Binary star evolution -- the Algol paradox		Roughly half the stars in the sky are in binary systems. One binary system that may seem puzzling is called Algol. What's puzzling is that it contains a blue main sequence star that's 3.7 times as massive as the Sun and a Red Giant star that's 0.8 times as massive as the Sun. What's so strange about that? Well, you'd expect that in a binary, both stars were born at around the same time. So the more massive star would leave the main sequence first (because more massive stars burn up their hydrogen faster.) But paradoxically, the more massive star is still on the main sequence, while the less massive star has evolved to the red giant stage. This site and especially this mpeg movie show what's happening. The star that's now a red giant did indeed start off as the more massive star. But as it evolved and became larger, its outer layers expanded until they came into the gravitational pull of the smaller main sequence star. Then the red giant's mass was transferred to the other star. How does this work? The above diagram shows equipotential surfaces. The point in the middle where the curves meet is called the L1 Lagrangian point. It's the special point where the gravitational forces of each of the two stars are equal. Therefore, it must be closer to the less massive of the two stars. (Actually, at the L1 point, the total force adds up to zero--including the gravity of each star pulling in opposite directions and the centrifugal force because the whole binary system is rotating.) A star on its own is spherical (neglecting rotation.) But in a binary system its shape can be distorted to one of these equipotential shapes. A star is normally spherical because on the surface of the sphere, gravity points entirely inward, never along the surface. The "equipotential surfaces" in this diagram are defined mathematically so that the total gravity of both stars pulls at right angles to the surface, never along the surface. The special surface that reaches the L1 point is called a "Roche lobe." What happened in Algol--and similar binaries called "Algol binaries" (logically enough!)--is that when the more massive star evolved, it expanded first into a red giant. It became big enough to fill its Roche lobe. Then gas at the surface near the L1 point--where the combined gravity of each star and the centrifugal force from the orbit total to zero--can freely flow into the Roche lobe of the blue main sequence star, and fall under its gravitational influence. The gas at the L1 point flows towards the blue star, but as you can see in the movie linked above, not in a straight line. That's because of the coriolis force. It's like throwing a baseball to a friend on a merry-go-round. It appears to fall behind because you're rotating. Over time, so much mass fell onto the blue main sequence star that it became the more massive star.
What happens next -- Cataclysmic Variables		What next (asked Plato's ghost!)? Well, eventually the red giant will become a white dwarf. And eventually the blue main sequence star will evolve off the main sequence. When it fills its Roche lobe, when its surface extends to the L1 point where it's no longer held in by any force, then you have a binary system where gas flows from a normal star onto a white dwarf star. As the gas flows from the normal star to the white dwarf, remember, it doesn't go in a straight line because of the coriolis "force". Instead the gas stream falls behind the white dwarf, and the white dwarf's gravity diverts it into a circular orbit. This forms an accretion disk, a disk of gas originating from the normal star that funnels onto the white dwarf star. Here is an artist's impression of a cataclysmic variable: Sometimes the white dwarf has a strong enough magnetic field that the gas is drawn onto its surface through the field instead of through the disk. These star systems are called polars. Here's an artist's impression of one: An accreting white dwarf/normal star binary system is often called a cataclysmic variable because there are several ways the light can burst to extraordinary brightness. In order of dimmest to brightest outburst: Dwarf nova outburst: this is caused by an instability in the accretion disk, causing it to brighten several times Nova: this is caused by runaway thermonuclear fusion on the surface of the white dwarf. The accreted gas from the normal star builds up on the surface of the white dwarf. When there is enough dense gas, it blows itself up in a fusion explosion. It can reach a brightness of 100,000 times the Sun's brightness over a period of days. However, the white dwarf star itself is still intact. It can become a nova again later, after more gas from the normal star has fallen onto it again. White dwarf supernova: the mass of the white dwarf gets dangerously close to the Chandrasekhar limit beyond which degenerate pressure of electrons can no longer hold off the force of gravity. What happens is that the star contracts and heats up enough that fusion of carbon (which the white dwarf is mostly made of) can begin. The fusion goes out of control, because the white dwarf is degenerate (because most of the pressure is not from heat, the heat from fusion doesn't cause the star to expand and cool off). This time, the whole star consumes itself in thermonuclear fusion of carbon! The explosion shines a billion times brighter than our Sun (109 times brighter!)
X-ray Binaries: Neutron Stars		These are the kinds of star systems I study in my own research. Sometimes you can end up with a binary star system where one of the two stars is a neutron star. Neutron stars are found alone as pulsars. They can be formed in a binary if a star in a binary goes supernova, and the explosion doesn't disrupt the orbit with the other, normal star. So these star systems are like cataclysmic variables, but with neutron stars instead of white dwarfs. They're called X-ray binaries. The first X-ray binary was discovered in 1962. A team of scientists from MIT wanted to start a new field of astronomy, X-ray astronomy. But they needed some way of getting funded. So, being the 1960s, when everyone was interested in sending a man to the Moon, they said that they were going to look for X-rays coming from the Moon. Just as the Moon reflects the Sun's light, the Moon could also reflect X-rays from the Sun. During solar flares, the Sun gives off X-rays. Unfortunately, when they sent up their rocket, the lens cap over their detector never opened. They tried again. This time, 2 out of the 3 Geiger counters they used worked, and showed that there were definitely X-rays coming from space! But they weren't coming from the Moon. They were coming from a modest looking blue star in the constellation Scorpius. It was called Scorpius X-1, and the science of X-ray astronomy was born. Scorpius X-1 is the brightest star in the sky... if you have X-ray vision! Why do these neutron star systems emit X-rays? Because the neutron star's surface is so much smaller than a white dwarf's surface, when gas falls onto it (actually swirls onto it through the accretion disk), it can pick up more energy by falling a further distance to where the gravity is stronger. So the gas picks up more energy than gas falling onto a white dwarf, and that means it can reach higher temperatures. There are several ways we can find out about the neutron stars in these star systems. In some cases, the magnetic field is strong enough so that the gas falls mainly onto the north and south pole of the neutron star. As with a radio pulsar (an isolated neutron star), or even with the Earth, the magnetic poles are not the same as the spin poles (Earth's magnetic north where a compass points is not the exact same as the North pole.) So as the neutron star spins about its spin axis, it rotates around its magnetic poles. When they face us, we see the X-rays become brighter; when they point away, the X-rays are dimmer. These systems are called X-ray pulsars. The X-ray pulsations help us figure out the exact nature of the binary orbit--the semimajor axis and eccentricity. How? Say the X-ray pulsar spins once every second. If the X-ray pulsar in its orbit is moving further away from us, then it's going to take a slightly longer time for the X-rays to travel towards us. The period of the pulsar will appear to become greater. Likewise, when the pulsar is in orbit moving towards us, the time between the pulsations becomes shorter. It's similar to the Doppler effect for the frequency of light, only this is for the frequency of X-ray pulsations. Another kind of X-ray binary is a burster. These are thought to have weaker magnetic fields, so that the gas spreads out equally onto the surface of the neutron star instead of going just to the magnetic north and south poles. Similarly to a nova on the surface of a white dwarf, the accreting gas can pile up on the surface of a bursting neutron star. Fusion of hydrogen into helium begins, and helium into carbon at a layer below. The fusion of helium is very sensitive to temperature, and as it heats up, it goes out of control. The X-ray burst is, like a nova, basically thermonuclear fusion on the surface of a compact star that gets out of control. X-ray bursts give us good evidence that we are dealing with neutron stars because their spectra are approximately blackbody shaped. The luminosity of a blackbody depends on a constant (sigma) times the surface area, times temperature T to the 4th power. The temperature can be measured, for example by Wien's law, by finding lambdamax, the wavelength where the light is brightest. Then from how bright the light is overall, we can know the surface area--which corresponds to the surface area of a neutron star (a radcius of about 10 km.) There are other neutron stars in binary systems that neither burst nor pulsate. Scorpius X-1, the brightest X-ray binary and the first to be discovered, is one of these. It's thought that here the magnetic field is even weaker. Instead of bursts or pulsations, we sometimes see "quasiperiodic oscillations"--a random flickering or twinkling up to a thousand times a second. We don't know what causes this, although there are many theories. X-ray binaries come in two general classes, depending on what the normal star in the binary system is like. If the normal star is a low mass star, say less than about twice the mass of our Sun, then the gas its way onto the neutron star probably through Roche lobe overflow--through the surface of the normal star reaching the zone of gravitational influence of the neutron star. The other possibility is that the normal star is a hot star with a strong stellar wind. Then instead of overflowing gas swirling into an accretion disk, the neutron star can sometimes just pull in some of the outflowing gas in the stellar wind, and that wind gas is enough to power the X-rays. A typical X-ray binary might be about 104-105 times brighter in X-rays than our Sun is overall. X-ray binaries are usually thought to be dimmer than their Eddington limit, which is when they are so bright that their radiation pressure is stronger than their gravity. The end result of an X-ray binary could be a single neutron star (the normal star's atmosphere can be blown away eventually by X-rays from the neutron star), a white dwarf/neutron star binary, or a neutro star/neutron star binary.