From Skeptic vol. 3, no. 4, 1995, pp. 42-45.

The following article is copyright © 1995 by the Skeptics Society, P.O. Box 338, Altadena, CA 91001, (626) 794-3119. Permission has been granted for noncommercial electronic circulation of this article in its entirety, including this notice.

IS THERE REALLY A COSMOLOGICAL CRISIS?

If The Stars Are Older Than the Universe Then We Have A Serious Problem

By Rick Shaffer

Although it certainly does not rival the attention given to the O.J. Trial, there is a polite controversy micro-raging within the world of astronomy. It seems that one group of astronomers, using data from the Hubble Space Telescope (HST), has measured the distance to a galaxy in a group of galaxies called the Virgo Cluster. Their measurement implies that the age of the universe is between 8- and 11-billion years.

If other measurements were consistent with this one, we would not have a controversy, so it should not surprise you to read that another group of astronomers has modeled the evolution of stars, and concluded that the oldest stars they have observed are approximately 15-billion years old! How can the oldest stars in the universe be older than the universe itself? Can the child be older than the parent?

Unless the universe is even stranger than our wildest dreams, the answer is that those really old stars may indeed be really old, but not older than the universe itself. So one of the measurements must be wrong. Right? Well, with apologies to Hertz Rent-A-Car, not exactly.

Although most people perceive physics and astronomy to be exact sciences, in many instances they are not. In this case, the age of the universe determined by each group is an estimate based on observations that have quite a bit of error built into them. That is why the figure quoted by the group using the HST is "between 8- and 11-billion years." The estimate of the age of the oldest stars--those in clusters of stars called globular clusters--has a similar range, possibly 13- to 18- billion years. The real controversy involves the fact that the "spreads" in the respective estimates do not overlap. Since this essay is part of an issue devoted to cosmology, I will not spend any time describing how the estimate of the age of the oldest stars was made. However, you should know that the estimate was provided by practitioners of the science of the physics of stars--the astrophysicists. I am also compelled to point out that this estimate was not made capriciously. Rather, it is the result of hundreds of person- years of effort, both on the part of astronomers making the observations, and of the astrophysicists who try to make sense of the observations. Nobody knows which of the competing estimates is closest to the truth. Since there is no "cosmic judge" to rule on the truth of either estimate, time and many future observations will tell us which is correct.

A thumbnail sketch of how cosmologists came up with their estimate of the age of the universe will serve two purposes. First, it will illustrate the problems associated with making measurements of a system- -the universe--only a minuscule part of which we will ever traverse. Second, it will illustrate the incredible leaps of reasoning that have allowed humans to travel the universe despite being confined, at least for the immediate future, to our solar system.

Another Brief History of Time

Not surprisingly, the first measurements astronomers made were of distances to nearby objects in the solar system. Those estimates were reasonable, but not without error. As time went on the estimates were refined and the error diminished. We now know the values of the parameters describing the size and shape of the solar system so accurately that we flew the Voyager II spacecraft through a gap in the rings of Saturn with impunity (although maybe we shouldn't have).

Early measurements of the distance to the nearest stars were made by measuring their parallax. This just means that astronomers measured the apparent position of a star in January, for instance, and then in July, when the Earth had moved to the other side of its orbit. If the star appeared to move relative to its more distant brethren, then it is a simple exercise in trigonometry to use our very accurate knowledge of the size of the Earth's orbit and the angle the star appeared to move to compute the star's distance. Parallax measurement is a foolproof way to measure the distances to the closest stars, but as astronomers tried to make parallax measurements of more and more distant stars, they discovered that the yearly "wobble" in the stars' positions was approaching the limit of their ability to measure it. So, parallax only allows us to measure the distance to stars that are within a few hundred light years from Earth.

Astronomers next used their studies of the physics of stars in clusters to make estimates of the distances of nearby stars that were too far for accurate parallax measurements to be made. Fortunately for all concerned, some of the stars in nearby clusters are of a type known as Cepheid variables (so named after the first one discovered in the constellation Cepheus).Cepheid variables are stars that periodically swell and shrink due to an instability in their outer layers. When a Cepheid has swollen to its maximum, it is at its dimmest; when it has shrunk to its minimum, it is at its brightest. How they do their swell- and-shrink act is not important to our discussion. However, it turns out that for all Cepheids of a certain type, there is a linear (straight- line) relationship between the period of variability of the star and its intrinsic brightness. Astronomers can make very accurate measurements of the brightness of stars using instruments known as photometers. Once they measure the apparent brightness of a Cepheid, and obtain a good estimate of its distance, they can easily compute its intrinsic brightness, using the well-known relationship that an object's apparent brightness is proportional to the inverse-square of its distance. Once they have the intrinsic brightness and the period of a number of Cepheids, they are able to establish a reasonably accurate period-luminosity relationship. They could then use Cepheids to measure the distances to many groupings with which the Cepheids appear to be associated.

All the methods I have mentioned so far have been used by astronomers to establish their estimates of the size of just our galaxy. (I have glossed over several intermediate steps in the process of sizing the Milky Way Galaxy, which is about 100,000 light years across.) The crucial things to remember are: (1) there are many links in the measurement chain; (2) each link has its own measurement error; and (3) the farther away from Earth we go, the bigger the potential error (as a percentage of the measurement)! This means that as astronomers make measurements of the size of the universe, the farther they measure, the less accurate their measurement is likely to be.

For an example, think about the next step in the distance chain. In 1923, Edwin Hubble identified a Cepheid variable in the Great Andromeda Nebula, as it was then called. He used a photometer to measure both its apparent brightness and its period of variability. Using the period- luminosity relationship, he was able to compute the Cepheid's intrinsic brightness. It was then a simple matter to compute its distance.

Hubble's answer was 1-million light years. This showed that the Great Andromeda Nebula is not a nebula at all. Rather, it is a galaxy quite similar to our own. More important for our discussion, though, is the fact that only a few years later a refinement in one link of the measurement chain forced Hubble to revise his estimate of the distance to the Andromeda Galaxy to 2-million light years! Further refinements have put our best estimate at 2.3-million light years. So, Hubble's initial measurement of the distance to the Andromeda Galaxy was off by more than a factor of two, yet it was one of the most important scientific measurements ever made. Hubble concentrated on the Andromeda Galaxy because it is the biggest and brightest of the spiral galaxies. He went on to use other methods to observe many other galaxies. What he found formed the basis of modern cosmology.

Around 1920, astronomer E. C. Slipher, of the Lowell Observatory, Flagstaff, Arizona, noticed a startling fact about the spectra of galaxies: when he compared them to a standard laboratory spectrum, their features were almost always shifted toward the red, or longer wavelength end of the spectrum. This implied that the galaxies are all receding from us, thus "stretching" the length of the waves of light they radiate to us. The bigger the red-shift, the faster the velocity of recession. (The waves of light are not really stretched; it is just an effect of the velocity of recession and our perspective. This phenomenon is commonly known as the Doppler Effect.) It was Edwin Hubble who took Slipher's observation further and supplied the correct interpretation of it. Hubble used the 100-inch Hooker telescope on Mount Wilson to make two fundamental measurements regarding galaxies: (1) their velocity of recession, as determined by the red- shift of their spectra; and (2) their distances, using a variety of methods, only a few of which I have outlined above.

Once Hubble had made both recession-velocity and distance measurements of a number of galaxies, he realized that the farther a galaxy is from us, the faster it is receding. Put another way, a galaxy's velocity of recession is directly proportional to its distance. This is known as Hubble's Law, and the constant of proportionality is known as the Hubble Constant. Its units are velocity-per-unit-distance, and it is commonly expressed as "so-many-kilometers-per-second-per- megaparsec." (A megaparsec is 3.26 million light-years.) For those who like equations, here is Hubble's Law:

Velocity of recession = (Hubble Constant) x Distance

Edwin Hubble, with a nudge from Slipher, had discovered the expansion of the universe. Hubble's discovery implied a lot more than just Hubble's Law. It also validated a powerful philosophical concept called the Cosmological Principle. The galaxies Hubble observed in discovering the expansion of the universe were in all parts of the sky visible from Mount Wilson. This implies that no matter what direction we look, the universe appears to be expanding at the same rate (i.e., isotropically). This means that if we look at a group of galaxies that are 10-million light years in one direction, and another group that lies 10-million light years in the opposite direction, we will find that they are receding from us with the same velocity. In like manner, if we look a billion light years from Earth in any direction, the galaxies we see at that distance will all be receding from us with the same (faster) velocity. If the universe were not expanding isotropically the various clusters of galaxies would tend to "bunch together" into lumps. We do not see that. Rather, the gross structure of the universe seems to be homogeneous. Although there does seem to be some organization to clusters of galaxies--the so-called "cosmic strings"--the strings observed in one direction appear not to differ much from those observed in any other direction.

The Vegetable Soup Model of the Universe

All astronomy students are familiar with the raisin-cake model of the universe. In trying to explain homogeneity to kids, I have often invoked that staple of kid-lunches, canned vegetable soup. I point out that the contents of one spoonful of soup may have a chunk of potato, an "x," two "v's," a slice of carrot, one totally un-ID-able "object," and a little broth. Missing might be a piece of celery (unless it is the "object"), one of those delectable pieces of "mystery meat," and all the other letters of the alphabet. The next spoonful would have a different distribution of ingredients. If we cared to inventory the whole bowl, we would probably find a distribution of ingredients very similar to the manufacturer's recipe. The whole pan of soup we heated would be even closer to the recipe, while the vat in which a day's production of soup was made would nail it.

It is not hard to see that each spoonful of soup is not homogeneous, but that each bowl of soup is much closer to being so. And, the pan is even more homogeneous than the bowl, while the vat is really homogeneous. Each spoonful of soup represents our immediate neighborhood, say the Local Group of galaxies to which we belong. (The one whose letters spell out E-A-R-T-H is ours!) The bowl might be our local supercluster of galaxies, while the pan might represent a string of galaxies. The vat of soup would make a fairly good homogeneous universe.

The vegetable soup analogy does fine with homogeneity, but not with the isotropic nature of the expansion of the universe. That's because those little bits of barley move around in the soup much faster than the other bigger ingredients, which tend to stick to the bottom. So, the manufacturer has to use enormous, powered stirring spoons in each vat. If you put each of the spoons up to your ear, you can just hear them chanting, "ooom-ogeneity, ooom-o-geneity, ooom-o-geneity, ooom-o- geneityÉ"

(By invoking this analogy-for-kids, I make two points: 1. thinking up analogies that both correctly illustrate a scientific theory, the barley notwithstanding, and that kids will like and understand, has really helped my understanding of cosmology; 2. my understanding of cosmology had a long way to come!)

For completeness, then, the Cosmological Principle states that, to an observer on a typical galaxy, the universe is expanding isotropically (looks the same in every direction), and is homogeneous (looks the same at every point).

Another way of expressing the Cosmological Principle is to say that the laws of physics we have deduced here on Earth and in our solar system do not change regardless of where in the universe we look. This may seem like a circular argument, but astronomers have seen nothing to suggest anything to the contrary.

Once we accept Hubble's Law and the Cosmological Principle, we can assume that, if we know an object's red-shift, and thus its velocity of recession, we can just "plug it into" Hubble's Law and solve the equation for the object's distance. Even more important, we should be able to use the Hubble Constant to determine the age of the universe. Right? WellÉagain, not exactly.

Both statements are true. However, notice that each invokes such modifiers as "assume" and "should be able." The reason the modifiers are used is that there is no general agreement as to the precise value of the Hubble Constant. The reason, of course, is all those pesky, error- prone links in the chain-of-distance measurement. Essentially, there is no consensus amongst astronomers as to what error to assign to each link in the chain. Nobody worries about the velocity measurement. The red- shift on which it is based can be measured to an accuracy of 1%. (Before you lower your respect for astronomers, find another example of anything else on which we humans are unanimous in our opinions, besides our love of chocolate and our seemingly universal admiration for Cal Ripken, Jr.)

In fact, the primary reason astronomers lobbied to get the Hubble Space Telescope funded was to allow them to make observations of galaxies that would then allow them to refine their estimate of the value of the Hubble Constant. And, of course, they are doing just that.

TimeSinceBang = AgeO'Verse

Before we look at how the HST is being used to refine the value of the Hubble Constant, let's take a short detour to see how the Hubble Constant can be used to make an estimate of the age of the universe. Most cosmologists believe that the universe began in an explosion of incredible magnitude that is popularly known as the Big Bang. A very simplistic view of what happened after the Big Bang goes like this: Despite all we have been told about how insignificant we are, we cling to our political incorrectness and believe that we are at the exact center of the universe. Since we are at the very center, the galaxies are all receding from us. At any particular time after the Big Bang, the very fastest galaxies are farthest away from us. Those galaxies, if they have been blasting along unimpeded, have traveled a distance defined below as:

Distance = Velocity x TimeSinceBang

If we multiply both sides of the equation by the factor (1/Time Since Big Bang), we get:

Distance x (1/TimeSinceBang) = Velocity

or,

Velocity = (1/TimeSinceBang) x Distance

This final version of the equation looks just like Hubble's Law, as long as we are willing to assume that:

(Hubble Constant) = (1/TimeSinceBang)

The quantity I have called "TimeSinceBang" is, of course, the age of the universe. So, our simplistic explanation of the history of the universe implies that all we have to do to find out the age of the universe is to find out the value of the Hubble Constant, and then find its reciprocal:

AgeO'Verse = 1/(Hubble Constant)

Amazingly, when astronomers plug their favorite values for the Hubble Constant into the above equation, they get values for the age of the universe of between 10- and 20-billion years, a value which agrees quite well with other data! But, how do we go from this simplistic view of the age of the universe to a realistic one?

The major consideration has to do with the assumption we made about those galaxies "blasting along unimpeded." Despite the power of the Big Bang, all those galaxies must have been attracting each other gravitationally, thus slowing them down. So, the earlier we go back in time in the "real" universe, the faster those galaxies must have been "blasting along." This means that the universe must have taken a shorter period of time to get to "now," making it younger than the age found for the simplistic "free-expansion" universe.

An important implication of this realistic "gravitationally-impeded" universe is that the Hubble "Constant" must change as the universe ages. It diminishes as time goes on. If it "passes through zero" to become negative, the universe will begin to contract, eventually imploding, possibly to begin another cycle. Will this happen? Right now astronomers have not found enough mass in the universe to allow for its expansion to be halted eventually. If the "missing mass" is really missing, the universe will continue to expand forever, or indefinitely, whichever comes later.

The +- Problem

It is now pretty obvious why determining the value of the Hubble Constant is important. It is one of the fundamental quantities we need to estimate the size and age of the universe.

The latest hoopla in the press is centered around the measurement of the distance to a galaxy known as M100 made by a group of astronomers using the HST. The group is headed by Wendy Freedman of the Carnegie Observatories in Pasadena, California. Her group determined that the distance to M100 is 56-million light years, with an estimated error of +/-13 light years. An earlier ground-based observation had determined that the distance to another member of the Virgo Cluster of galaxies is 49-million light years, with a similar estimated error.

The M100 team used Cepheid variable stars to determine the distance to galaxy M100. They chose M100 because it is a spiral galaxy in which many Cepheids are likely to be found. (The fact that the images of M100 made by HST are breathtakingly beautiful surely did not bother the NASA PR folks either.) They found Cepheids, and the HST's now-perfect optics, and its position above Earth's atmosphere, allowed the team to accurately measure the apparent brightness of M100's Cepheids. It was then a simple matter to compute the distance to M100 using the method outlined above.

When the 56-million light years figure and the measured recession velocity of M-100 are plugged into Hubble's Law, the result is a Hubble Constant of 80 +/-18 kilometers/sec/megaparsec. That value implies that the age of the universe is "only" 8-11 billion years. As I have already mentioned, that certainly upsets the astrophysicists' applecart, as their model of stellar evolution suggests that the oldest stars are something like 15-billion years old. The Hubble Constant that corresponds to that age of the universe is 50.

Those astronomers who favor an older universe, and therefore a smaller Hubble Constant, point out that M100 may be much closer to us than the average distance for the whole Virgo Cluster. And, since galaxies in a cluster tend to move relative to each other, only the distance of the center-of-mass of the whole cluster is valid for estimating the Hubble Constant. Furthermore, the Virgo Cluster is so massive that it is attracting our own galaxy toward it, and itself to us. The M100 team's detractors say that the team has not properly accounted for this effect.

In fact, the M100 team mentioned all these objections (and more) in their paper announcing their results. They further pointed out that making the same measurements of the distance to a spiral galaxy in another cluster of galaxies--the Fornax Cluster--should improve the confidence they have in their results.

Over the next few years, the M100 team will observe at least two spiral galaxies in the Fornax Cluster, looking for Cepheids to use to determine the galaxies' distances. They will also observe several more spirals in the Virgo Cluster. If their results are consistent with a high Hubble Constant, and, thus, a young universe, the astrophysicists may have to modify their model of the age of the oldest stars. However, if they cannot find any errors in their model, the controversy might continue. Ultimately, the cosmologists might have to re-think their cherished assumptions.

What fun!

 

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