Chapter 25 (and end of 24): Lecture Notes In order to understand the Hubble Law and its implications both for estimating distances and for interpreting the evolution of the universe, you have to be comfortable with the “distance ladder” that we have been building throughout the semester. So we begin with basic ideas of making a map of the local, and then not-so-local, universe. (Continuation from Chap.24: Review of sec. 24.2): How are the different kinds of galaxies distributed in space? We are trying to make a map of the entire universe, by locating all its contents. To do this we need: 1. Big telescopes (to see faint objects, since they are far away), and 2. Some method to get distances to very distant objects. So we are still “climbing the distance ladder” (the pyramid your book has been constructing). Groups of galaxies— We can use Cepheid variables (from their period-luminosity relation) to make a map of our “local” galactic neighborhood (can get distances out to about 15 Mpc with this method). We find that nearby galaxies are clustered. Our Local Group—About 50 galaxies within about 1 Mpc of each other. (Look at Fig. 24.13) (1 Mpc = 1000 kpc = (roughly) 10 x size of our Galaxy. This will be our unit of distance from now on: the megaparsec.) Most of the mass of the Local Group is in the large spirals Milky Way and Andromeda (M31). Most of the number of galaxies are small dE and dIrr galaxies. Many of these are satellites of larger galaxies (e.g. 3 or more satellites of Milky Way are LMC, SMC, and Sgr dwarfs, a few others that are more distant; Andromeda has several small satellites.To get to larger distances, must use brighter standard candles. The next technique in the ladder of standard candles is: The Tully-Fisher relation ⇒ very tight relation (for disk galaxies) between rotational velocity (from broadening of galaxy’s spectral lines—see Fig. 24.11) and luminosity. (Think why this makes sense: the galaxy’s rotation is balancing its gravity, which is due to its mass, related to its luminosity…) So for a galaxy too far away to use any other method, just obtain a spectrum (21 cm neutral hydrogen line is best) and measure width of line; the Tully-Fisher relation then gives you the luminosity, so (knowing the apparent brightness) you get the distance. This method can be used out to about 200 Mpc ⇒ allows us to make a map of the relatively nearby universe, but far beyond our Local Group. Another method, supernova light curves, was already discussed in class and in the textbook; see the slides corresponding to that lecture. Before looking at the results, there is one more rung in the ladder of distance indicators or standard candles, called the Hubble relation or Hubble’s law, to consider. But it is much much than simply a technique for obtaining distances: It is our first big clue about the origin of the universe.Hubble’s Law (Sec. 24.3) “Hubble’s law” is the basis for our ideas about how the universe formed (the “big bang” theory), so important to understand it. Using galaxies of known distance (e.g. using Cepheids, Tully-Fisher effect), find that most galaxies, especially the more distant ones, are moving away from us (or we from them): Also, The velocity of recession (redshift) increases linearly with distance (24.16, 24.17). Indicates that universe is expanding. Mathematical version of this statement: Recession velocity = constant (H0) x distance ⇒ Hubble’s law The constant of proportionality is called the Hubble constant, which is a fundamental measure of age of the universe (next section of course—for now we just want to use it to get distances and map the universe). Think about how the value of the Hubble constant is determined, and then how it can be used to obtain distances to any object whose spectrum you can detect. See Fig. 24.18 on the “cosmic distance ladder.” You should understand what these different distance indicators are, and why each can only be used out to a certain distance. (Notice that supernovae, as standard candles, actually belong at the top of the pyramid—we will see why this is important a little later.) [Textbook discusses active galactic nuclei, including our own, at this point, sec. 24.4 and 24.5; we are not going to cover that material, either in class or on the exam.]______________________ Now go to sec. 25.5, The Universe on Large Scales, to continue along the same theme. We will not follow the material in the same order as in the book, but will come back to the early material in chapter 25 after we complete our “tour” of the structure of the universe.Galaxies and Dark Matter (Ch. 25, starting with 25.5, The Universe on Large Scales) Mapping distances to more and more distant galaxies, we find that galaxies occur not only in small groups like ours, but in larger galaxy clusters. The nearest substantial cluster is the Virgo Cluster, whose center is about 20 Mpc away. It contains about 2500 galaxies, within a size of about 3 Mpc. We are located in its outskirts. i.e. our Local Group is in a sense a satellite of the Virgo Cluster. Redshift surveys as maps of the universe Using the Hubble relation, we can get distances to galaxies even farther away if we can obtain their spectra, so we can get their redshift and calculate the distance from the equation given earlier. But we do need a lot of spectra to get all these redshifts: We needed redshift surveys. [Think: redshift survey = survey giving distances to a large number of galaxies using redshifts and Hubble’s law. See Fig. 25.23] The earliest redshift surveys showed that the Virgo Cluster is only one of many clusters that make up our local, or Virgo, “supercluster” (see Fig.25.21, 25.22), which is about 100 Mpc in size, containing about 10,000 galaxies. Notice the Virgo Cluster and our Local Group near the center of these pictures. We are interested in the blobby patterns in Fig. 25.22, the frothy structure in Fig. 25.24, as showing us the structure of the universe: The galaxies were just “tracers” of this structure, which is our true target. This is the “large scale structure” of the universe, scales so large that even galaxies become just millions of points distributed in some fashion. Also: in the spectra of distant galaxies, we can see that intergalactic space is littered with the gas clouds, the “Lyman alpha forest” (25.25).
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