Hubbles Law and Hubbles Constant

It has been known since the early twentieth century that every spiral galaxy observed (sufficiently distant) exhibits a redshifted spectrum—they are all moving away from us. Recall from Chapter 17 the Doppler effect: Wavelengths grow longer (redshift) as an object recedes from the viewer. The conclusion is inescapable: All galaxies partake in a universal recession. This is the apparent general movement of all galaxies away from us. This observation does not mean that we are at the center of the expansion. Any observer located anywhere in the universe should see the same redshift.

In 1931, Edwin Hubble and Milton Humason first plotted the distance of a given galaxy against the velocity with which it receded. The resulting plot was dramatic. The rate at which a galaxy is observed to recede is directly proportional to its distance from us; that is, the farther away a galaxy is from us, the faster it travels away from us. This relationship is called Hubble's Law. This law relates the velocity of galactic recession to its distance | ^ from us. Simply stated, Hubble's Law says that the re cessional velocity is directly proportional to the distance.

Astronomer's Notebook

Hubble's Law turns on Hubble's constant (H0), the constant of proportionality between the velocity of recession and the distance from us. The value of H0 is expressed in kilometers per second per megaparsec (a mega-parsec [Mpc] is 1 million parsecs) and is found to be 60-65 km/s/ Mpc. Sort of. Actually, the precise value of H0 is the subject of dispute. Why should its value be so hotly debated? Because it can be used to determine nothing less momentous than the age of the universe. A different Hubble constant gives the universe a different age.

Picture a bunch of dots on the surface of a toy balloon. Our Galaxy is one of the dots, and all of the other galaxies in the universe are the other dots. As you inflate the balloon, the surface of the balloon stretches, and, from the point of view of every dot (galaxy), all the other dots (galaxies) are moving away. The farther away the dot, the more balloon there is to stretch, so the faster the dot will appear to recede.

One benefit of Hubble's Law is that it can be used to extend our cosmic distance scale to extraordinary distances. While the Tully-Fisher technique will get us out to about 200 million parsecs, and Type I supernovae to a bit less than 1 billion parsecs, Hubble's Law will go farther. In fact, Hubble's Law gives us the distance to any galaxy for which we can measure a spectrum (in order to get the Doppler shift). With the velocity from that spectrum, and the correct value of the Hubble constant, we arrive quite simply at the distance.

But there is a twist. We have assumed that the universal expansion happens at a constant rate. Is this a good assumption?

Recent observations suggest that the universe has not always been expanding at the same rate. Two magnificent forces are in opposition. There is the expansion of the universe (as we will see, set into play by the Big Bang), and there is the force of gravity, pulling every two particles with mass together, diminished by distance squared. If there were nothing pushing things apart, the universe would, due to gravity, collapse to a point. This would be a problem. And Einstein recognized it as such. When he was working on general relativity, he needed to add a term—the cosmologi-cal constant—to his equations to balance the force of gravity. This term was needed to keep the universe static, as it was then thought to be.

But then Edwin Hubble came along and showed that the universe was hardly static, but that, in fact, everything was rushing away from everything else, and while gravity might eventually win out, the universe wasn't going to collapse to a point any time soon. Einstein later called the introduction of the constant into his equations a "blunder."

As it turns out, however, Einstein's "blunder" may have been a useful one. Recent observations made by scientists of very distant ("high-redshift," in astronomer parlance) Type Ia supernovae show something very surprising. These "standard candles" can be seen out to 7 billion light years, and the distances to the galaxies that they are in show that the universe appears to have been expanding more slowly in the past than now. So not only is everything rushing away from everything else, but it's rushing away more quickly these days. In other words, the expansion of the universe is accelerating.

What is causing it to accelerate? Well, it might be the "vacuum energy" that Einstein thought he needed to support the universe from collapsing on itself. Interestingly, this force increases with distance (as opposed to gravity, which weakens with distance).

But we come back to the debated value of the Hubble constant. Our distances determined in this way are only as good as our value for the Hubble constant.

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