The extragalactic distance scale: agreement at last?
THE SCALE OF THE UNIVERSE has long presented a quandary for astronomers. It would be invaluable to know how far away galaxies are, since many fundamental questions about the cosmos depend on the distance scale. But until recently we just couldn't accurately determine galaxy distances.
Of course, it's a difficult problem to attack from our terrestrial platform, only 12,000 kilometers across. It is remarkable that we can measure any distances at all (even inaccurate ones) for objects 100,000 million million million km away. But astronomers need to know these distances precisely. The age of the universe, its history and future, and the geometry of space are some of the properties we can't investigate without knowing cosmic distances.
THE CONTINUING GREAT DEBATE
Until recently knowledge of the distance scale had been in a remarkably unsatisfactory state. Two different approaches to its investigation had been pursued by some of the world's most preeminent extragalactic astronomers, and they gave strikingly different answers.
On one hand was Allan Sandage who, having had Edwin Hubble's mantle placed on his shoulders, spent a great deal of his early scientific career working on the problem. He refined the methods and philosophy laid down by Hubble in this century's first quarter. Sandage believed he should concentrate on the most reliable indicators for each different distance range. Starting in 1974, he and Gustav Tammann published a series of papers in which they gradually worked their way from the nearest galaxies to the realm of the Hubble flow -- where an object's radial (line-of-sight) velocity is dominated by the expansion of the universe rather than by local effects.
If a galaxy is far enough away to be in the Hubble flow, its spectral redshift indicates its distance. Practically speaking, the galaxy must be receding at greater than a few hundred kilometers per second, as the random motions of galaxies in nearby space can account for up to 200 km per second of recession velocity. Therefore Sandage and Tammann's first efforts were to find reliable distance indicators for the Virgo cluster, the nearest large cluster of galaxies, which has a mean velocity of about 1,150 km per second.
At first they believed this cluster would be a good determinant of the Hubble parameter -- the number that converts a measured recession velocity into a distance in the expanding universe. However, the cluster's gravitational influence on nearby galaxies, including our own, distorts the measurements. Our galaxy and others nearby are falling toward the Virgo cluster at about 300 km per second. Therefore Sandage and Tammann also looked at galaxies in other directions, applying various methods to select a sample of galaxies at a uniform distance. Regardless of the technique used or the region of space explored, they found a Hubble parameter of about 50 km per second per megaparsec, with a 10 percent uncertainty. (A megaparsec is equal to 3.26 million light-years.) This value implies a very large, very old universe.
On the other hand was Sandage's contemporary, Gerard de Vaucouleurs, whose parallel series of papers reflected a different approach. De Vaucouleurs felt that the "most reliable" distance indicators should not stand alone but be combined with all possible techniques in all distance regimes. His approach was more statistical in nature than Sandage and Tammann's and resulted in a very different value for the Hubble parameter. In each of his tests de Vaucouleurs found a value close to 100, implying a universe half the size and age of Sandage and Tammann's. So who is right?
This dispute carried with it important implications about cosmology and left uncertain many of the astrophysical conclusions to be drawn from studies of distant galaxies. In the nearly 20 years since the dispute began, many astronomers have expended large amounts of energy and telescope time to resolve the discrepancy. This effort may now be paying off, because agreement among astronomers on the issue (with the exception perhaps of the original protagonists) seems nearly at hand.
RR LYRAE VARIABLES
Great improvements have been made in traditional distance indicators, and new ways of gauging cosmic scale have been discovered. For example, even the RR Lyrae method -- used by Harlow Shapley at the turn of the century to measure the Milky Way's size -- has shown considerable progress recently.
The brightness of an object falls off as the inverse square of its distance. Therefore the difference between its intrinsic brightness (absolute magnitude) and apparent brightness reveals its distance. All RR Lyrae variables have nearly the same absolute magnitude, so they are especially useful as distance indicators. A problem with them, however, is that they aren't very luminous. Although fairly easy to see in the Magellanic Clouds, they proved too faint, until recently, to be detected in most other nearby galaxies. Walter Baade tried in vain to detect these variables in M31, the great spiral in Andromeda, using first the Mount Wilson 100-inch and then the Palomar 200-inch telescope.
Success with M31 was finally achieved in 1987 by Chris Pritchet and Sidney van den Bergh, using a CCD detector attached to the Canada-France-Hawaii Telescope, which takes advantage of the frequent superb seeing on Mauna Kea in Hawaii. Combined with new determinations of the absolute magnitudes of RR Lyraes, the result gives a new and independent distance for M31, one of the crucial rungs of the "cosmic distance ladder." (The revised value is 2.5 million light-years.)
Additional nearby galaxies have recently revealed their RR Lyrae variables as well. Pritchet and van den Bergh discovered some in M33 in Triangulum, while other astronomers found them in many of the Local Group's smaller members -- most recently the faint irregular galaxy IC 1613. All of these discoveries strengthen alternate distance criteria that rely on accurate distances to members of the Local Group as starting points.
A new and surprisingly reliable distance indicator for nearby galaxies is the brightness of planetary nebulae. Objects like the Ring nebula and the Dumbbell nebula, for example, have very nearly the same intrinsic brightnesses, with only small differences resulting from size-of-sample effects and chemical-composition variations. Luminous planetaries have been discovered in galaxies in the Local Group, other nearby groups, and even in the Virgo cluster.
This method is especially powerful for determining the distances to early-type galaxies (ellipticals and SOs, or "armless spirals"), where the planetaries are easy to distinguish and reddening due to dust is rare. For galaxies in which more traditional methods are also used, the distances determined from planetaries agree superbly. Planetaries seem to work for more remote galaxies as well, yielding, for example, a distance to the Virgo cluster of 49 million light-years. Using a velocity for the cluster that has been corrected for our own infall toward it produces a Hubble parameter of 74 km per second per megaparsec, about halfway between the values of Sandage and Tammann, and of de Vaucouleurs.
NOVAE IN VIRGO GALAXIES
Because novae reach great brilliance, and because this brightness can be calibrated locally in our galaxy, these stellar explosions have long been used as extragalactic distance indicators. The novae in M31 were among the first clues Hubble used in the 1920s to show the extragalactic nature of that system, and a few novae have since been found in other Local Group galaxies. However, novae occur infrequently in galaxies much less luminous than our own, so they are used to gauge the distances for massive galaxies only.
An important breakthrough in the use of novae occurred in 1985, when Pritchet and van den Bergh detected them in the Virgo cluster's giant elliptical galaxy M87. Two years later they found some in three other Virgo-cluster ellipticals -- M49, M60, and NGC 4365. Their data indicated a distance to the cluster of 63.6 million light-years and a Hubble parameter of 69.
The correlation of a Cepheid variable's period and its luminosity was discovered in 1914 by Henrietta Leavitt, and it has been a cornerstone of astronomical distance measurements ever since. Among the more significant recent developments in this method has been the use of near-infrared data for several members of the Local Group, which has led to improved distances for these important calibrating galaxies.
The detection of Cepheids beyond the Local Group has proven difficult. Sandage and his colleagues have found them in several dwarf irregulars and in the spiral NGC 2403, a member of the M81 group in Ursa Major. The farthest Cepheids reported so far are two variables in the giant spiral M101, giving a more reliable distance to that group (24 million light-years). All of these new developments have led to an increased reliability of Cepheid-based distances, making it possible to obtain distances for galaxies as remote as M101 to an accuracy of about 15 percent.
Being luminous objects that are easily recognizable in other galaxies, globular clusters have been used as indicators of distance since Hubble's initial studies of those in M31. The first attempt to infer cosmic distances from them came in 1955, when William Baum found the distance to the Virgo cluster by assuming the globulars of M87 to be like those of M31.
More recently astronomers have shown that the luminosity function of globular clusters (the curve showing the number of clusters of each different luminosity) is reasonably independent of the properties of the host galaxy. Distances can be measured by finding the apparent magnitudes of a large sample of a galaxy's cluster population and comparing them with the expected absolute magnitudes.
This method works best for giant elliptical galaxies, where there are as many as 1,000 globulars and reddening by dust and confusion by other kinds of clusters don't interfere. Because globulars are highly luminous, it should be possible to measure distances out as far as 160 million light-years. Refinements are still being applied and tested, but it is already clear that the method is a powerful one. It could be employed -- with a corrected Hubble Space Telescope (HST) -- on clusters that have radial velocities as great as 35,000 km per second. So far, studies of nearer clusters indicate that the Hubble parameter must be close to 75 km per second per megaparsec.
The internal dynamics of a galaxy are related to its luminosity and size. In 1974 the measured width of the 21-centimeter neutral-hydrogen line, an indicator of rotation rate, was found to correlate with a galaxy's absolute magnitude -- luminous galaxies spin faster than dim ones. This concept was fully developed in 1977 by Brent Tully and Richard Fisher and soon became known as the Tully-Fisher relation. It extended the realm of measurable galaxy distances far beyond the Virgo cluster.
A particularly important aspect of this relation is that it can give geometrical distances to galaxies, both within and outside of clusters, to distances beyond where velocities are influenced by the Virgo cluster's mass. (Before it was available, astronomers had to infer distances in that realm primarily from radial velocities.)
With the advent of a method independent of velocities, it became possible to look for irregularities in the expansion of the universe. Although the universe was at first assumed to be expanding uniformly, the wholesale use of the Tully-Fisher relation revealed large-scale departures from uniformity. The most famous is that attributed to the Great Attractor, which seems to be influencing galaxy motions in one particular part of the cosmos. The attractor was hypothesized in 1988, and since then additional large-scale flows have been mapped in other parts of the sky, most based on Tully-Fisher distances.
An improvement to the original form of the relation was the use of near-infrared magnitudes for the galaxies (thus avoiding the problems associated with reddening). As an example of recent progress, a 1992 study of the Virgo cluster arrived at a distance of 49 million light-years, implying a Hubble parameter of about 75.
The explosions of supernovae sometimes reach luminosities rivaling that of the entire host galaxy, and therefore they can be seen at very large distances. They are rare events, occurring only a few times a century even in a very massive galaxy, but there are so many galaxies in nearby space that we can now detect a new supernova virtually every week. Many of the recent discoveries are in galaxies so far away they aren't cataloged and don't have names.
The best supernovae for the distance scale are those of Type Ia. They are found in elliptical galaxies or the old populations of spirals, and they result from the nuclear detonation of white-dwarf stars. Tests indicate that they behave like "standard candles" -- that is, they have about the same peak absolute magnitude regardless of their environment. Measurements in galaxy clusters suggest that supernovae of this type range over only about 0.1 magnitude.
A problem arises, however, in trying to determine the actual value of this peak brightness. Various methods give different answers, with a range of about 1 magnitude, but one very recent result may signal the solution at last. In 1992 astronomers determined the distance to the galaxy IC 4182 in Canes Venatici using a well-observed supernova of Type Ia that occurred there in 1937. (The only other nearby example occurred in the peculiar Centaurus galaxy NGC 5253 in 1972.) With this distance the absolute magnitude of Type Ia supernovae at maximum is found to be -18.8 in blue light, with an uncertainty of about 0.3 magnitude. When this is applied to Virgo-cluster supernovae a Hubble parameter of 86 km per second per megaparsec is obtained.
Object Distance (million of light-years) Cepheids RR Lyrae TRGB LMC 0.16 0.15 0.16 IC 1613 2.50 2.33 2.33 M31 2.52 2.43 2.52 M33 2.75 2.85 2.84 New methods are cropping up all the time to measure the distance to galaxies. One of the latest, called the "tip of the red giant branch" method (TRGB), involves the similarity in brightness of a certain class of low-mass red-giant stars. Although this technique has not yet been widely used, it gives results similar to other more established methods such as those using Cepheid and RR Lyrae variables.
Measuring surface-brightness fluctuations in nearby galaxies is a new type of distance criterion. Amateur astronomers are perhaps familiar with the effect called incipient resolution -- a globular cluster, for example, may be just too far away to be clearly resolved with a particular telescope, but the fuzzy image shows a characteristically mottled look, hinting that resolution is almost achieved.
In 1988 John Tonry showed that it is possible, with detectors such as CCDs, to measure the degree of "bumpiness" of an unresolved image. A galaxy twice as remote as another, for instance, will have bumpiness half as great. A quantitative measure of this phenomenon thus gives the galaxy's distance. This method works especially well for elliptical galaxies and for the central bulges of spirals. When the method is applied to Virgo ellipticals, it provides a distance of 51.8 million light-years and a Hubble parameter of 84.
A spectacular new distance method became available when gravitational lenses were discovered in 1979. As its name implies, a gravitational lens is the general-relativistic equivalent of a glass lens. A massive galaxy acts to bend the light from an object far behind it to form a displaced image or images, or even arcs and rings. The most commonly lensed objects are quasars, which are very distant, extremely bright, small, and easily perceived when their images are distorted gravitationally by intervening galaxies.
The trick of using these lenses for the distance scale comes when the lensed object flickers in brightness, as quasars are prone to do. For a quasar that has been lensed into twin images, and whose light has proceeded to us along two paths of different lengths, there will be a difference in the arrival time of the flicker for each image. If the mass distribution in the lensing galaxy can be determined (equivalent to measuring the shape of a glass lens), then the galaxy's distance can be inferred from the time difference.
An example of such a measurement was published in 1991, based on observations of a double quasar that exhibited a time difference in flickers of about 1 1/2 years. From this astronomers deduced that the Hubble parameter must be less than 85. Accuracy of this measurement will increase when we can better determine the mass distribution in the lens. As we take further advantage of these immense natural magnifications, they will surely become an important element in the distance-scale enterprise.
AGREEMENT AT LAST?
It is tempting to say "yes, finally!" there is agreement on the Hubble parameter. All of the values mentioned above fall within the range of 69 to 86 km per second per megaparsec, each comfortably within the others' estimated errors. Compared with the situation a few years ago, this is gratifying. Rather than having to choose between values of 50 and 100, we can confidently use 75, knowing that our choice is correct to within about 15 percent.
Or can we? Four considerations lead some of us to continue worrying. First, on earlier occasions we believed we had a well-established value for the distance scale, and in those cases new discoveries showed our evaluation to be overly optimistic. Second, the recent findings of large-scale motions and immense inhomogeneities in the expansion of the universe may imply that there isn't a unique Hubble parameter.
The third worry is that the value of 75 km per second per megaparsec leaves us in a quandary regarding the age of the universe. Straightforward models scaled to that value give an expansion age for the universe of about 15 billion years, depending on certain details still to be measured accurately. But in our galaxy we find globular clusters that seem to have ages greater than this, 16 billion years or more. Even if we stretch the numbers a bit, the best we can do is make the clusters as old as the universe, which is absurd. We still have to allow time for the formation of matter, the gathering of matter into galaxies, and the concentration of that material into clusters before stars can form. The timing is just too close for comfort.
One solution is to settle for a more complicated universe, perhaps one in which the mysterious "cosmological constant" plays a role. This number, first introduced by Einstein and later rejected by him as too arbitrary, could solve the puzzle by adjusting the age of the universe calculated from the present expansion rate. However, most cosmologists find it distasteful to introduce the constant into their calculations, especially without any clear physical understanding of it or a way of determining its value from other considerations.
Now for the fourth problem. One of the most important tasks planned for HST was the determination of the extragalactic distance scale. Although it is still too early for a definitive answer from the spacecraft -- the team has just begun to acquire the necessary data -- some first results are available that seem to cloud the picture. Sandage and several collaborators used HST to measure Cepheids in the key galaxy IC 4182. The Cepheid distance has turned out to be much greater than the one determined from the 1937 supernova in that galaxy, and Sandage's group derived a Hubble parameter of only 45, consistent with the position he has held all along!
Where does this leave us? Until more galaxies have definitive distances measured by HST, we remain in a state of doubt. While many different kinds of ground-based data endorse a value of 75 km per second per megaparsec for the Hubble parameter, the first results from the HST Cepheid program indicate a much lower value. Complications may also arise because of the nonuniformities of the Hubble flow and other cosmological considerations. As we so often say in astronomy, much more work has yet to be done.
Paul Hodge is a professor of astronomy at the University of Washington and editor of the Astronomical Journal. He has worked on a variety of key problems in stellar, galactic, and extragalactic astronomy. His first article for Sky & Telescope appeared in the February 1961 issue.