Okay gang, let's roll! And welcome back to analyzing the universe. Today, I want to talk to you about some of the incredible things that we can tell from looking at the stars. It is truly astonishing that the feeble light from objects apparently so very dim, can illuminate so brightly our knowledge of the heavens in so many ways. The story begins over 100 years ago when the world of physics was truly shaken to its roots by the discoveries of the quantum world. Several key surprises had fundamental implications for the study of astronomy. The first surprise was the requirement of specific orbits for electrons as they traveled about the nucleus. Unlike planets, for example, that could orbit their stars at any distance, quantum mechanics forbade all but a very specific set of distances for the electrons to reside in. Indeed, this understanding became a triumph, as it explained with incredible accuracy, the heretofore mysterious occurrence of the dark lines in stellar spectra. So the idea is that in the case of planets for instance, you have a sun, and you have planets going around the sun. But those planets could inhabit any region external to the Sun. There was nothing to prevent Mercury, for instance, fundamentally from being in a slightly different position relative to the Sun than it is today. That is not the case with atoms. In atoms, there are very specific, discreet levels that allow the electrons to reside in. And those discrete levels give rise to discrete energies, corresponding to the change in those levels within the atom. What you see on the screen right now, is the light output of over a dozen different stars. In the visible part of the spectrum, from red, the low energy photons, to blue, the high energy photons. You can see many, many dark lines which correspond to unique energies in the spectrum. These energies correspond to an electron in a particular atomic element, or compound, jumping from one discrete level to another. Thus, these lines give us valuable hints as to the chemical composition of the stars. The way this mechanism works is as follows. Radiation comes from the center of the stars in all wavelengths. And they pass by an electron. The electron ignores all those photons. Except the ones corresponding to the energy necessary to jump to a higher orbit. So the situation might be that the blue photon continues on its merry way, the red photon continues on its merry way. But the yellow photon can be absorbed by the electron, which then jumps up to a higher energy orbit. So this would correspond on our little energy diagram here, to an electron say, in the ground state, going into say, the second excited state, and that energy difference has to correspond exactly to the photon that has been absorbed by the electron. What happens next is that the electron usually, almost immediately, falls back to the lower energy state and re-emits the photon. So the electron can go back to this energy level. And re-emit the photon, but here's the kicker. The direction of this re-emitted photon is random, and usually different from the incident direction. Electron comes down, re-emits the photon. In a different direction. And this is shown in the following animation. Furthermore, the electron may retrace its steps differently, and re-emit different wavelength light altogether. In other words, the electron can instead of jumping immediately down to the ground state, can come down here, re-emitting a different Energy photon, and then come back down to the ground state re-emitting yet another energy photon. And that would be the same as going like this in our energy level diagram. In either event, the net result is that light of a specific wavelength is subtracted from the overall output, hence the dark lines in our spectrum. Now let's look at those spectra again carefully. Notice that not only are the lines different, but the overall output or color is different as well. The sample stars near the top have distinctly more blue light than those at the bottom. Where it is clear that the red light predominates and this, in fact, is indignative of the different colored stars that we see in the sky. Which brings us to the second part of our story, which was the discovery by Max Planck of the radiation law that governs how stars emit light, the so-called Blackbody Radiation Law. What we see here is that as the temperature goes up, not only does the total energy output per surface area element go up, but also the maximum of the radiation shifts towards the blue. The hotter stars around 10,000 kelvin are much bluer than the cooler stars around 3,000 kelvin. Incidentally the kelvin is just another temperature unit based on the fact that zero kelvin corresponds to the absolute minimum possible level of atomic activity. But where are the dark lines? It turns out that these are departures from black body radiation. A true black body would have only continuous radiation. But when you put it all together, black body plus lines, you get something like this. Which is the solar energy spectrum. It is very close to a black body, with lots of dark lines superimposed on it. And so now, we get to our final chapter of our little story, which is what our understanding of what a star's radius is. In the late 1800s, Joseph Stefan deduced from experimental data, what the total radiation output must be for objects close to a black body. It turns out to be the following expression. Sigma t to the 4th. Sigma is a constant, based on thermodynamic considerations. And t is the temperature raised to the fourth power. Now remember that our black body spectrum was the energy output for each surface area element of the object. Well in order to find out the total then, we must take our expression here, and multiply by the whole surface of the star. Where R is the radius of our star. That is the luminosity, or total energy output of any black body radiator that is spherical in shape. And the units on this luminosity, depend on what units we measure for sigma, and what units we measure for the radius. T is always going to be in Kelvin. So for instance, if this was in CGS units, we would have ergs per second here, and R would be measured in centimeters. Now you can see the effects of the high power that luminosity has on temperature. A mere factor of 10 in temperature corresponds to a factor of 10,000 in luminosity. But if all we can see is the apparent brightness of the star in the sky, how can we find out the luminosity, or total energy output that the star has. Only if we can find the luminosity can we deduce what the radius of the star is. Clearly we need to determine the distances to the stars. Only with distances in hand can we deduce the actual parameters related to our observations of these faint pinpoints of light in the sky. And that is the subject of our next lecture.
