Type Ia supernovae are caused by a completely different mechanism than the more well-known type II supernovae. Type Ia supernovae occur in a multiple (usually binary) star system, where one of the stars is a white dwarf. The white dwarf creates a strong gravitational field, and if its companion star is close enough, it begins to suck matter away from the star in an accretion disk. White dwarfs are composed mainly of carbon and oxygen nuclei. When the increasing mass of the white dwarf reaches about 1.3 times the mass of the sun, it reinitiates nuclear fusion, burning oxygen into carbon. Since the white dwarf is in an electron-degenerate state, the temperature of the star is independent of the pressure. Therefore the white dwarf heats up very quickly but does not expand, which causes it to heat up more, and eventually leads to a runaway fusion extravaganza.
The Chandrasekhar limit dictates that a white dwarf cannot exist as a white dwarf if it is more massive than about 1.4 times the mass of our sun. As it approaches this limit, the temperature rises to an extreme and the star is finally forced to expand. The temperature is once again dependent on pressure, and the expansion produces a cooling that slows down the nuclear fusion, which cannot produce any elements heavier than iron. The energy released in this expansion completely destroys the star (and sometimes its neighbor), by causing the outer layers to be expelled at speeds exceeding 10^4 km/s, or 1/10 the speed of light.
Type Ia supernovae particularly interest astronomers because they are all about the same brightness, or absolute magnitude. This is because the Chandrasekhar limit requires all white dwarfs undergoing this process to be about the same mass. Astronomers can then use these events as standard candles to gauge the distances of galaxies accurately.
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