Objective
In this exercise, you will learn about the expanding universe, Hubble's Law, and how we compute the age of the universe. You will determine the value for Hubble's constant and compare this to results obtained by scientists. This result can then be used to calculate a maximum age for the universe.
Contents
Equipment
Hubble Space Telescope images of Cepheid variables in distant galaxies
Scientific calculator
During the 1770s, Charles Messier made the first catalog of nebulae ("clouds" in Latin), not because he had a particular interest in them, but because he didn't want to mistake them for comets, which were his major interest. Today, Messier's catalog of 110 "Messier Objects" is a famous listing of some of the most spectacular objects in the night sky. These objects are frequently denoted with a capital M and a number, such as M1 (the Crab Nebula).
Astronomers came to realize that these nebulae could be divided up into a number of distinct groups, two of which were the planetary and spiral nebulae. By the early 20th century a debate arose concerning the nature of these nebulae with some astronomers claiming that they were all within our galaxy, the Milky Way. Others believed that only the planetary nebulae were in our galaxy. This second group of astronomers believed that the spiral nebulae were actually other galaxies, far outside the limits of the Milky Way. But seen through the telescopes of the late 18th and 19th centuries, all the nebulae looked like vague, fuzzy patches of light, sometimes mixed with stars. It would take much superior telescopes to achieve the necessary resolution to answer this question.
The controversy over the nature of the planetary and spiral nebulae came to a head shortly after World War I. In 1920, the National Academy of Sciences sponsored a "debate", which actually consisted of two consecutive lectures by Heber Curtis and Harlow Shapley, about the nature and extent of the Milky Way. Curtis insisted that the nebulae must lie far outside the Milky Way, while Shapley argued that all nebulae lie within the Milky Way. Shapley based his conclusion on the work of another astronomer, Adriaan van Maanen. Van Maanen claimed to have measured the rotation of the spiral nebulae by photographing them at times spaced several years apart. His observations, if true, would imply that most spiral nebulae take a few hundred thousand years to rotate once. If so, then the spiral nebulae could not possibly be as large as the Milky Way, for it is easy to show that the outer edges of the nebulae would have to be traveling at a speed in excess of the speed of light. Thus Shapley, relying on van Maanen's observations, concluded that the spiral nebulae must be far smaller than the Milky Way, and must lie within the outer reaches of our own galaxy, which he believed included everything. But van Maanen's analysis of his photographs was simply incorrect. Today, we know that spiral nebulae (actually, spiral galaxies) do rotate, but with rotation times of hundreds of millions of years.
The debate was finally settled by the American astronomer, Edwin Powell Hubble (1889 - 1953). Hubble used the 2.5 meter (100 inch) telescope of the Mount Wilson Observatory overlooking Los Angeles, then the largest telescope in the world, to study galaxies through night after night of long duration photography. In 1923, Hubble found that several of the spiral nebulae, including the Andromeda nebulae, contained periodic variable stars, called Cepheid variables. Cepheids are pulsating stars whose intrinsic brightness (absolute magnitude) can be determined by their pulsation period. Comparing its real brightness to its apparent brightness allows us to calculate how far away the star is from us, and therefore, the distance to the galaxy in which it lies. Hubble noticed that these Cepheid variables in Andromeda had periods that matched those of well studied Cepheids in the Milky Way. He therefore concluded that the stars had the same luminosities. Then, by using the inverse-square law, he compared the apparent brightness of the two stars and obtained the relative distances. This comparison put the Andromeda Galaxy well beyond the outer reaches of our galaxy.
Hubble made the assumption that ALL Cepheids behave in the same manner and that the light from these stars had not been absorbed by dust. While both of these assumptions have subsequently been shown to be wrong and the value that he obtained for the distance to the Andromeda Galaxy was about 700,000 light years, about one third of the value calculated today, which is about 2.1 million light years, his results demonstrated conclusively that Andromeda was outside the Milky Way and was a galaxy, not a nebula.
Hubble continued his work, and working with Milton Humason, made estimates of the distances to a number of galaxies. In 1929, when he combined these distances with the Doppler shift measurements of the velocities of galaxies, he came to the remarkable conclusion that the universe is expanding! He was able to come to this conclusion by finding a general trend that the more distant a galaxy, the higher was its velocity away from us. Hubble concluded that each galaxy has some random velocity of its own relative to other galaxies, and that this random velocity can add or subtract a relatively small amount to or from the overall trend. This explains, in part, the scatter about the straight line in his plot. The rest of the scatter is due to inaccuracies in determining distances. But the trend represents Hubble's greatest contribution to astronomy. If galaxies' recession velocities increase in proportion to the galaxies' distance from us, then the entire universe must be expanding!
But why does this mean the universe is expanding? Why can't we explain this observation with the conclusion that all galaxies are simply moving away from us and we are the center of the universe? The answer to this lies in the principle of mediocrity, which states that there is no special significance to the point in space we occupy, or any other point either. In other words, the principle of mediocrity states that all points are equal and that there is no center of the universe. Therefore, if we were able to travel to another galaxy, we would still find that all other galaxies were moving away from us. To envision this, imagine a loaf of raisin bread dough with the raisins spread uniformly throughout the dough. As the dough expands, the distance between each of the raisins would increase. So, if you could sit on any of the raisins, the other raisins would all appear to be moving away from you, and this would be true, no matter which raisin you chose to sit on.
Hubble used these observations to obtain his law for the expansion of the universe, now called Hubble's Law. This law states that a galaxy's recession velocity is equal to its distance from us times some constant, called the Hubble constant. In algebraic form, Hubble's Law is
(1) v = Hod
where v is the recession velocity in km/s, d is the distance between us and the other galaxy in megaparsecs, and Ho is Hubble's constant. In this equation Ho is measured in units of km/s/Mpc. Ho represents how fast the universe is expanding. We can obtain the velocity to within 1% by measuring the Doppler shift of galaxies. Therefore, if we know the value of Hubble's constant, we can find out how far away the galaxy is from us. But to find Hubble's constant, we must first work with some galaxies for which the distance has been measured by some other method.Ironically, Hubble was not actually the first to come to this conclusion. In 1916 Albert Einstein presented his General Theory of Relativity which contained equations that dealt with the large-scale structure of the universe. In 1917, the Dutch astronomer Willem de Sitter pointed out that a consequence of these equations was that the universe was expanding. Because there was no observational evidence to indicate that this was true, Einstein introduced a special term, the cosmological constant, in his equations to make the universe static. After Hubble showed that the universe really was expanding, Einstein removed that special term and called this the greatest scientific mistake of his life.
Other experiments you have done this semester have taught you the importance of graphs. A similar technique can be used to determine Hubble's constant. Since the recession velocity and distance to the galaxy are proportional, if these two quantities are graphed, the result will be a straight line. The slope (or the ratio, rise/run of the line) gives the constant Ho.
The problem with Hubble's Law is that we are unable to obtain a precise value for Hubble's constant, since we do not have enough reliable data for the accurate distances to galaxies for which the recession velocities are known. Obtaining these measurements is very difficult, and the values for Hubble's constant have varied wildly. One camp has calculated the value to be between 40 and 50 kilometers per second per megaparsec, while another camp has it between 80 and 100 kilometers per second per megaparsec. As a result, 70 kilometers per second per megaparsec is currently the most commonly used value. This, we believe, provides us with the means to measure the distance to other galaxies with an accuracy of plus or minus 25%.
There is another interesting scenario that emerges from Hubble's Law. If the universe is expanding, and we imagine a reversal of this expansion, there was some point in time when all the universe was located at one point. This is when the expansion began and is called the "Big Bang". Since Hubble's constant is in units of distance per time per distance, or if we simplify and express both the distances in the same units, then Ho has the units 1/time. If we invert Hubble's constant, we will get units of time and 1/Ho will yield the amount of time, in seconds, since the Big Bang, assuming the universe has expanded at a constant rate. Since we are sure that the expansion rate is slowing down, this will actually provide us with the maximum age of the universe. This amount of time is called the Hubble time. The importance of the value of Hubble's constant is that the higher the value, the younger the universe.
The Hubble Space Telescope is being used to determine the distance to nearby galaxies with great accuracy, thus allowing us to obtain a definitive value for Hubble's constant. The idea was to use the telescope to measure the distance to galaxies in the Virgo cluster. These galaxies are far enough away that their own motion is less than their motion due to the expanding universe, and at the same time they are still close enough for us to see individual stars with the space telescope. Specifically, we are interested in seeing Cepheid variable stars. Once we observe Cepheids, we can determine the distance. Combining this distance with the galaxies' redshift would then yield Hubble's constant.
Other teams, such as one from Indiana University, have used telescopes on Mauna Kea in Hawaii, equipped with new technology optics that permitted them to see three Cepheids in a galaxy in the Virgo cluster, to gather similar data. They determined that Hubble's constant has a value of 87 plus or minus 7 kilometers per second per megaparsec. Since then, NASA researchers have used the Hubble Space Telescope to measure the distance to another galaxy in the Virgo cluster and obtained a value of 80 plus or minus 17 kilometers per second per megaparsec, which is in agreement with the Indiana results.
They were able to obtain these results by determining the period of the Cepheid variables they observed. By measuring the period, they were able to obtain the absolute magnitude of the stars, M. Then, by measuring the apparent magnitude, m, they can determine a value, which we'll call 'x', which can be found with the equation
(2) x = (m-M+5)/5
The importance of this equation is that it can now be used to find the distance to the star by using the equation
(3) d = 10x
These results have presented astronomers with a difficult problem. The ages of the oldest stars are calculated to be about 13 billion years old. However, these values for Hubble's constant yield a value for Hubble time of less than this. This would mean that the oldest stars in the universe are older than the universe itself! Critics of these values point out that the Virgo cluster is very large and the galaxies used by these teams were far removed from the center of the cluster, and thus much closer to us, while the velocity value is for the cluster center. This would have the effect of inflating their calculated value for Hubble's constant.
Dispute over the value of Hubble's constant is not new. In fact, Hubble himself originally calculated a value of 500 kilometers per second per megaparsec, which yielded an age for the universe of about 2 billion years. Understandably, geologists disagreed with this value because they already knew the Earth was older than this.
Work is continuing and, hopefully, within a decade or so, we will have a good value of Hubble's constant that everyone will agree on. The value in this is that Hubble's constant is one of the most important numbers in cosmology. With it, we are able to estimate the size and age of the universe, determine the intrinsic brightness and masses of stars in nearby galaxies, and examine those same properties in more distant galaxies and galaxy clusters. This can in turn help us to deduce the amount of dark matter present in the universe, obtain the scale size of faraway galaxy clusters, and serve as a test for theoretical cosmological models.
PRE-LABORATORY QUESTIONS
This lab was developed by MKS Publishing, Inc. - Dallas, Texas
