By Joshua Winn, Princeton University
Why are the galaxies rushing away from us? Does that mean we’re sitting at the center of the universe, the location of the Big Bang? That seems wrong and it is. Does the Hubble Diagram identify a privileged galaxy at the center of the universe? Is there a unique ‘center’ of the expansion?
We can measure how fast a galaxy is moving toward, or away, from us from the Doppler shift. The fractional shift in wavelength is equal to the radial velocity, divided by the speed of light. If the wavelengths are being stretched to larger values, toward the red end of the spectrum, Delta_lambda is positive and the galaxy is moving away from us. Likewise, if the spectrum is blueshifted, the galaxy is coming toward us.
When we do this for the few dozen brightest galaxies in the sky, we find the radial velocities are all over the place. Andromeda and Triangulum are coming toward us, and others are zooming away from us. But when we do this for fainter galaxies, a strange thing happens. They’re almost all redshifted. They’re all speeding away from the Milky Way. This was first discovered by Vesto Slipher in the early 20th century.
Computing distances is traditionally the hardest part of astronomy. One way to do it relies on Cepheid variable stars. Cepheids pulsate, glowing brighter, then fainter, with a regular period. And the period is found to be closely linked to the luminosity. So, if we can measure the period, we can calculate the luminosity. They act as standard candles. So, we can use the flux-luminosity relation, and solve for the distance d.
But individual Cepheids can’t be detected beyond about 50 megaparsecs. To reach out further, we use standard explosions: Type Ia supernovas, which always seem to explode with about the same energy, or, at least, nearly the same. They’re predictable enough so that if we measure the color and duration of the afterglow, we can calculate its luminosity to within a few percent. And their great advantage is that they’re bright enough to see all the way across the universe, billions of light-years away.
This article comes directly from content in the video series Introduction to Astrophysics. Watch it now, on Wondrium.
The Hubble Diagram
When we measure radial velocities and distances to lots of galaxies, and plot one against the other, we see an obvious pattern, a straight line: V is proportional to D. A diagram of this type, published by Edwin Hubble in 1929, was the first clear evidence for the Big Bang. That’s because V proportional to D is what you expect from an explosion.
However, the story isn’t as simple as galaxies coasting away from a single point. Their velocities need not be constant. After all, gravity acts to slow the galaxies down and bring them back together. Additionally, the Hubble Diagram doesn’t imply that there’s any sort of privileged galaxy at the center of the universe.
No Unique ‘Center’
A helpful analogy is with raisin bread. Imagine being inside a lump of dough, sitting on a raisin, with other raisins all around. The oven comes on, and the dough expands; the bread rises. We’ll see all the raisins receding from each other, with velocity proportional to distance. And here’s the point: if one hops over to a different raisin, they’ll still see all the other raisins receding from them, with velocity proportional to distance. There’s no unique ‘center’ of the expansion.
Our universe is filled with a large number, a potentially infinite number, of raisins, or, galaxies, each with position vector r. One day, we measure the positions, r-i, and velocities, v-i, of all the other galaxies. We use a coordinate system in which our galaxy, the Milky Way, is at the origin. We discover the Hubble expansion: r-i equals v-i times t.
Flying to a Different Galaxy
Then, let’s say, one builds an intergalactic spaceship and flies to a different galaxy, say, galaxy number one. They r-measure the distances and velocities of all the galaxies, relative to their new home galaxy, in a coordinate system where galaxy one is at rest at the origin. Let’s call those new data r-prime and v-prime. What will be the relationship between them?
We can deduce it using vector algebra: r-i-prime is the vector going from galaxy number 1 to the i-th galaxy. That’s equal to r-i minus r1. As for the velocity, whenever the stationary person measures a velocity v-i, the one who moved will measure v-i minus v1, since they’re moving along with galaxy 1. So, v-i-prime equals v-i minus v1.
Now, let’s take the r-prime equation, and replace the r’s with v-t’s, based on the Hubble relation observed in the Milky Way. We factor out the t, and then recognize the vector in parentheses as v-i-prime. We thereby deduce that those having moved will find r-i-prime equals v-i-prime times t. Their measurements, too, will show that velocity is proportional to distance, with the same proportionality constant. Everybody, everywhere, draws the same conclusion.
Turning Back the Clock
But, what happens if we turn back the clock? The galaxies come closer and closer together, so doesn’t that mean they’ll all land on a single point? Not necessarily. For one thing, the theory of general relativity describes the Big Bang as the expansion of all of space from a condition of infinite density, not an explosion that took place at a single location.
In the world of baking, we need to imagine an infinite loaf of raisin bread. If we reverse the clock, and watch the bread ‘un-rise’, the raisins get closer together, but it’s still infinite in all directions. We just bring in more and more raisins into our field of view, and the bread gets denser and denser, until at time zero it’s infinitely dense everywhere.
Common Questions about the Expanding Universe
We can measure how fast a galaxy is moving toward, or away, from us from the Doppler shift. The fractional shift in wavelength is equal to the radial velocity, divided by the speed of light.
Individual Cepheids can’t be detected beyond about 50 megaparsecs. To reach out further, we use standard explosions: Type Ia supernovas, which always seem to explode with about the same energy.
The Hubble Diagram doesn’t imply that there’s any sort of privileged galaxy at the center of the universe.