Outward Bound

Not everybody gets to have something named after them. In everyday life, units of measure such as watts, volts, amps, and celsius degrees are so common that we may miss the reference to the scientists for whom they were originally named: James Watt, Alessandro Volta, André Ampere, and Anders Celsius. An even higher honor is to have your name attached to a physical constant, which is a single measured quantity that happens to reveal itself in many and varied ways throughout the physical world.

The general public may be amused by how much enthusiasm the community of scientists can display over certain physical constants. In a changing world, those things that are the same in time or place bring comfort. Why? The history of science has shown that what is found to be constant often becomes a cornerstone to a fundamental part of our understanding of the universe. Some important constants include Avogadro’s number (named for the nineteenth century Italian physicist Amadeo Avogadro), which laid the foundation that enabled us to measure atomic weights, Newton’s constant (named for the seventeenth century English physicist Isaac Newton), which enables us to calculate the gravitational force between any two objects in the universe, and Planck’s constant (named for the turn-of-the-century German physicist Max Planck), which launched the era of quantum mechanics.

When the next millennium arrives, and a tally of the greatest scientific discoveries of the twentieth century is made, somewhere near the top of the list you will find the expanding universe. Credit the American astronomer Edwin Hubble for the discovery of a constant in 1929, that first described the rate at which galaxies are moving away from each other. Hubble’s constant launched the modern era of cosmology.

Some discoveries are amazing even when they are fully anticipated. Finding planets orbiting other stars and finding evidence of past life on Mars are among them. Hubble’s discovery of the expanding universe, however, was not inspired by an official prediction, nor was it anticipated in any other way, so it caught everybody by surprise. Nobody thought to think it. Your average astrophysicist had simply assumed (in the complete absence of data) that the universe was static and unchanging—a position embarrassingly reminiscent of the Aristotelian notion that the stars were fixed and unchanging upon the dome of the night sky.

Albert Einstein’s equations of gravity, published in 1916 and which superseded those of Isaac Newton, contained a description of the entire universe that allowed for three scenarios: contracting, static, or expanding. The mathematics showed that the static solution was unstable; it described a universe that will spontaneously contract or expand. A similar fate greets a ball balanced on the top of a hill; the ball’s position is unstable so it will roll down in one direction or another at the slightest nudge. With a non-static universe staring him in the face, Einstein botched the opportunity to predict it and, out of aesthetic preference, instead favored the static model. This required that he introduce to his equations a balancing constant that countered the effects of gravity to prevent cosmic contraction or expansion. While mathematically legitimate, the constant had no physical basis and Einstein later regretted having introduced it.

In the 1920s, Edwin Hubble had access to the 100-inch telescope on Mount Wilson, California, the most powerful telescope in his day. Fully armed, Hubble was able to deduce that the spiral fuzzy things in the sky were entire spiral galaxies—island universes that were not unlike the Milky Way in shape and appearance. By 1929, he had assembled a list of several dozen galaxies whose velocities were reliably measured by his own efforts and by those of the American astronomer Vesto Slipher of the Lowell Observatory in Arizona. Slipher already noted that most of the spiral systems had very high velocities that were directed away from the Milky Way, but he drew no further conclusions.

Hubble’s next task was to calculate the distances of all these objects—measurements that are notoriously difficult to obtain. Unfortunately, we can’t just strap on a pedometer and count our paces to the galaxies. We can’t (yet) fly to the galaxies and consult our odometer. Nor do we live long enough to wait for a radar signal to be bounced back. Curious about how these galaxies’ distances might vary with velocity or position on the sky, Hubble derived the distance to each by relying primarily on Cepheid variable stars as a yardstick. The entire class of Cepheid variable stars, which oscillates in brightness in predictable patterns, is named for its prototype, Delta Cephei, the sixth brightest star in the constellation Cepheus. These stars are not only bright enough to stand out among surrounding stars in distant galaxies, but the time it takes for their brightness to cycle, which is trivial to measure, is correlated with their luminosity. Once you derive the luminosity, the distance to the Cepheid variable (and by association, to its host galaxy) pops out from a simple formula that connects the two.

To give a terrestrial analogy, if light bulbs somehow flickered at a characteristic rate that depended on their wattage, you could deduce the bulb’s wattage at any distance by simply noting its flickering rate. You then mathematically ask the question, How far away must a bulb of that wattage be to appear as dim as I see it?

What Hubble found would forever change human conception of the universe. He might have found that all galaxies were haphazardly moving away from the Milky Way. But they weren’t. All galaxies might have had recession velocities that decreased with distance. But they didn’t. Or, perhaps, all galaxies parked themselves at the same distance from us. But they hadn’t. Hubble found that, for nearly all galaxies in his sample, the recession velocities were directly correlated with distance. The farther away a galaxy was, the faster it was moving away from us. In other words, if one galaxy were twice the distance of another, it was moving away from us at twice the speed. Ten times farther, ten times faster, and so forth. The inference from this particular signature, and no other, was that we were part of an expanding universe. The discovery even had a ready-made theoretical context as one of the solutions to Einstein’s theory of gravity. Just as Earth was dethroned as the center of the system of planets, a new world order was at hand where now everything was in motion, even the universe itself.

One needn’t be a math whiz to understand how to derive a numerical value for the Hubble constant. It’s simply the slope of the line through the galaxy data in a plot of velocity versus distance. The Hubble constant’s units are therefore velocity divided by distance. Depending on what distance indicators are available, and depending on the reliability of these indicators, the Hubble velocity-distance diagram has yielded very different slopes. Indeed, Hubble’s originally derived constant was significantly overestimated due to flawed assumptions about the Cepheid calibrations.

Consider it to have been an omen, because even when finally corrected in the 1950s, there remained just enough uncertainty in the Cepheid distances and in other calibrators to allow two competing camps of astronomers to favor very different values of the Hubble constant by selecting some distance indicators while rejecting others. The low value hovered around 15 kilometers per second per million light years of distance as championed by the American astronomer Alan Sandage and his colleagues, while the high value of 30 kilometers per second per million light years was championed by the French-born, American astronomer Gerard deVaucouleurs, a former mentor of mine. Brief standoffs at the crest of scientific discovery are not uncommon, but measurements of an uncertain quantity are usually scattered over a range of values until better and better experiments serve to narrow the range of uncertainty. If anything other than this convergent process takes place, then nonscientific factors (such as hard-headedness) may be at work.

Its importance and elusiveness has made the Hubble constant somewhat of a Holy Grail of cosmology. A major source of uncertainty is the effect of “random” galaxy motions relative to one another on the total expansion rate. The farther out you go, the more significant the expansion of the universe compared with the random motions and the more reliable your measurement of the Hubble constant. A handful of the galaxies closest to the Milky Way have random velocities that exceed the general flow from the expanding universe and are thus moving towards us rather than away. The nearby Andromeda Galaxy, a mere 2.2 million light-years distant, illustrates the point well: the expansion of the universe contributes less than fifty kilometers per second to Andromeda’s motion away from us, which is inadequate to overcome our general (and typical) 100 kilometer per second motion toward each other.

What we need are good calibrators that can be traced to distances far beyond where the random motions of galaxies matter. For example, Cepheid variable stars have only recently been discovered as far away as the famous collection of galaxies known as the Virgo Cluster—50 million light years away along the line of sight through to the constellation Virgo. Only barely reachable from ground-based telescopes, the discovery of Virgo Cepheids had always been a priority project for the orbiting Hubble Space Telescope. At the Virgo cluster’s distance, the expanding universe imparts about a 1,000 kilometers per second recession velocity, further reducing the extent to which random galaxy motions contaminate the measured velocity.

When combined with a half-dozen other distance calibrators, including exotic objects such as supernovae and gravitational lenses, a consensus value for the Hubble constant has now emerged (revealed at a recent Princeton conference titled “Unsolved Problems in Cosmology”). As you might have guessed, it falls almost exactly between the two previous stubbornly held estimates: 23 kilometers per second per million light years with an uncertainty of less than 15 percent. Stated in sentence form, the Hubble constant would read: “For every million light years distant, an object can be expected to recede from you by an extra 23 kilometers per second with an uncertainty of about 3 kilometers per second either way.”

I can live with that.

Incidentally, my professional career recently (and briefly) overlapped the Hubble constant debate when I participated in a multi-author research paper that used a distant supernova’s change in luminosity as a distance calibrator. We derived a Hubble constant of 25 kilometers per second per million light years—consider it part of the consensus.

Distances to galaxies beyond the base calibrators can now be computed with confidence directly from the Hubble relation itself:

At the nearest quasar, 3C273, the recessional velocity provided by the expanding universe is nearly 50,000 kilometers per second. Note that at this expansion velocity, random motions of a few hundred kilometers per second are of little arithmetic consequence. Applying the Hubble relation, we get a distance of about 2,000 million (2 billion) light years, which is nearly a thousand times farther from the Milky Way than the Andromeda Galaxy.

Now that the Hubble Grail has been found, we can turn our attention to the next level of challenging questions that face cosmology, such as, How far away (or equivalently, how far back in time) does the value of the Hubble constant remain valid? If the collective gravity of the universe is serving to slow down the cosmic expansion then the Hubble constant must have been higher in the past. And if the universe one day stops expanding and starts to collapse then the Hubble constant will drop through zero to become negative! For these reasons, the Hubble constant is more correctly identified as the “Hubble parameter.” These Hubble hijinks are officially described through the “deceleration parameter,” which contains deeper information about our expanding universe such as answers to the questions: Will we indeed expand forever?, or Will we one day collapse?

And Einstein’s original constant—introduced mathematically to stabilize the universe—has recently been exhumed in several circles as a tool to reconcile some peculiar observed features of the universe. Look for that one too. It’s called lambda.

As I write this sentence, my newborn daughter, Miranda, turns fourteen days old. She will grow up knowing only a world in which the expansion rate of the universe is well established. Seventy years ago, her grandparents were born when galaxies were thought to be simple fuzzy smudges floating in the Milky Way. Yes, we are living the golden age of cosmic discovery.