16.5: The Expanding Universe

A Changing Universe

Astronomers now know that the universe is expanding. Before we describe how the discovery was made, we should point out that the first steps in the study of galaxies came at a time when the techniques of spectroscopy were also making great strides. Astronomers using large telescopes could record the spectrum of a faint star or galaxy on photographic plates, guiding their telescopes so they remained pointed to the same object for many hours and collected more light. The resulting spectra of galaxies contained a wealth of information about the composition of the galaxy and the velocities of these great star systems.

Slipher's Pioneering Observations

Curiously, the discovery of the expansion of the universe began with the search for Martians and other planetary systems. In 1894, the controversial and wealthy astronomer Percival Lowell established an observatory in Flagstaff, Arizona, to study the planets and search for life in the universe. Lowell thought that the spiral nebulae might be planetary systems in the process of formation. He therefore asked one of the observatory's young astronomers, Vesto M. Slipher, to photograph the spectra of some of the spiral nebulae to see if their spectral lines might show chemical compositions like those expected for newly forming planets.

The Lowell Observatory's major instrument was a 24-inch refracting telescope, which was not at all well suited to observations of faint spiral nebulae. With the technology available in those days, photographic plates had to be exposed for 20 to 40 hours to produce a good spectrum to reveal a galaxy's motion. This often meant continuing to expose the same photograph over several nights. Beginning in 1912, working for over 20 years, Slipher managed to photograph the spectra of more than 40 of the spiral nebulae which would all turn out to be galaxies.

To his surprise, the spectral lines of most galaxies showed an astounding redshift. A redshift, a type of Doppler shift, is when the lines in the spectra are displaced toward longer wavelengths or the red end of the visible spectrum. A redshift is seen when the source of light is moving away from us. Slipher's observations showed that most spirals are moving away at high speeds. The highest velocity he measured was 1800 kilometers per second. Only a few spirals, such as our close neighbors, the Andromeda and Triangulum Galaxies and M81, turned out to be approaching us. All the other galaxies were moving away. Slipher first announced this discovery in 1914, no one at the time quite knew what to make of this discovery.

Hubble's Law

In 1927, the astronomer Georges Lemaître published a paper in which he suggested that we live in an expanding universe. The title of the paper, translated from French, is "A Homogenous Universe of Constant Mass and Growing Radius Accounting for the Radial Velocity of Extragalactic Nebulae." Lemaître had discovered that Einstein's equations of relativity were consistent with an expanding universe, as had the Russian scientist Alexander Friedmann independently in 1922. Lemaître then went on to use Slipher's data to support the hypothesis that the universe actually is expanding and to estimate the rate of expansion.

In the meantime, Edwin Hubble was making observations of galaxies with the 2.5-meter telescope on Mt. Wilson, which was then the world's largest. Hubble carried out the key observations in collaboration with Milton Humason. They photographed the spectra of faint galaxies with the 2.5-meter telescope. Hubble had found ways to improve the accuracy of the estimates of distances to spiral galaxies, and he was able to measure much fainter and more distant galaxies than Slipher could observe with his much-smaller telescope. When Hubble laid his own distance estimates next to measurements of the recession velocities, the speed with which the galaxies were moving away, he found something stunning: there was a relationship between distance and velocity for galaxies. The more distant the galaxy, the faster it was receding from us. In 1931, Hubble and Humason jointly published the paper where they compared distances and velocities of remote galaxies moving away from us at speeds as high as 20,000 kilometers per second and were able to show that the recession velocities of galaxies are directly proportional to their distances from us, just as Lemaître had suggested.

Figure \(\PageIndex{1}\) includes the two charts of recession velocities of galaxies with distance. Chart (a) is from earlier work published in 1929 and includes galaxies up to 6 light years away traveling at speeds between 500 and 1000 km/s. The data roughly agree with a linear relationship between distance and recession speed with a lot of variability in galaxies at similar distances. Chart (b) includes the data from Chart (a) but adds data of galaxies out to 100 million light years away. The additional data confirms the linear relationship between distance and recession speed. We now know that this relationship holds for every galaxy except a few of the nearest ones. Nearly all of the galaxies that are approaching us turn out to be part of the Milky Way's own group of galaxies, which have their own individual motions.

Figure \(\PageIndex{1}\) : Hubble's Law. Comparing Hubble's 1929 data to Hubble and Humason's 1931 data shows how quickly astronomers extended the known range of galaxy distances and velocities, strengthening the case for a linear velocity-distance relation. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Alternative description of Figure \(\PageIndex{1}\).

Written as a formula, the relationship between velocity and distance is

\[v = H \times d \nonumber\]

where v is the velocity, d is the distance, and H is a number called the Hubble constant. This equation is now known as Hubble's law. In 2020, the International Astronomical Union suggested that it would be more fair to call it the Hubble-Lemaître law. In telling the history in this textbook, we have acknowledged the role Lemaître played, and we urge our readers to keep his contributions in mind as they read on.

Astronomers express the value of Hubble's constant in units that relate to how they measure speed and distance for galaxies. In this book, we will use kilometers per second per million light-years as that unit. For many years, estimates of the value of the Hubble constant have been in the range of 15 to 30 kilometers per second per million light-years. The most recent work appears to be converging on a value near 22 kilometers per second per million light-years. If H is 22 kilometers per second per million light-years, a galaxy moves away from us at a speed of 22 kilometers per second for every million light-years of its distance. As an example, a galaxy 100 million light-years away is moving away from us at a speed of 2200 kilometers per second. This behavior confirms Lemaître's theory that we live in an expanding universe.

Measuring Distance

The regularity expressed in Hubble's law has a built-in bonus, it gives us a new way to determine the distances to remote galaxies. First, we must reliably establish Hubble's constant by measuring both the distance and the velocity of many galaxies in many directions to be sure Hubble's law is truly a universal property of galaxies. But once we have calculated the value of this constant and are satisfied that it applies everywhere, much more of the universe opens up for distance determination. Basically, if we can obtain a spectrum of a galaxy, we can immediately tell how far away it is. The procedure works like this. We use the spectrum to measure the speed with which the galaxy is moving away from us. If we then put this speed and the Hubble constant into Hubble's law equation, we can solve for the distance, demonstrated in Examples and Exercises.

Variation of Hubble's Constant

The use of redshift is a very important technique for determining distances because, as we have seen, most of our methods for determining galaxy distances are limited to approximately the nearest few hundred million light-years. In addition, these measurements have large uncertainties at these distances. The use of Hubble's law as a distance indicator requires only a spectrum of a galaxy and a measurement of the Doppler shift. With large telescopes and modern spectrometers, spectra can be taken of extremely faint galaxies.

But, as is often the case in science, things are not so simple. This technique works if, and only if, the Hubble constant has been truly constant throughout the entire life of the universe. When we observe galaxies billions of light-years away, we are seeing them as they were billions of years ago. What if the Hubble constant was different billions of years ago? Before 1998, astronomers thought that, although the universe is expanding, the expansion should be slowing down, or decelerating, because the overall gravitational pull of all matter in the universe would have a dominant, measurable effect. If the expansion is decelerating, then the Hubble constant should be decreasing over time.

The discovery that type Ia supernovae are standard bulbs gave astronomers the tool they needed to observe extremely distant galaxies and measure the rate of expansion billions of years ago. It turns out that the expansion of the universe is accelerating over time! While a decelerating universe could easily be explained by gravity, there was no force or property in the universe known to astronomers that could account for the acceleration. Astronomers proposed that the source of energy for this expansion was dark energy.

In any case, if the Hubble constant is not really a constant when we look over large spans of space and time, then the calculation of galaxy distances using the Hubble constant won't be accurate. The accurate calculation of distances requires a model for how the Hubble constant has changed over time. The farther away a galaxy is, and the longer ago we are seeing it, the more important it is to include the effects of the change in the Hubble constant. For galaxies within a few billion light-years, however, the assumption that the Hubble constant is indeed constant gives good estimates of distance.

Models for an Expanding Universe

A uniformly expanding universe is one that is expanding at the same rate everywhere. In such a universe, we and all other observers, no matter where they are located, must observe a proportionality between the velocities and distances of equivalently remote galaxies. Here, we are ignoring the fact that the Hubble constant is not constant over all time, but if at any given time in the evolution of the universe the Hubble constant has the same value everywhere, this argument still works.

To see why, first imagine a ruler made of stretchable rubber, with the usual lines marked off at each centimeter. Now suppose someone with strong arms grabs each end of the ruler and slowly stretches it so that, say, it doubles in length in 1 minute. In Figure \(\PageIndex{2}\ the ruler has ants sitting at various positions. Consider an ant sitting on the mark at 2 centimeters, which we will name Ant, a point that is not at either end nor in the middle of the ruler. Ant measures how fast other ants, sitting at the 4-, 7-, and 12-centimeter marks move away from Ant as the ruler stretches.

The ant at 4 centimeters, originally 2 centimeters away from Ant, has doubled its distance in 1 minute. It therefore moved away at a speed of 2 centimeters per minute. The ant at the 7-centimeters mark, which was originally 5 centimeters away from Ant, is now 10 centimeters away. It had to move at 5 centimeters per minute. The one that started at the 12-centimeters mark, which was 10 centimeters away from Ant, is now 20 centimeters away, meaning it must have raced away at a speed of 10 centimeters per minute. Just like the galaxies moving away from us in space, the recession speed of the other ants away from Ant increases with distance. Notice in our example that all the ruler was doing was stretching uniformly. Also, notice that none of the ants were actually moving of their own accord, it was the stretching of the ruler that moved them apart.

Figure \(\PageIndex{2}\) : Stretching a Ruler. As the ruler stretches uniformly, ants farther apart move away from each other faster than ants close together, an analogy for how the expansion of space causes more distant galaxies to recede at greater speeds. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Alternative description of Figure \(\PageIndex{2}\).

For a three-dimensional analogy, let's look at the loaf of raisin bread in Figure \(\PageIndex{3}\). The yeast in the bread dough causes the dough to expand in all directions. It doubles in size during the next hour, causing all the raisins to move farther apart. On the figure, we again pick a representative raisin that is not at the edge or the center of the loaf and include the distances from it to several others in the figure before and after the loaf expanded.

Figure \(\PageIndex{3}\) : Expanding Raisin Bread. As the loaf rises uniformly, every raisin's distance from a reference raisin doubles, showing why more distant raisins, like more distant galaxies, appear to recede faster during uniform expansion. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Alternative description of Figure \(\PageIndex{3}\).

 

Our two analogies are useful for clarifying our thinking, but you must not take them literally. On both the ruler and the raisin bread, there are points that are at the end or edge. You can use these to pinpoint the middle of the ruler and the loaf. While our models of the universe have some resemblance to the properties of the ruler and the loaf, the universe has no boundaries, no edges, and no center.

What is useful to notice about both the ants and the raisins is that they themselves did not cause their motion. It was the stretching of the medium, the ruler or the bread, that moved the ants or the raisins farther apart. Galaxies are also passive participants in the expansion of space. As space stretches, the galaxies are carried farther and farther apart much as the ants and the raisins were.

The expansion of the universe, by the way, does not imply that the individual galaxies and clusters of galaxies themselves are expanding. Neither raisins nor the ants in our analogy grow in size as the loaf expands. Similarly, gravity holds galaxies and clusters of galaxies together, and they get farther away from each other, without themselves changing in size, as the universe expands.

If the universe is expanding, what is it expanding into? There is nothing whatsoever that we have measured, or can measure, that will show us anything about this larger space. Everything that we measure is within the Universe, and we see no edge or boundary or center of expansion. Thus the Universe is not expanding into anything that we can see, and therefore scientists can't study it.

Examples and Exercises

Example: Hubble's Law

Hubble's law (v = H × d) allows us to calculate the distance to any galaxy. Here is how we use it in practice.

We have measured Hubble's constant to be 22 km/s per million light-years. This means that if a galaxy is 1 million light-years farther away, it will move away 22 km/s faster. So, if we find a galaxy that is moving away at 18,000 km/s, what does Hubble's law tell us about the distance to the galaxy?

Solution

\[d = \frac{v}{H} = \frac{18{,}000 \text{ km/s}}{22 \text{ km/s per million light-years}} = \frac{18{,}000}{22} \times 1 \text{ million light-years} = 818 \text{ million light-years} \nonumber\]

Note how we handled the units here: the km/s in the numerator and denominator cancel, and the factor of million light-years in the denominator of the constant must be divided correctly before we get our distance of 818 million light-years.

Exercise: Hubble's Law

Using 22 km/s/million light-years for Hubble's constant, what recessional velocity do we expect to find if we observe a galaxy at 500 million light-years?

Answer

\[v = d \times H = 500 \text{ million light-years} \times \frac{22 \text{ km/s}}{1 \text{ million light-years}} = 11{,}000 \text{ km/s} \nonumber\]