Welcome back. Now what I'd like to do is take some of the ideas we've developed about quantum mechanics and pressure that we talked about with metals, some of the ideas that we talked about for stellar structured evolution, and apply them to the lowest mass stars and to planets like Jupiter. Jupiter and low mass stars and the things in between form a sequence that often call "brown dwarfs". So here's a sequence going from the sun to an M8 star, star with a temperature about 2200 degrees, down to Jupiter. So we're looking here over a very wide range of mass from the planet the mass of Jupiter to a planet seventy five times the mass of Jupiter. And we're looking at a very wide range in temperature. Jupiter has a surface temperature of 125 degrees. Well, these brown dwarfs have temperatures of around twelve hundred, and seventeen hundred, and twenty two hundred degrees. So we're looking at a factor of 20, or so in temperature, a factor of more than 70 in mass, and yet, all these up objects all these sort of brown dwarf class, and Jupiter class objects have about the same size. These L and T dwarfs lie beyond the edge of the sequence we've talked about before. Up to now we've talked about O, B, A, F, G, K, M stars ending in these red dwarfs. That's the sequence of stars that are hydrogen burning named sequence stars. If your mass gets small enough, below about 80 solar masses or so. These stars are no longer able to burn hydrogen in their core. These objects are not dense enough, they're not really even stars. It's why we call them "brown dwarfs". They're not supported by hydrogen burning in their center. They're a different class of objects. They're actually in their centers a lot more like the metals we talked about earlier. They're supported not by high temperatures, but by degeneracy pressure. So in brown dwarfs and in Jupiter when we balance gravity against pressure- remember, in stars we balance gravity against pressure by having material in the center that was hot and dense. Because in stars the pressure was basically described by the ideal gas Law, pressure is n k T. So you can be hot and high pressure in a star. And a brown dwarf, an object like Jupiter, the center isn't very hot. It's supported by degeneracy pressure primarily. It's mostly just dense. So we have dense material on the center, that's fairly cold, and diffuse material on the outside. And the pressure gradient between the center and the outside is provided largely by degeneracy pressure. And recall, for degeneracy pressure, pressure goes as density to the five thirds. Well, in this case we can now figure out the relationship between radius and mass. In a brown dwarf or actually also the white dwarf. The central pressure in a star is going to go with the strength of gravity times the density. So GM over R times density. So the pressure is going to go with GM squared over R to the fourth, where I plug in the density goes as mass divided by radius cubed. The number of electrons is going to depend on the mass times the average weight of the nuclei divided by radius cubed. So I can plug all this into compute the Fermi pressure and balance that against the central pressure. This says "The Fermi pressure goes- scales like this, and that implies when I go through the algebra here. And those of you are interested in working out some of the details can check this. Those who aren't- take my word for it. The radius of a star supported by this degeneracy pressure, by being dense in the center and supported by the fact that it can't squeeze in the electrons anymore. Heisenberg tells you that you can't squeeze stuff so much before they start moving faster and faster and has energy associate with the moving of electrons. This, when is supported by degeneracy pressure, your radius has gone a scale as mass to the minus one third. That's a very weak scaling. And that's why when we look at the relationship between radius and mass, we have this relationship that for planets like Mercury, and Earth, and Saturn as the planet gets more massive, the radius increases. And once we get to Jupiter, it rolls over and the mass- the radius starts to decrease with mass until we get to stars. So in this radius-mass relationship, this region here is described by degeneracy pressure while these two regions here, the ideal gas law is a better approximation. So we can have an understanding of the relationship between radius and mass. Now, one of the reasons I want to describe this is this was the understanding that I had about the properties of stars and most of us had when we were- before we had any data on large numbers of objects like this. And we thought that when the data came in and we measured the radius and mass of these brown dwarf and planets, they would all lie right on this relationship. That's why we were surprised when more data came in about certain objects and we found that sometimes they were a lot bigger than we thought they would be. And the first example of this, and this is really one of the first objects that we were able to study in some detail, is a planet with the musical name HD 209458b which is the planet sometimes called "The Cyrus." So we'll use that name to describe it today. This was- this planet is around a star that's an eighth magnitude G star. So was G star is a star like our sun, that's about 50 parsecs are about 150 light years away. Now, this planet was first detected by a radial velocity technique. So we were able to measure the mass of the planet. It's very close to the star and it was this planet that was first seen as the first extraterrestrial transit. It was relatively speaking an easy transit to see because there was about a 2 percent dimming seen roughly about every three and a half days. And this dimming happened, as we talked about with transits earlier, every time the planet passed in front of the star. So this gave us enough information to infer the mass and the radius of the planet. Well, the interesting- Here is the measurement of the planet's properties. And one of the interesting things when we look at its basic numbers is the planet was less massive than Jupiter but its diameter was much bigger. So the planet actually turned out to be bigger than our initial theoretical expectations. It was an expanded hot planet. As people study the planet in more detail, we learn more and more about its properties. This is a planet that undergoes a secondary transit. So as we discussed when we talked about transits, this is a planet where we were actually able to match the global temperature distribution and see how the temperature varies across it. But most dramatically for what we want to talk about for the rest of this lecture, we were able to study the planet's atmosphere in detail. This planet passes in front of the star and we can measure the spectrum of the material around the planet by looking at the stars spectrum. As the planet passes in front of the star, the planet's atmosphere absorbs light from the star. As we talked about earlier, you can look at the spectrum and figure out what's in the atmosphere by seeing what's absorbed. And this actually shows the actual data taken from the Hubble space telescope of a spectral line of hydrogen. And the black curve shows the spectrum that was seen when the planet wasn't in front of the star. When the planet passed in front of the star, we have the red spectrum. The amplitude went down. That's because the atmosphere of the planet had hydrogen in it and absorbed radiation. Now, this was roughly what was expected, that we'd see things like hydrogen. But what was surprising was that astronomers looked more closely and studied the properties of the hydrogen line. They saw hydrogen both coming towards us and away from us relative to the star. And by looking at the amount of hydrogen, they found there's a lot of hydrogen. In fact, the picture that we have of what's going on in the system is it's a planet roughly Jupiter size whose whole atmosphere is being evaporated by its host star. This planet is so close to its host star, temperatures of around 2000 degrees, and this planet is being evaporated by the star and an enormous wind is being blown off the star. This is a wonderful system to study and it really represents one of our first opportunities to study atmospheres of planets in detail. And to use the atomic spectra to figure out what's there and what's going on. So this process- this transit spectroscopy, this ability to observe the absorption lines due to planets against the atmosphere- against the star, lets us fingerprint the properties of the atoms and molecules that make up the atmosphere of the planet. This gives us the opportunity to begin the really detailed study of the properties of planets. Not only can we infer the mass and the radius of the planet, we can start to see what's going on in the atmosphere. We can see what the atmosphere is made of. We can even see in some of the dramatic cases the atmosphere being blown away as it's evaporated by the host star. These observations by the Hubble telescope really open up a new way of getting detailed observations of planets around other stars. This is really just the beginning of what we're going to learn. The next big step in this will come with the launch of the James Webb Space Telescope scheduled to launch in 2018. The James Webb telescope will be much larger than the Hubble telescope and will operate in the infrared. Well, the wonderful things about infrared wavelengths is that there are many absorption features of atoms, and particularly molecules, accessible in the infrared. So by studying planets seen in transits in the infrared, James Webb Space Telescope will be able to potentially detect things in its atmosphere like carbon dioxide, methane, and perhaps, if we're truly fortunate, through transits spectroscopy will be able to discover the signs of life.
