Imagine that the distance between the Sun and Pluto is the length of a soccer field. The Sun would be a globe just 2 centimeters in diameter. The Earth would be 2.3 meters away from the Sun and just 2 millimeters across. At the other end of the field, Pluto would be nothing more than a speck of dust. Where would the nearest star be?—In the crowd?—In the parking lot?—In the next street? All wrong. The nearest star would be 645 kilometers (401 miles) away. And that is nothing on the cosmic scale.
Measuring the size of the Universe is unlike any other measuring job in human history. On Earth when you want to measure a distance, you can pace it out, or send a radar beam or laser ray to do the pacing for you. In the vast reaches of space this is usually impossible; the distances are simply too large. Bouncing laser beams or radar signals off celestial objects is only feasible for the Moon and the nearest planets. To measure other distances, astronomers have developed a filigree of different techniques for different distance ranges, called the “cosmological distance ladder.” The variety of approaches is essential because no single distance determination method can serve across all scales of the Universe. Some celestial objects are too faint to be seen far away, others are too rare to be found nearby. Where the techniques do cover the same range, they serve to reinforce each other and improve the overall accuracy of the system.
Central to the cosmological distance ladder is the concept of the standard candle. This is a type of celestial object that releases the same amount of energy regardless of where in space it is found. Its distance is therefore the only thing that affects how bright it appears from Earth. One of the best types of standard candle is the so-called Cepheid variable star. The first example of such a star to be observed, Delta Cephei, caught a young astronomer’s attention in 1784. John Goodricke of York charted the way it rose in brightness and faded again, deducing that the entire cycle took 128 hours and 45 minutes to complete. At this time astronomers knew of a handful of other variable stars, but each of those dropped in brightness suddenly and then restored themselves sometime later. Delta Cephei was the only one to exhibit a gradual change.
“Measure what is measurable, and make measurable what is not so.”
GALILEO GALILEI 17TH CENTURY ASTRONOMER
By the first decade of the 20th century, many more examples of Cepheids had been discovered, some with shorter pulsation periods, some with longer. Henrietta Swan Leavitt, an assistant at the Harvard College Observatory, compiled a list of Cepheids in a nearby galaxy called the Small Magellanic Cloud. Rather than list them in random order, she wrote the 16 entries out according to how long they took to pulsate. Her curiosity was piqued by the fact that listed in this way the stars also appeared in order of average brightness: the longer the pulsation period, the brighter the star. By 1912, Leavitt had investigated a further nine Cepheids in the Small Magellanic Cloud and confirmed that each one’s period of pulsation was tied to its average brightness. This immediately suggested that the Cepheids could be used as standard candles.
Final confirmation of this was supplied by British astrophysicist Arthur Stanley Eddington when he explained the behavior of Cepheid variables. He proposed that the surface of the star trapped some of the outflowing radiation, causing the surface to swell up before releasing that radiation and shrinking again. What was more, he showed that the density of the star determined the period of pulsation. This means that all Cepheids pulsating with a period of say five and a half days will be identical to one another. Thus, any two can be compared and the difference in their observed average brightness can be used to calculate how much further one is than the other. The comparison of Cepheid variable stars from one galaxy to another is one of the most heavily relied upon methods in distance determination.
A brighter standard candle is an exploding star, the supernova type Ia. The explosion is triggered when the burned-out core of a dead star siphons gas from a nearby, active star. The gas builds up on the surface of the dead star, increasing its mass. When this crosses a well-defined threshold called the Chandrasekhar limit (after Subrahmanyan Chandrasekhar, the Indian physicist who computed its value), the star can no longer support its own weight and collapses, setting off an enormous explosion. Because every supernova of this type is caused by the collapse of the central star when it reaches this mass limit, every one of these stellar cataclysms releases the same amount of energy into space. The brightness of a supernova type Ia is vastly greater than that of a Cepheid variable star; in fact it can outshine 100 billion (100,000 million) normal stars put together, rendering it visible across the entire Universe. The drawback is that these celestial detonations are impossible to predict because astronomers cannot see the doomed stars until they explode. Statistically, a supernova will occur about once a century in any given galaxy and this makes spotting one a task that requires constant vigilance.
Once a supernova type Ia has been seen, the distance of its host galaxy can be calculated relative to any other galaxy that has displayed a similar supernova. The same is true of galaxies seen to contain Cepheid variable stars. So, to join these two rungs of the cosmic distance ladder together, astronomers need to see a supernova in the same galaxy as they have seen a Cepheid. The more galaxies they can do this for, the better the accuracy of the join. Both methods give only relative distances, telling us for example that one celestial object is ten times farther away than another. What astronomers really want to know is the actual distance in kilometers or miles. To do this, they need to put a solid first rung on the cosmological distance ladder—one that supplies absolute distances. Luckily there is a method to do this and it is called “parallax.”
The orbital motion of the Earth around the Sun causes a seasonal shift in position of the nearest stars due to the effect of parallax. Astronomers began trying to observe stellar parallax during the 16th century, before the invention of the telescope. At the time, they were less concerned with measuring the distance to the stars than investigating the radical new proposal by Nicolaus Copernicus that the Earth was not immobile but in orbit around the Sun. They reasoned that if they could see the stars apparently shift position, they would be able to prove that the Earth moved.
“Scarce any problem will appear more hard and difficult, than that of determining the distance of the Sun from the Earth.”
EDMOND HALLEY 17TH CENTURY ASTRONOMER
Parallax can be easily demonstrated. Hold a finger in front of your face and close one eye. Notice the position of your finger in relation to some distant object, say a tree out of the window or a picture on the wall. Now change eye, keeping your finger stationary. Notice how the positions of your finger and the distant object have apparently changed. That is parallax, caused by the distance between your two eyes.
On the cosmic scale, stellar parallax occurs because the Earth is on the opposite side of its orbit every six months. As our viewpoint changes by almost 300 million kilometers (186 million miles)—the diameter of Earth’s orbit—there will be subtle movements in the apparent positions of the nearest stars. The closer the star, the greater will be the movement. If the concept is simple, the execution is anything but. Despite many attempts, no parallax could be found in the 16th or 17th centuries. Not even Galileo’s telescopes and their subsequent improvements allowed any hint of confirmation that the Earth moved. The reason was that the stars are so far away that their movements were too small to be seen by those early telescopes. Not until 1838 was the effect finally observed. Friedrich Wilhelm Bessel repeatedly measured the position of the star 61 Cygni and found that it displayed a minuscule parallax which allowed him to calculate (by trigonometry) that the star was around 93 trillion kilometers (58 trillion miles) away, or 9.8 light years.
PARALLAX: THE MOST ACCURATE FORM OF DISTANCE DETERMINATION
Bessel’s parallax measurement was swiftly followed by results for other stars from other astronomers. Despite this triumph, the work was painstaking and prone to error. By the first decades of the 20th century, astronomers had measured only about 100 stellar parallaxes. Today, satellite measurements have supplied parallaxes for over 100,000 stars, but all well within the Milky Way at distances of less than 1000 light years. Fortunately, some of these stars are Cepheid variables, so this has allowed the absolute brightness of Cepheids to be calibrated and the bottom rung of the distance ladder to be joined to the rest.
In 1929, a discovery was announced that caused a revolution in cosmological thinking. American astronomer Edwin Hubble had found evidence that the Universe is expanding. As well as changing forever the way we think about the Universe, this provided another crucial rung in the cosmological distance ladder, allowing astronomers to measure distances across the largest imaginable swathes of space.
The seeds for Hubble’s discovery were sown in the 1910s when astronomers recognized an exploding star in a fuzzy celestial cloud. These fuzzy clouds were known as “nebulae” and at the time most astronomers thought that they were pockets of gas within our own Galaxy. Upon sight of the supernova explosion, some astronomers began to voice a very different opinion, that these nebulae were highly distant collections of stars—a view that became known as the “Island Universe” hypothesis. Others clung to the status quo, maintaining that the nebulae were nearby. The debate was settled in 1924, when Hubble succeeded in finding a Cepheid variable star in the largest of the clouds, known then as the “Andromeda Nebula,” while using the 100-inch telescope on Mount Wilson in Southern California. He calculated the distance to Andromeda as 900,000 light years. Although we now know that the Andromeda Galaxy, as it was renamed, is 2.2 million light years away, Hubble’s much lower estimate was at that time three times larger than the accepted size of the entire Universe. It proved not only that the Universe was vastly larger than previously believed, but that individual galaxies were dotted throughout space and that each one of these galaxies was a huge conglomeration of stars.
Spurred on by this, Hubble began a systematic study of the galaxies. He placed them into three classes: spiral, barred-spiral and elliptical galaxies (see What is the Universe?). He estimated the distance to as many of them as he could, and he studied the light from them. The key to his final discovery was noticing that the light from each galaxy displayed a “redshift.” In 1842, Christian Doppler had proposed that if the distance between a source of light and an observer were shrinking, the light would be “squashed.” This would shorten the wavelengths and so turn the light bluer, because blue light has a shorter wavelength than red light. In the opposite situation, when a source and observer are moving apart, the wavelengths are lengthened and the light becomes redder. This stretching is what we call redshift, and Hubble became an expert at measuring it in the light from galaxies.
THE DOPPLER EFFECT: THE MOTION OF A SOURCE OF LIGHT AFFECTS THE WAVELENGTH OF THAT LIGHT
Hubble plotted the distances of 46 galaxies against their redshifts, and saw something amazing: the further away the galaxy, the greater its redshift. According to the Doppler effect, this meant that the further away a galaxy was from the Milky Way, the faster it was receding. It was as if everything was exploding away from everything else in space. At a time when the prevailing view was that the Universe was static, this seemed incredible.
In 1916, several years before Hubble undertook this work, Albert Einstein presented his General Theory of Relativity to the world. General relativity provided the mathematical framework within which to properly understand the meaning of Hubble’s subsequent observations. It too proposed that the galaxies were separating from one another, but rather than individual galaxies speeding through space, its premise was that space itself was expanding, carrying the galaxies along with it. A useful way to visualize this is by thinking of a raisin cake mixture. Before rising in the heat of the oven, it is a small dense lump with closely packed raisins. After it has risen, the raisins have not moved through the mixture but they have been driven apart by the expansion of the cake. So it is with the galaxies; space itself is endowed with the ability to expand and, as it does so, it drives the galaxies apart. The more space between a pair of galaxies, the faster they are driven apart and the greater the redshift. When astronomers talk about a redshift of 1, they mean that the light has been doubled in wavelength. To do this, the Universe must have doubled in size while the light has been traveling along. A redshift of 3 means the light’s wavelength has quadrupled, hence the Universe has doubled in size twice, meaning it is now four times as big as when the light started its journey.
“The history of astronomy is a history of receding horizons.”
EDWIN HUBBLE 20TH CENTURY ASTRONOMER
Getting back to our aim of measuring cosmological distances—if we know a galaxy’s redshift, we can convert it to a distance once we know how fast the Universe is expanding. The expansion rate of the Universe is known as the “Hubble constant,” but measuring it confounded astronomers for most of the 20th century. Hubble himself got it wrong by a factor of almost seven. Although the 100-inch telescope he was using was then the largest in the world, it was incapable of resolving Cepheids throughout his sample of galaxies. So, although Hubble showed us how to measure the size of the Universe, the technological restrictions of his day meant that he could not complete the job—not even when he started using the 200-inch Hale telescope on Mount Palomar, California.
In the last two decades, astronomers have had another Hubble—the Hubble Space Telescope—which has allowed them to finish the task, thanks to its vantage point above Earth’s atmosphere. Although Hubble’s mirror is only about half the size of the Hale Telescope, it has identified Cepheids out to around 60 million light years and supernovae type Ia across billions of light years. It has enabled astronomers to calculate a definitive figure for the Hubble constant, which tells us that for every million light years that separates two galaxies, they are driven further apart at a speed of 22 kilometers per second (14 miles per second).
Using the now well-constructed cosmological distance ladder, astronomers today are confident that the Universe stretches on for billions of light years in all directions. The most distant celestial object yet observed has a redshift of just over 8. This means that the Universe has doubled in size eight times during the time it has taken for the light to reach us. It converts into a distance of around 13 billion light years, and this is our current estimate for the minimum possible size of the Universe. It has taken the light from that celestial object 13 billion years to cross the Universe and in all that time the Universe has continued to expand.
To calculate the full extent of the Universe, the only recourse is to create computer models of the expanding Universe based upon the laws of general relativity. These suggest that during those 13 billion years, the Universe has swollen to at least 95 billion light years in diameter. As if that were not brain-bending enough, there is one final sting in this tale. The Universe may extend way beyond 95 billion light years, but there is no way for us to see beyond even 13 billion years because there has not been enough time since the origin of the Universe for the light from such distant regions to reach us. If we wait another billion years, then the light from the next billion light years of space will arrive and we will be able to study it. Like a television soap opera, the study of the Universe seems destined to be a never-ending series of revelations.