I. Binary Stars -- Roughly half of the points of light we see in the night sky are actually two stars that orbit each other, too close together for our eyes to be able to resolve them separately -- Sometimes the two stars are close enough that they can interact with each other, usually by exchanging some mass, which alters their evolution as stars. These are called "close pairs". -- Other binaries are widely separated, so can be considered to be two independent stars that just happen to be orbiting each other. These are "wide pairs". -- There are three types of binaries: visual, which means you can actually see the two stars in a telescope (no orbiting binaries have a wide enough separation to be seen with the naked eye); spectroscopic, which means you can see the presence of the orbit due to the Doppler shifting of the stellar spectral lines; and eclipsing, which means you know there is a binary there because one gets in the other's way periodically during its orbit. Surprisigly, it was this last method that was first used to suggest that binary stars were possible, but their existence was not immediately accepted.
II. Visual Binaries -- visual binaries include Mizar in the Big Dipper (though don't be confused by nearby Alcor-- you can see these two with the naked eye, so they are not orbiting each other), and Castor (alpha Geminorum). Castor had an important place in binary star discovery, because Herschel used it in 1801 to demonstrate the binary-star orbit and prove it was indeed a binary. -- the orbital period of visual binaries is very long (recall Kepler's law, and note that to be visual, the separation must be huge). For example, the two stars in Castor (called the primary and the secondary) orbit each other every 467 years. -- visual binaries are very important because they allow us to determine the mass of the system. Remember that the force of gravity depends on the masses of both stars, and by looking at the orbit, we can tell what the force of gravity has to be. It turns out that what can be derived is the sum of the two masses (not their product). Without this information, we would not have been able to determine the relationship between mass and luminosity for stars in the H-R diagram.
III. Spectroscopic and Eclipsing Binaries -- spectroscopic binaries are seen from their line spectrum, by following the Doppler shifts as the stars orbit each other. -- to see these, you need big velocities, not big separations. That means you need the stars to be close to each other, not far away. So these types of observations can detect exactly the stars that visual techniques cannot. -- Typical periods of spectroscopic binaries are measured in days, not years. The orbital speeds are tens of kilometers per second, similar to Earth's orbital speed around the Sun. -- eclipsing binaries can only be seen when we view the orbit edge-on, so that the stars will occasionally get in each other's way. So only a small fraction of binaries can be seen to eclipse. -- the first eclipsing binary observed was Algol (beta Persei). In 1783, John Goodricke found that Algol dimmed periodically to about a third of its normal brightness. -- the eclipse is very important for understanding the size of the stars, because big stars can block out a lot of light, and small stars only a fraction of the light. So eclipsing binaries also provide an important piece in the puzzle of understanding the attributes of stars.
IV. Formation of Binaries -- wide binaries: tidal capture or conucleation models have been suggested -- close binaries: fragmentation or fission (for very close binaries)
V. Close Binaries and Stellar Evolution -- Algol is an interesting system. There are actually more than just two stars, but we'll focus on the close binary (the third star is well separated from these two). Calculations show that the two stars are a hot dwarf and a cool giant. The hot dwarf looks just like a 3.7 solar-mass main sequence star, and the cool giant looks like a 0.8 solar-mass red giant. What's wrong with this picture? -- If both stars formed at the same time as a binary, and then evolved the way single stars do, by the time the low-mass star became a red giant, the hot high-mass star would no longer be on the main sequence: in fact, it would have gone supernova. -- How can you have a high-mass main sequence star that is the same age as the low-mass red giant? You need a different evolutionary path. The evolution is affected by mass exchange in the binary. Thus the higher mass star used to be the lower mass star, so is taking longer to evolve, but then when the originally lower mass star becomes a red giant, it loses most of its mass to the other star. In this way, the star that ends up with more mass is actually less evolved.
VI. Mass Exchange and the Roche Lobe -- How does a star lose mass to a binary companion? As we move farther from one star and closer to the other, the force of gravity shifts from being mostly toward the first star to being mostly toward the second. Thus gas that is far away from the center of one star can end up being pulled onto the other star. -- The region around each star inside which the star will be able to pull gas in is called the Roche Lobe. It looks like a figure 8. -- Originally, both stars will be well within their Roche Lobes, so will evolve normally as if they were alone. But when the higher-mass star evolves faster into its red giant phase, its radius increases so much that it fills up its Roche Lobe. As it continues to expand in size, the mass that leaves the Roche Lobe gets pulled over onto the companion star. This gives the exchange of mass that completely changes the evolution.
VII. General Consequences of Mass Exchange -- Binary stars revolve about their center of mass, and have a fixed angular momentum which is conserved as mass is exchanged. If mass moves from the lower mass star to the higher mass star, it moves from being farther from the center of mass to being closer. But to conserve angular momentum, this means that the rest of the lower mass star has to move farther away from the center of mass. So the distance between the stars must increase. If instead mass moves from the higher mass star to the lower, then it is moving farther from the center of mass. To conserve angular momentum, the lower mass star has to be pulled in closer to the center of mass, so the distance between stars would decrease. -- Thus mass transfer affects the binary separation, and the two stars are always at their closest when their masses are equal. Normally, what happens is the high-mass star evolves faster, so expands into a red giant. But before it gets to a red giant, it fills its Roche lobe and begins to transfer mass to the other star. Since this brings the two masses closer to each other, it also brings the two stars closer together, which assists the mass transfer and makes it occur very fast. Eventually the first star has transferred so much of its mass to the other star that the distance between the stars increases again, and the mass transfer stops. The less massive star now was once the more massive! -- The star that was stripped of mass is still on its way to becoming a white dwarf, neutron star, or black hole, depending on the mass of its core as usual. If it goes supernova, the binary may actually survive, and create exotic systems like pulsars or black holes orbiting a main-sequence star. -- A key point to remember in all this is that close binaries alter stellar evolution by changing the mass of the stars, but otherwise, once you know the mass, the individual stars appear much as they would if they were simple isolated stars. So the basic evolutionary scheme proceeds normally before and after mass transfer.
VIII. Type Ia Supernovae -- Of particular interest is when you have a close binary with stars with masses not too much more than the Sun, and one star evolves into a white dwarf. Then when the other puffs out into a red giant for the first or second time, it can pass some of it mass over to the white dwarf. But remember that if a white dwarf has its mass go above 1.4 solar masses, say by mass transfer from its companion, then its electrons will go relativistic (move at close to the speed of light), and under those conditions, degeneracy pressure is not as efficient and cannot hold up against gravity. So the white dwarf, when it gets to pretty much exactly 1.4 solar masses, will collapse under its own gravity. However, the white dwarf is probably mostly carbon at this point, so it has lots of fuel that has not yet undergone nuclear burning. When it suddenly contracts, instead of a core-collapse supernova (where the energy comes from gravity), the rapid fusion of carbon will generate enough energy to completely explode the entire star-- there is no core left to collapse. We say this type of supernova is a thermonuclear runaway, much like a huge fusion bomb. It's jargony name is a type Ia supernova, and the reason it is so important is that it tends to have very consistent properties-- and is bright enough to be seen at huge distances. Thus it makes a good "standard candle", which is a constant search in astronomy, because it makes it very good at determining the distance to the galaxy in which the supernova occured. This will have cosmological importance, as we shall see. Week 11 notes