Lecture 13. An Expanding Universe

We've seen that knowing distance is the KEY to determining the properties of astronomical sources. The way it works is one step builds on the previous one, so its often called a distance ladder. Firstly we need to know distance to our sun, which is done using radar, bouncing radio signals off the planets and timing how long the echo takes to come back - its a bit like sonar systems used by bats or submarines. Then we know the distance of our sun, so we can find its absolute luminosity from its apparent brightness. we can also find the distances to nearby stars by trigonometric parallax, and so get absolute luminosities to other types of stars. THESE ARE THE ONLY DIRECT DISTANCE MEASURES! everything else builds on them.

We can look at star clusters (all stars at same distance and chemical composition and age). Their HR diagram gives a main sequence, and we know that luminosity of some types of main sequence stars, so we can get the distance to the cluster. do this for lots of clusters and we get the absolute luminosity of all types of stars. so then for any star we can get its spectra so know its spectral type and hence get their distance by comparing their absorlute luminosity with their apparent brightness via the inverse square law. This is spectroscopic parallax.

To go to distant objects we need very bright stars which are easy to spot - OB stars or cepheid variables! then to go even further we need even brighter objects - supernovae type 1a (NOT massive star supernovae - don't know mass of initial star, but if have a white dwarf in a binary system then it can accrete material from the companion star. get enough material and push the white dwarf over the mass limit of 1.4x mass of Sun!). Galaxies themselves are very bright, but not all galaxies are the same - big galaxies have more stars so are brighter. But we can use kinematics of stars in spiral galaxies (tulley fisher) or ellipticals (faber-jackson) to calibrate this. See the exhaustive discussion of all these techniques (and more!) for finding distances.

But even easier, we saw in lecture 11 that the galaxies had spectra which are generally redshifted, and that the redshift was proportional to their distance (the Hubble law). This is a nice and very easy way to find distance, but what does it mean ? Is our galaxy at the center of this expansion ? At first glance it seems so since we see most of the galaxies rushing away from us ? But its not true. Suppose we can see a galaxy receeding from us - from that galaxy an observer would see US receeding from THEM with exactly the same velocity. If we were sitting on any galaxy we would see all the other galaxies rushing away from us. All galaxies would see the same Hubble law.

The redshifts are often talked of in terms of a doppler shift, to give a recession velocity. But if everything is receeding from everything else then the universe must be expanding. The general analogy used is that of blowing up a balloon. but this can be a little misleading as it looks as if the balloon expands INTO space. Einstein's general theory of relativity tells us that space (or rather space-time) is the same thing as a gravitational field. So matter can't exist apart from spacetime, the two are linked. So what we are seeing is not a universe expanding through space, but space itself expanding.

So if its expanding, then at some time in the past the universe must have been much smaller than it is now. As things expand they cool, so the early Universe must also have been much hotter, as well as much denser. Taking this to its logical conclusion then the Universe must once have been incredibly hot and dense, expanding explosively outwards. This is the hot big bang model. We can look at the rate of expansion now (the Hubble law), and use this to get an estimate for the time when the universe was created - the age of the universe! (for those who want to see the maths). For those who don't it comes out to about 10-20 billion years

But whats the evidence! In general we trust a theory if several (the more the better) independant lines of evidence come up with the same story. Where is the corroborating evidence for this ? The wilder the story, the more evidence we'll need to justify it, and this is pretty wild.

If the Universe was originally incredibly hot and dense, then it would radiate like a blackbody, with photons and electrons interacting. Electrons couldn't recombine with nuclei to form atoms because another photon would come along and knock it out of the atom. But as the universe cools, these blackbody photons would cool along with it. Eventually the Universe would get to a temperature where photons no longer had enough energy to immediately knock any electron out of an atom (3000 K at about 300,000 years after the Big Bang) - this is the era of recombination. The blackbody photons then don't interact with the electrons any more. So the blackbody cools with the expansion of the universe. If you take the expansion from the Hubble law, then this predicts that this cooling blackbody radiation left over from the hot early universe should be at temperatures of only a few Kelvin i.e. that this peaks in the microwave region of the spectrum. This cosmic microwave background radiation was found experimentally at much the same time as it was predicted theoretically!