These notes will help you to review material presented in class about binary star systems, accretion disks, and white dwarfs. Again, you should be able to read and understand Chapters 3-5 from what we've talked about in class. Something like half the stars in the sky are actually in binary star systems. If the stars are really far apart from each other (so if the gravity from one star does not appreciably affect the other star), the stars will simply go about their individual stellar evolutions independently. If the stars are close enough together, however, the evolution of one star can affect the evolution of the other star. You'll want to study the figures from Oct 9 and 21, especially, for the material we're talking about here. You'll also want to study the figures in the book. We talked about the concept of center of mass, and described this idea for the Solar System and for a binary star. Since stars are orbiting the center of mass, sometimes they're moving towards the observer and sometimes they're moving away. We can use this fact, and the phenomenon of the Doppler Shift, to use spectra to measure these motions. This is how we use "the laws of gravity" to measure masses. So be familiar with Doppler Shift (sometimes called "Redshift" in a cosmological context). Figure 3.1 in your text shows the "spheres of gravitational influence" of each star in a binary. These are caled the Roche Lobes, and the point of intersection is called one of the Langrangian points. The important point of this figure is that if the star is smaller than its Roche lobe, it doesn't contribute to the evolution of the other star. But if the star is bigger than the Roche lobe, material will funnel onto the other star. The figure in the Oct 9 figures section of the website shows the evolution of a pair of stars. Initially the star on the right is 20 solar masses and the star on the left is 8 solar masses. the star on the right evolves more quickly, becoming a giant, and getting bigger than its Roche Lobe. It dumps material onto the star on the left. Eventually, the star on the right ends up as a 5 Solar Mass star, and the star on the left has gained mass to become a 23 solar mass star. In this particular model, the 5.3 solar mass object is the core of the former star, and it's sortof like a white dwarf or neutron star. It ends up blowing up as a supernova, rather like the scenario Jane later describes for a core-collapse supernova. It leaves behind a neutron star. Eventually, we have this 23 solar mass star orbiting with a 2 solar mass neutron star. The 23 solar mass star evolves quickly and dumps material onto the neutron star, creating lots and lots of energy. Why/how does matter falling from one star onto the other create lots of energy? [Let's ignore the details of accretion disks for a bit] Well, you've got particles from one star FALLING A LONG WAY onto the other star. As they get closer and closer, they're pulled on harder and harder because gravity is an inverse-square force. To understand how much energy is involved, let's try two thought experiments. In the first, let's take a particle from the edge of the Sun and move it to a large distance. This is equivalent to sending a rocket a long distance. You know that you have to burn a lot of fuel to send a rocket a long distance (or more precisely, to get it to escape a source of gravity). Because gravity is an inverse-square force, "all of the pulling" is done when the rocket is closest to the gravitating object. The second thought experiment is the same as the first, except that we're taking a particle from the surface of a 1 solar mass neutron star (ignore the fact that such an object doesn't exist). Both the sun and the neutron star have the same mass, but sonce the neutron star is so much smaller, the force of gravity at its surface is much higher than at the surface of the Sun. So it takes a huge amount of fuel to get the rocket from a few miles from the center of the neutron star (only a few miles from its center) to a few hundred thousand miles away (the former edge of a star like the sun). So reversing the process, to have matter falling in, a huge amount of energy is gained into falling onto a compact object, versus falling onto the sun. Some numbers, which we won't ask you to calculate, will be useful here. The energy released when a gram (one spider) of hydrogen falls from far away onto the surface of a white dwarf is 2x10**17 ergs. The energy released in fusing one gram of hydrogen is 6x10**18 grams. So you're better off, if you want to make energy, fusing the hydrogen on the surface of the white dwarf, as in a nova. But what about in a neutron star? The total energy given off is 2x10**21ergs, or a factor of 30 greater than fusion can give. So having material fall onto a compact object can creste tremendous amounts of energy, thus making highly energetic photons. These sorts of binary stars can be found by looking with Xray or Ultraviolet telescopes. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Some details about mass transfer from one star to another. The size of the Roche lobe of each star depends on its mass and on the distance between the two stars. If a star overflows its Roche lobe, it loses mass and weighs less, so its Roche lobe gets smaller. Now it's even bigger than its Roche Lobe so it loses mass even faster. Another part of what goes on concerns angular momentum. the smaller star was orbiting faster, and it has a certain amount of angular momentum. Now it weighs more. All things being equal, that gives it more angular momentum. But there's a conservation law saying angular momentum is conserved (in Jane's immortal words, think about Brian Boitano figure skating). To conserve angular momentum in this scenario, the two stars move closer together. This is all described in section 5 of Chapter 3. So not only is mass dumped from one star to another, but the distances between the stars change. There is a setup in which one star is trying to dump material so fast that it can't be accomodated by the second star, or in which both stars are losing mass, in which matter goes into orbit about both stars, in a big cloud. This is the common-envelope phase. We've described this a couple of times in class, and it's as if a star is orbiting through jello instead of through empty space. the star loses orbital energy by crashing into these particles, and the stars spirla closer together. To create another class-note-anachronism, Jane described this process as a way in which two stars can actually spiral together forming a single star. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ We haven't really talked much about gravitational radiation (the end of ch 3). For our purposes right now, a changing gravitational field sends out gravity waves, just as a changing electrical field sends out electromagnetic radiation. The energy has to come from somewhere, and it comes from the orbit. This causes the orbit to spiral in as well. For normal stars, the total energy released in this way is miniscule. But in a pir of neutron stars, this energy release can be large. We still do not have to technical capability to detect gravitational waves directly (there is an experiment called LIGO which hopes to make this detection someday, thus giving us a way to find merging neutron stars). But we can predict how fast the orbit will lose energy, thus how fast the orbits get smaller. we'll be talking in class about "the binary pulsar" in which we can actually see the orbits decaying at exactly the predicted rate. So while we can't see gravitational waves yet, we know they exist since we can see their effects.