Hubble’s Law: The Starting Point for All Things Cosmological

by Tony on February 5th, 2007

This week as part of the Just Science Week challenge, I’ll be posting on cosmology, the study of the origins and nature of the universe taken as a whole.

In an effort to be methodical and somewhat coherent when presenting concepts and research on cosmology this week, I’ll use this post to build the foundation you’re going to need to understand what follows. Any discussion of the origin and behavior of our universe needs to begin with Hubble’s Law.

The fundamentals of this law are pretty easy to describe in words, but its not so easy to fully appreciate what it means.

In 1929, Edwin Hubble put forth the idea that the speed with which galaxies were traveling away from us was related to how far away they were. Hubble noticed that galaxies which were very far away were traveling very fast, much faster than the closer galaxies.

That’s it. That’s Hubble’s Law.

Another interesting observation is that most of the galaxies in the universe are all speeding away from us. Nothing seems to be heading our way. The exception are the galaxies grouped in clusters. There are galaxies within clusters which are heading toward each other and these galaxies collide all the time (in fact our sister galaxy, The Andromeda Galaxy is heading right at us at 130 km/sec or 300,000 miles per hour and will hit us in about 5 billion years), but as a whole, galaxies are speeding away from each other. All of them.

Distances in the Universe

How did Hubble know how far away these galaxies were? There are a variety of ways of telling how far away things are. One of the best techniques (and the one Hubble used) involve comparing the brightness of a star or galaxy with something else, like a cepheid variable star of a known distance and brightness, from which the distance is inferred.

Hubble used these techniques to compile a list of galaxies with their inferred distances into a table and then set about measuring their velocities. By pointing a spectrograph at a galaxy, Hubble recorded the spectra of dozens of galaxies.

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When you look at a galaxy with a spectrograph, you’re spreading out that light into a spectrum of colors. Embedded within that spectrum are a series of dark lines that exist in very specific, well understood spots. These dark lines, known as absorption lines, are a fingerprint of specific elements in the periodic table, like Calcium or Oxygen. Where these dark lines should appear within a spectrum are measured very carefully in a lab and are known to great precision.

In the above image, the spectrum on the left would be a reference spectra, while the right is one taken from a galaxy. Each dark line represents the absorption of photons at a well understood wavelength, with each one corresponding to a chemical element, like Oxygen.

When Hubble looked at where these dark lines appeared in the spectra of his list of galaxies, he noticed that they were shifted from where they should be, they were shifted towards the red. This is known as redshift and is caused by the fact that the galaxy being measured is moving, in this case, away from us. If the galaxy were moving toward us, those dark lines would be shifted toward the blue.

The spectrum of the Andromeda galaxy is blueshifted, and the amount of that shift tells us the speed with which it’s heading toward us: 130 km/sec. The units of red and blue shift are given in km/sec.

It is a very cool thing that by measuring how much the dark lines have shifted compared to the laboratory spectra gives the velocity. Large shifts equal high velocities, small shifts, lower velocities. In my opinion, spectroscopy was one of humanity’s greatest achievements and is the cornerstone tool that has helped us understand virtually everything we know about the universe.

So, after Hubble assembled his list of galaxies and their distances, he then listed the velocities he obtained from their redshifts and made the following plot:

Illustration Credit: Ned Wright

By plotting the distance versus the redshifted velocity, and assuming that the relationship between these two parameters was linear, Hubble fit the data to get the straight line above. The slope of this line was in units of velocity per unit distance or km per sec per megaparsec. This parameter has become known as the Hubble constant, H0. The value of the constant using the above data was 464 km/sec/Mpc.

This parameter gives us the speed something is moving away from us and is a function of time and distance. It is a measure of the rate of expansion of the universe and because the universe is expanding and accelerating as it does so, this value will change over time. The term Hubble constant is probably not the best one, since this constant really isn’t.

As pointed out in Ned Wright’s Cosmology Tutorial, Hubble’s data weren’t the best. He used data that only went out to 1200 km/sec. Later observations put the value of the Hubble constant at 71 km/sec/Mpc.

Here’s a more recent plot using data from Type 1a supernovae:

Illustration Credit: Ned Wright

The above data are much more accurate, but cosmologists are constantly using new data from the latest spacecraft to tweak this value.

Here is a simple representation of Hubble’s Law in a formula:

v = dD/dt = H0*D

In words: the velocity (v) of a galaxy is defined as the time rate of change of the distance (dD/dt) which is equal to the Hubble constant (H0) times the distance (D).

The Age of the Universe

Hubble’s Law tells us the rate at which the universe is expanding, and we can use that information to run the clock backward and get the age of the universe. By taking the inverse of the Hubble constant, we can get the age of the universe (take the line above and invert it). The value of 1/H0 is approximately 13.7 billion years.

This value is confirmed with observations of the oldest globular clusters, measuring the ages of white dwarf stars and radioactive dating of the old stars.

The Universe is Accelerating

As mentioned above, the Hubble constant is a function of time, it will be different depending on WHEN you take measurements. As of right now, today, that value is 71 km/sec/Mpc, it was smaller in our past and will get larger in the future. The reason? The universe isn’t just flying apart, it’s speeding up as it does so.

Now you have the tools we need to move forward in later posts. I will be discussing topics like the size of the universe, which if you aren’t very careful will lead to conclusions like the universe is expanding faster than the speed of light or that there are galaxies out there that are older than the universe. I’ll write about all of these ideas from the reference frame of Hubble’s Law.

Hubble’s Law is deceptively simple. The idea behind it and the math aren’t that hard to get, but fully appreciating the implications are humbling and mind-numbing.

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