down we can proceed to use parallax. Parallax is a very reliable method--it doesn't depend on any properties of the thing we're looking at. Six months apart, look at a star, and find how it moves as a result of the Earth's orbit--that tells you the distance! The only thing to be careful about is stars may also have some sideways motion of their own--but that won't return them back over 1 year because of the Earth's orrrbit--parallax will. But parallax is limited. In most cases, you can only use it to measure distances to nearby stars (100 light years or so). The further away something is, the less of a parallax shift it will have. (Likewise, your stereo vision from having 2 eyes is useless in telling, from sight, whether the Moon or stars are further away!) Main sequence fitting is the next rung on the ladder. This is similar to what you used in your lab, although you used horizontal branch stars instead of main sequence stars. The basic idea is shown in the diagram below (from your textbook): If you have a cluster of stars of unknown distance, you can compare how bright the stars on its main sequence appear with how bright the stars in a cluster of known distance appear. In the example above, the stars in the Pleiades (an open cluster) are 7.5 times dimmer than the stars in the Hyades (also an open cluster), and so must be further away. You can use the inverse-square law (apparent brightness = true luminosity / 4 pi R2) to show that the Pleiades is sqrt(7.5) times further away than the Hyades. But even this method breaks down eventually. Why? Because in other galaxies it becomes hard to make out individual main sequence stars. Below we see the period-luminosity relationship for Cepheid stars. These are variable stars whose period of variability is related to their true luminosity. (They vary by a factor of 2 or so in brightness.) By measuring the period of variation, we can find the true luminosity. For example, from the plot below (from the textbook--based on studies of Cepheid variable stars whose distance was verified by other means), a Cepheid variable with a period of 10 days has 3,000 times the luminosity of our Sun, and a Cepheid variable with a period of 30 days has a luminosity of 10,000 times that of our Sun. Even the very dimmest of the Cepheids shown has a luminosity of 5,000 times that of our Sun--the brightest is more than 30,000 times as bright! So these stars can be seen much further out than sun-like stars. Two general kinds of methods we have for figuring out distances are standard candles and standard rulers. Basic idea: things further away look dimmer and look smaller. If something has a known size we call it a standard ruler, and can judge its distance by its apparent size (angular size). If something has a known luminosity, we call it a standard candle, and can judge its distance by its apparent brightness. Astronomers are having much success in using white dwarf supernovas as standard candles. Because white dwarf supernovas result when stars of a known mass blow up (white dwarfs have a mass limit of 1.4 times the Sun's mass), they explode with similar brightness. There are some differences between individual white dwarf supernovas, but the truly bright ones also take a long time to become dim. If a white dwarf supernova takes a long time to become dim, we know it has to be truly bright. So even when we look so far away that Cephid variable stars can't be distinguished (and they get 30,000 times brighter than our Sun!), we can still use white dwarf supernovas, which become a billion times brighter than our Sun! Two separate teams have been using white dwarf supernovas as standard candles to measure distances in our Universe; here is a giant poster from the Berkeley team and here is a web site from the Harvard team. Another method is called the Tully-Fisher relation. If you measure how fast the gas in a spiral galaxy is in orbit around the center, the true luminosity of the galaxy is proportional to that velcotiy v raised to the 4th power, or L=k v4. A relationship like this makes sense because a more massive galaxy is also usually a brighter one and also pulls its gas to move around faster.
The Hubble Law		Edwin Hubble, astronomer and amateur boxer, was the first to make a plot of how fast galaxies are moving vs. their distances from us. A modern version of his plot is shown above. It shows that a straight line described by the equation v=H0 d describes the data very well. This means that the further away a galaxy is from us, the faster it is moving away from us! Why are the galaxies moving away from us? What's so special about our galaxy? Nothing! The galaxies are all moving away from each other! It's like they are dots on the surface of a balloon that I "accidentally" let go of: Each dot sees all the other dots moving away from it! Another way to think about the expansion of the Universe is to imagine an infinite raisin cake. (Actually we don't know whether the Universe is finite or infinite.) The galaxies are the raisins (those must have been some grapes!). As the cake bakes, it expands, and the raisins get further and further apart--each sees the velocity of all the others as being directed away from it. The further apart any two raisins, the faster they are moving away from each other. The slope of this line, H0, is the Hubble constant. It tells us the expansion rate of the Universe. A larger value means that galaxies are moving faster away from us. The Hubble Constant is also related to the age of the Universe (as you figured on your final lab!) If galaxies are expanding faster away from us, that means that it didn't take them as long to get where they are now. The Big Bang would have happened sooner. So the age of the Universe is inversely proportional to the Hubble constant. Mathematically, we have v=H0 d and also the definition of velocity as distance=rate x time gives us d=v T, where T is the age of the Universe. So substituting this value of d into v=H0 d, we get v=H0 v T, and dividing each side by v, we get 1 = H0 T, or 1/H0=T. So the age of the Universe is the inverse of the Hubble Constant! Right now, our best measurement of the Hubble Constant is H0=70+/-10 km/s/Mpc, where Mpc is megaparsecs, 106 parsecs, or 3.09x106 light years. The age of the Universe is thought to be somewhere between 12 and 16 billion years.
Quasars		Now that we know the relation between the redshift of a galaxy and its distance, we can figure things out the other way around, too! If we know the redshift of a galaxy, we can use Hubble's law to find the distance (v=H0d means that d=v/H0). In the 1960s, a bunch of surprising objects were found. They appeared like stars--tiny points--and yet they gave off very bright radio waves. When the spectra of these stars were examined, it was found that they had huge redshifts. Not stars at all, these things are far away! That means they are giving off a huge amount of energy. Essentially, they are giving out thousands of times as much energy as the Milky Way, from within the size of our solar system! We know that quasars have a small size because their brightness changes noticably over days. If they were bigger than light-days, then light from the different parts of a quasar would take different times to reach us, and there would be no way that such a varation could take place from all parts of the quasar in concert and appear to us to change. Below are 1996 Hubble Space Telescope images of quasars. Now we know that they are coming from galaxies. The faint outlines of spiral and elliptical galaxies can be seen in these images. In fact, in about 75% of cases, it appears that quasars are coming from colliding galaxies. Quasars and their "host galaxies" viewed with the Hubble Space Telescope. Click for more information. Our current theory is that the huge energy output of quasars is driven by a massive black hole at the center of the galaxy. As gas spirals in to the black hole through an accretion disk, it gets heated and radiates. Somehow the collision with another galaxy may drive the gas to fall in to the black hole. For whatever reason, we don't see quasars at low red-shifts--in other words, by the Hubble relation, quasars are all far away. Because when we look at things billions of light years away, we're also seeing them billions of years ago, this means that we see quasars only in our distant past--like the dinosaurs they're pretty much extinct nowadays. There are galaxies with active galactic nuclei (the nucleus means the center of a galaxy) that have intense radiation and shoot out jets of gas. However, they are not nearly as powerful as quasars. They may represent a later stage of development as the quasar is becoming dormant.