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# Is the Hubble constant in the neighborhood of 100 km/s/Mpc?

Viewpoint: Yes, observations have raised the estimate of the Hubble constant from 50 to near 100 km/s/Mpc.

Viewpoint: No, the best observations regarding the age of objects in the universe require a Hubble constant significantly below 100 km/s/Mpc.

One of the most familiar of scientific phenomena is the Doppler shift of sound—the change in pitch of sound being emitted by an object moving toward or away from a listener. The pitch of a train whistle invariably appears to lower as the train passes the listener, and this change is caused by the compression and elongation of sound waves by the motion of the object. Longer-wavelength or, analogously, lower-frequency sound waves are perceived by the listener as having a lower pitch.

The same phenomenon applies to light. Light waves emitted by an object moving toward or away from an observer are subject to the same compression or elongation of wavelength. If the object is moving toward the observer, the detected wavelength is shorter, or shifted toward the blue end of the spectrum. Conversely, if the object is moving away from the observer, the light is seen as shifted toward the red end of the spectrum. The mathematics governing the amount of wavelength shift and the velocity of the moving object is quite simple; it is a direct proportional relationship. If object A is moving away from an observer at twice the velocity of object B, the redshift of object A will be exactly twice that of object B.

The Doppler shift of light underlies what is arguably the most important astronomical discovery of the twentieth century. In 1912, the American astronomer Vesto Melvin Slipher (1875-1969) of the Lowell Observatory in Arizona noticed that the spectra of distant objects we now know to be galaxies all had their spectral features shifted toward the red end of the spectrum. This discovery ultimately led Edwin Hubble (1889-1953), working at the Carnegie Institution's Mount Wilson Observatory in California, to notice in 1929 that the amount by which the spectral features of galaxies were red-shifted was directly proportional to their distance from Earth.

The farther away a galaxy was, the faster it appeared to be receding. Put in the simplest mathematical terms, the relationship governing a galaxy's recession velocity is V = H 0 x D, where V is the recession velocity in kilometers per second (km/s), D is the galaxy's distance in megaparsecs, and H 0 is a quantity known as the Hubble constant.

One megaparsec (Mpc) is 1 million parsecs, or about 3.26 million light-years—rather a long way by terrestrial standards. A bit of work with a pencil will show you that to make the units in the equation above work out, the Hubble constant must have units of km/s/Mpc (kilometers per second per megaparsec). If the Hubble constant were, say, 50, then galaxies at a distance of 1 megaparsec would be receding, on average, at 50 km/s (30 mi/s); galaxies 2 Mpc away would be receding at 100 km/s (60 mi/s), and so on.

Determining the value of the Hubble constant is the subject of a decades-long debate in the astronomical literature. The essays that follow discuss points of view taken by the two main camps in the controversy. On one side are the eminent American astronomer Allan Sandage (1926-) of the Carnegie Observatories in Pasadena, California, and his collaborators, who have steadily maintained that the value of the Hubble constant is in the neighborhood of 50 km/s/Mpc. Sandage was challenged in the 1970s by the French-born American astronomer Gerard de Vaucouleurs and his collaborators, who found a Hubble constant closer to 100 km/s/Mpc. The implications of these differing points of view are enormous. The Hubble constant is a measure of the rate of expansion of the universe, and therefore affects estimates of its age, current size, and ultimate fate. For example, the larger the Hubble constant, the faster the universe is expanding and the less time it will have taken to reach its present size. Thus, de Vaucouleurs was arguing, in effect, for a younger universe than Sandage.

The Hubble constant has proven enormously difficult to determine, and as with many problems in astronomy, this stems from the sheer distance to the objects in question. Astronomers cannot bring objects into the laboratory; they must observe them at a distance and infer their properties from the light they emit. Happily, some things are easy to measure, and Doppler shift is one of them. Features in spectra lie at well-known "rest wavelengths," which are the characteristic wavelengths of the feature when observed in a nonmoving object. Comparing the observed wavelength to the rest wavelength and determining the velocity needed to produce the observed shift is straightforward. However, distance is another matter entirely. Direct measures of distance are available only for the nearest objects, and for other galaxies only indirect measures of distance are available. So, although V is easy to measure from the spectra, D is extremely difficult to measure, and the remaining unknown H 0 remains in doubt. This is why, in the following essays, you will see general descriptions of the Doppler shift, but protracted discussions about standard candles—methods of measuring distance. The most difficult problems always warrant the most extensive discussion, and the problem of measuring the distance to galaxies is extremely difficult. What methods are used, how good the observations are, and how they are interpreted are all subject to scrutiny and criticism.

One final concept to keep clearly in mind when reading the following essays is the nature of the expansion of the universe itself. The recession of the galaxies is an apparent velocity caused by the expansion of the universe. It is not that all galaxies are flying away from the Milky Way as if in response to some cosmic offense, but rather that space itself is expanding, pushing galaxies apart as it does so. Discovering whether this expansion continues forever, gradually halts, or eventually reverses and brings all matter in the universe back together in what has been called the "big crunch," is another reason for arriving at a well-determined value for the Hubble constant.

—JEFFREY HALL

## Viewpoint: Yes, observations have raised the estimate of the Hubble constant from 50 to near 100 km/s/Mpc.

The modern picture of the universe began to emerge in the early 1920s, when Edwin Hubble (1889-1953) studied the fuzzy patches in the sky, or nebulae, using the 100-in (2.5-m) telescope at the Mount Wilson Observatory near Pasadena, California. Some of these nebulae turned out to be huge "island universes," enormous galaxies of stars like our own Milky Way.

Hubble was interested in measuring the distance to these galaxies using the convenient properties of a type of star called Cepheid variables. These stars brighten and dim in a regular pattern with a period inversely proportional to their brightness. The brighter they are, the more slowly they pulsate.

Astronomers already knew the apparent magnitudes of these stars, their brightness as seen from Earth. From the pulsation period, they could now figure out their absolute magnitude, or actual brightness. The difference in the two brightness numbers allowed calculation of the distance between Earth and the Cepheid variables, and thus of the galaxies in which they were found.

### Hubble Develops His "Constant"

In 1912, the American astronomer Vesto Melvin Slipher (1875-1969) of the Lowell Observatory in Arizona had made the surprising discovery that the spectra of some galaxies; that is, the characteristic wavelengths at which their gas molecules absorbed light, were shifted toward the longer wavelength, or "red" end of the spectrum. This "redshift" is analogous to the lowering of the pitch of a siren as an ambulance moves into the distance. The faster an object is receding, the larger the shift will be. Thus, measuring the difference between the observed spectrum and that which would be expected for a particular class of object is a way to determine its velocity. Hubble compared the distances to various galaxies with their red-shifted spectra and discovered an unexpected pattern. The farther the galaxy was from Earth, the faster it seemed to be receding. The galaxies were speeding away from Earth like fragments from an exploding bomb.

At first, the idea that Earth seemed to be at the center of this rapid expansion gave scientists pause. But Albert Einstein's 1915 general theory of relativity, in which gravity was related to the warping of space and time, helped to explain the situation. The galaxies are not receding from Earth in particular. Instead, everything, including our own galaxy, is receding from everything else, as the fabric of space-time expands like a balloon. This expansion is the result of the "big bang," the massive cataclysm by which most astronomers believe the universe originated.

The key number in understanding the expansion of the universe is the slope of the straight line that Hubble drew through his plot of galactic velocity and distance. The Hubble law states that a galaxy's distance is proportional to its redshift velocity. The slope of the line, which came to be called the Hubble constant, or H 0 (pronounced "H nought"), was by Hubble's 1929 estimate 530 km per second per megaparsec. This would mean that for every 1 million parsecs (about 3.26 million light-years) away a galaxy is, it would be moving 530 km (about 330 mi) per second faster.

### The Work of Sandage

After Hubble's death, his protégé Allan Sandage (1926-), of the Carnegie Observatories in Pasadena, California, began making more measurements of distances and redshifts. The more measurements he made, the more Sandage realized that the Hubble constant needed some adjustment. Hubble himself had been able to use the reliable Cepheid measurements only for the nearby galaxies, where these stars could be seen. Farther out, he relied on redshifts in the spectra of the brightest stars in the galaxy and, at even greater distances, on the spectra of the galaxies themselves. Sandage also discovered some errors in measurements Hubble had used.

By the 1950s, Sandage had estimated a Hubble constant of about 180, or approximately one-third of Hubble's original value. This smaller Hubble constant was a result of correcting the distance of the galaxies; they were now believed to be three times farther away. Thus a smaller Hubble constant implies a larger universe. It also implies an older universe, since it would have taken the galaxies three times longer to get to their recalculated positions.

Sandage continued to work for decades on measuring the expansion of the universe using the Mount Wilson telescope, as well as the 200-in (5-m) telescope at the Palomar Observatory operated by the California Institute of Technology (Caltech) in northern San Diego County, California. By 1975, his estimate for the Hubble constant had settled on about 50, implying an age for the universe of about 20 billion years. Sandage's calculations have hovered near that number ever since.

For many years, Sandage's numbers were essentially uncontested. To many, it seemed unthinkable to argue with the esteemed astronomer, clearly the most experienced man in the field and the anointed successor of Hubble himself. That situation changed dramatically when, at a 1976 meeting of the International Astronomical Union, Gerard de Vaucouleurs (1918-1995), a French-born American astronomer of the University of Texas at Austin, stood up and said that Sandage and his colleague, Gustav Tammann of the University of Basel in Switzerland, were wrong.

### The Work of de Vaucouleurs

De Vaucouleurs based his claim on his analysis of six papers by Sandage and Tammann, in which he claimed to find a dozen "blunders," and on measurements he had made. The Hubble constant was actually about 100, de Vaucouleurs said, which would make the universe half as large and only about 10 billion years old.

Given Sandage's eminence in the field, de Vaucouleurs's claims were at first met with alarm and disbelief. However, he persisted, and constructed an elaborate scale incorporating not only the "standard candles" (objects for which the absolute magnitudes are known) employed by Hubble, Sandage, and Tammann, but new ones as well, such as bright star clusters and ringlike structures within certain galaxies. To decrease the risk that any one error would skew the results, De Vaucouleurs used some measurements to verify and cross-check others, and then averaged all the methods.

De Vaucouleurs presented his ideas around the astronomy conference circuit, winning many adherents. In addition to making the argument that his distance scale was more robust and less error-prone, he accused Sandage's camp of making unwarranted assumptions about the smoothness of the universe. If the distribution of astronomical objects was not as uniform as Sandage and his supporters had assumed, then the cosmic expansion would likewise be uneven, and their distance scale would be wrong. In fact, de Vaucouleurs asserted, Earth is part of a local supercluster of galaxies that is slowing down cosmic processes in our own astronomical neighborhood.

De Vaucouleurs also objected to the way Sandage and Tammann had used spiral galaxies as standard candles. In extrapolating the characteristics of large, well-studied galaxies to smaller, dimmer ones, he believed they had made another assumption about uniformity in the universe. Also, according to de Vaucouleurs, Sandage and Tammann had neglected to account for the effects of interstellar dust on the brightness of the objects they observed.

There was one obvious problem with de Vaucouleurs's 10 billion-year-old universe. Studies of some ancient globular star clusters had pegged their age at 17 billion years. Clearly the universe cannot be younger than its oldest stars. De Vaucouleurs was not alarmed by this development; he pointed out that the models that arrived at the stellar ages could just as easily be wrong. Since Sandage's value for the Hubble constant had fallen over the years, de Vaucouleurs intimated that the final drop from 100 to 50 had been prompted by a desire to provide a universe old enough to accommodate the globular cluster results. Sandage indignantly denied this charge.

### Later Astronomers

But de Vaucouleurs was not to be Sandage's only critic. In the 1970s two young astronomers, Brent Tully and Richard Fisher, were looking for a new standard candle. They reasoned that the rotation rate of a spiral galaxy should be related to its luminosity, because a faster rotation is required to maintain the stability of the orbits of stars against the gravitational force of a larger total mass inside those orbits. More mass means more stars, yielding a brighter galaxy. Rotation could be measured by radio astronomy, based on the Doppler shifting of the energy emitted during transitions in hydrogen atoms. Using their new way of calculating brightness and thus distance, Tully and Fisher came up with a Hubble constant of about 100, just like de Vaucouleurs.

Using a variation of Tully-Fisher method in which the brightness of the galaxies was measured in the infrared wavelengths to limit the effect of interstellar dust, another group of astronomers, Marc Aaronson, John Huchra, and Jeremy Mould, estimated a Hubble constant of between 65 and 70. In recent years, many measurements have yielded numbers between 70 and 90.

Although de Vaucouleurs had once dismissed such a solution as a compromise for "sissies," younger astronomers have inherited little of the historical and personality clashes that led their elders to hold their ground so tenaciously. As the evidence mounts, the Hubble constant seems increasingly likely to converge on a number significantly higher than Sandage's, but not quite so high as de Vaucouleurs's.

—SHERRI CHASIN CALVO

## Viewpoint: No, the best observations regarding the age of objects in the universe require a Hubble constant significantly below 100 km/s/Mpc.

Since 1929, when the American astronomer Edwin Hubble (1889-1953) first observed the relationship between a galaxy's distance from Earth and its apparent recession velocity, the Hubble constant (H 0) remains the most fundamental, yet most poorly determined, parameter of modern cosmology. The difficulty in constraining the Hubble constant is understandable. Astronomers must determine both the velocity and distance to the galaxies they are measuring. The velocity poses little problem. Modern spectrometers, which analyze light from distant galaxies, can accurately determine the recession velocity by observing the galaxy's redshift. But even in this age of high-resolution space telescopes, determining the distance to an object is no easy task. Measurement errors of 50 to 100% are common, and reducing these down to 10 to 20% requires special methods and careful observations. But the challenge is worth the reward. The Hubble constant contains information about the origin and fate of the universe, the nature of our cosmology, and—perhaps most interesting of all—the ability to estimate the age of the universe.

Current estimates of the Hubble constant give results ranging from 50 to 100 km/s/Mpc (kilometers/second/megaparsec), with most measurements clustering around 50 to 55 and 80 to 90 km/s/Mpc. Such discrepant results have huge implications for the age of the universe. The upper value of 100 km/s/Mpc indicates the universe is no more than 6.5 to 8.5 billion years old (just barely older than the age of the solar system); the smaller value suggests an age of 13 to 16.5 billion years old. But, determining the "true value" is a murky proposition—one cannot just average the results. Instead, scientists must make sure the results fit the following criteria: 1) the method for determining the Hubble constant must be based on sound physical—rather than empirical—principles; 2) the value of the Hubble constant must be consistent with the physical parameters of the universe; and 3) derived results from the Hubble constant and other cosmological parameters must be consistent with other observations of objects in the universe.

### The Problem of Distance

Many problems in astronomy are really problems of distance. Determining the size of a planet, computing the true velocity of an object moving through space, measuring the brightness of a star—all these problems require an accurate knowledge of the distance to the object to find the correct answer. Over the years, astronomers have put together an ingenious toolkit for finding the distance to celestial objects. For nearby objects, direct measurements such as parallax can be used. The parallax method capitalizes on the apparent change in position, from the perspective of a moving observer, of an object relative to the more distant background. Just as the passenger in a car sees nearby objects, such as trees and bushes on the roadside, moving past faster with respect to the horizon than objects that are further away, like a farmhouse, the apparent motion of objects in the sky as Earth moves around its orbit depends on distance. This direct and relatively precise method based on simple geometry can measure the distances to the planets and nearest stars. The satellite observatory Hipparcos has measured direct distances out to 1 kiloparsec (kpc).

After that, the solutions become murkier. Astronomers search for objects to use as distance indicators, sometimes referred to as "standard candles." Just as a driver at night can gage the distance of an oncoming car by the brightness of its headlights, if astronomers can deduce the intrinsic luminosity of the standard candle, identify it at great distances, and measure its apparent brightness, they can determine the distance to the object.

Determining the Hubble constant requires finding the distances to some of the most far away galaxies in the universe. A number of methods exist. Some, like parallax, are firmly based on the principles of physics—that is, astronomers understand the physical process that makes the standard candle operate. Others are based on empirical relationships, the physics of which may be partially or completely unknown. Well-understood standard candles make better distance indicators.

Astronomers have identified two standard candles with a reasonable basis in physics to explain their behavior, which can also be used to measure the distances to galaxies. First, very luminous, pulsating stars known as Cepheid variables have the surprising characteristic that the frequency of their pulsations and their intrinsic luminosity are correlated, so an accurate measurement of the period of the pulsations gives the luminosity of the star. Since they are bright, Cepheids can be seen a great distances. In addition, the pattern of the pulsation—the specific oscillations in the star's brightness as it pulsates—is characteristic, so that Cepheids can be distinguished from other types of variable stars. Once they are identified, their apparent brightness can be measured, and a distance to the star, along with its host galaxy, can be deduced. Until recently, these Cepheids were of little use in measuring the Hubble constant, since they could only be distinguished in the galaxies nearest to our own. However, large ground-based telescopes, particularly the Hubble Space Telescope, allow detailed observations of Cepheids in distant galaxies out to 5 to 10 Mpc.

Another standard candle is a particular kind of stellar explosion known as a Type Ia supernova. These explosions occur only in binary star systems when one star—a compact object known as a white dwarf—accretes mass from its companion star. The white dwarf detonates under the same physical conditions for all Type Ia supernovae, and the resulting explosions have a characteristic light profile and similar peak luminosity. Since these explosions can outshine the entire host galaxy, astronomers target distant galaxies and patiently wait to observe these rare events. Type Ia supernovae have been used to determine distances out to 100 Mpc or more.

Astronomers have some understanding of the physical processes of both these indicators, the pulsating stars and the supernovae explosions, and are therefore more confident in the distances determined by these methods. Although other problems, such as extinction of the light due to intergalactic dust, can still make these measurements imprecise, they are thought to be accurate within the measurement uncertainty. Recent measurements made by Hubble's protégé Allan Sandage (1926-), of the Carnegie Observatories in Pasadena, California, and his colleagues, of supernovae distances coupled to Cepheid distances, measure the Hubble constant at 55 +/-8 km/s/Mpc.

### How H 0 Fits with Other Cosmological Parameters

However, direct measurement of the Hubble constant is only part of the story. The standard cosmology can be used to more accurately measure the Hubble constant. In other words, whatever the value of the Hubble constant, it should not directly conflict with measurements of other cosmological parameters.

Astronomers describe the bulk properties of the universe with several parameters. The Hubble constant measures the expansion rate of the universe. If the expansion is constant, and there is no other force acting to accelerate or decelerate it, then the Hubble constant directly indicates the age of the universe. This is the same as measuring the expansion rate of a balloon, and using that to determine how long it took to blow the balloon up. But, unfortunately, the universe is not so simple, and several other features make the calculation more challenging.

First of all, the expansion rate may not be constant. The deceleration parameter, q 0, indicates whether or not the universe is accelerating (q 0 < 0), decelerating (q 0 > 0), or expanding at a constant rate (q 0 = 0). This deceleration parameter depends not only on the Hubble constant, but also on [.Omega] 0, the parameter describing the density of the universe. If the density parameter is greater than one, the universe contains enough mass to halt the expansion due to gravity and collapse back on itself. If it is less than one, the universe will expand forever. And even that is not the entire story. Recently, astronomers have found evidence for third parameter, the cosmological constant, denoted by [.Lambda]. The cosmological constant, if it is not equal to zero, also affects the expansion rate of the universe.

All these fundamental parameters are interdependent, and together measure the curvature of the universe. Therefore, determining the curvature of space, figuring the acceleration and deceleration of the expansion, and finding the value of [.Lambda] can all constrain the Hubble constant. Recent observations of the cosmic microwave background (CMB) by the balloon-flown microwave telescope Boomerang have important implications for the Hubble constant. The detailed measurements of the bumps and wiggles in the CMB indicate the universe is flat—it will continue to expand until the mass in the universe brings it slowly to a halt. If the cosmological constant is zero, this means the Hubble constant can directly determine the age of the universe. However, if this model is correct, some objects in the universe are older than the age predicted by large values of the Hubble constant.

### Globular Clusters: An Independent Constraint on the Age of the Universe

Whatever the cosmology of the universe, it must be consistent with the other objects within the universe. Since one of the primary features of the Hubble constant is its ability to help determine the age of the universe, astronomers can use the known ages of objects in the universe to constrain the values of the Hubble constant.

Evidence from meteorites indicates that the formation of our solar system, and presumably the Sun, dates back 4.55 billion years ago. Nearby stars and our own galaxy are also reasonably young. However, associations of stars known as globular clusters, whose ages can be readily determined and that represent some of the oldest objects in the universe, perhaps predate galaxies themselves.

Globular clusters are associations of anywhere from 10,000 to over 1 million stars, all of which formed in the same place and at the same time. These stellar associations exist in the distant halo of the Milky Way and other galaxies. Using detailed observations, astronomers can study the characteristics of the stars in the cluster and determine when the cluster formed. These measurements are straightforward, and the method for deriving the cluster ages is well founded in stellar astrophysics.

The results from the dating of globular clusters are compelling. The clusters, on average, date back nearly 15 billion years. Not only do they represent the oldest objects in the galaxy, they put hard constraints on the value of the Hubble constant. For the given cosmology, H 0 must indicate a universe as old or older than 15 billion years. Therefore, either the Hubble constant is smaller than 100 km/s/Mpc, or the cosmological model is incorrect.

### Conclusion

Hubble's first measurements of H 0 and the expansion of the universe, in principle, seemed straightforward to refine. Astronomers needed only two measurements—velocity and distance—to find the answer. As it turns out, H 0 is more difficult to determine than any other fundamental parameter in cosmology, forcing researchers to use a variety of methods to achieve a result. And with so many disparate answers, the evaluation of the Hubble constant must rely on a number of subsequent analyses. The distance indicators must be firmly based on physical principles, H 0 must be consistent with all other determinations of the cosmological parameters, and it must not conflict with independent measurements of the age of objects in the universe. Given these criteria, the smaller value of the Hubble constant, somewhere in the range of 50 to 60 km/s/Mpc, is favored. However, modern cosmology is still an active field of research. Models change and new ideas are put forth all the time. Therefore, astronomers must continue to search for new methods of determining the Hubble constant until a consensus—or more evidence—is found.

—JOHN ARMSTRONG

Overbye, Dennis. Lonely Hearts of the Cosmos: The Scientific Quest for the Secret of the Universe. New York: HarperCollins, 1991.

Peebles, P. J. E. Principles of Physical Cosmology. Princeton, N.J.: Princeton University Press, 1993.

Trimble, Virginia. "H 0 : The Incredible Shrinking Constant 1925-1975." Publications of the Astronomical Society of the Pacific 108 (December 1996): 1073-82.

## KEY TERMS

### APPARENT BRIGHTNESS:

Brightness of an object seen at a distance. The farther away the object is, the smaller its apparent brightness.

### COSMIC MICROWAVE BACKGROUND (CMB):

The background radiation throughout the universe. Because this electromagnetic radiation is at a very low temperature, only a few degrees above absolute zero, most of the radiation energy is in the microwave region of the electromagnetic spectrum.

### INTRINSIC LUMINOSITY:

Brightness of an object, or the amount of energy it emits per unit time. This is independent of distance, and is a fundamental property of the object.

### KPC:

Kiloparsec, or 1,000 parsecs.

### MPC:

Megaparsec, or 1 million parsecs.

### PC:

Abbreviation for parsec, a unit of distance equal to3.26 light-years.

### REDSHIFT:

Shift in the wavelength of light caused by the motion of an object. Redshifted light indicates the object is moving away from the observer. Since galaxies recede from us, and at an every increasing rate with distance, the distance to galaxies is sometimes indicated by their redshift.