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Supernovae of type "Ia" are those without helium present, but with evidence of silicon present in the spectrum. The most accepted theory is that this type of supernova is the result of mass accretion on a carbon-oxygen white dwarf from a companion star, usually a red giant. This can happen in very close binary star systems. Both stars have the same age and models indicate that they almost always have a similar mass. But usually one of the stars is more massive than the other and the more massive star evolves faster (leave the main sequence) before the lower mass star does. A star with less than 8-9 solar masses evolves at the end of its life into a white dwarf, binary systems would consist of a white dwarf and a red giant which has greatly expanded its outer layers.

During the explosion an amount of carbon undergoes fusion that a normal star would take centuries to use up. This enormous release of energy creates a powerful shockwave that destroys the star, ejecting all its mass at speeds of around 10,000 km / s. The energy released in the explosion also causes an extreme increase in brightness, so these supernovae become the brightest of all, emitting around 10^44 J (1 foe). Normally there are no traces of the star that caused the cataclysm, but only traces of superheated gas and dust that is rapidly expanding.

What happens to the neighboring star?

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As of this writing, and probably for some years to come, the full story of what Type Ia SNe even are has yet to be figured out. They may be CO WD's reaching the Chandradekhar limit; they may be merging WD's; they may be WD-NS mergers; they may be... You get the idea. Actually, there may very well be several entirely different mechanisms at work. –  Chris White Dec 26 '12 at 7:48
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In answer to your question of "What happens to the neighboring star?", according to the John Hopkins folks, it gets blown away: Type Ia dynamics(Credit John Hopkins)

I would be a little skeptical of the certainty of this claim only because we have not been able to observe any of these Type Ia explosions up close while it is happening. That's why the Type Ia PTF 11kly is so important to us. It is merely 21 million light years away, instead of a billion.

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Type Ia supernovae have Helium lines, the distinction between type I and type II is the presence or absence of Hydrogen (absent in type I, present in type II). Type I is divided into types Ia (where helium is present) and Ib/c, with the latter two types likely massive Wolf-Rayet stars that have lost their outer envelopes via strong stellar winds.

The type Ia supernova is believed to be due to an accreting carbon-oxygen white dwarf undergoing explosive nuclear burning as it approaches the Chandrasekhar limit which generates so much energy that it completely unbinds the star (as it's supported by degeneracy pressure, it does not expand and cool in response to nuclear burning as a conventional star would). Models suggest that contrary to the common view, a carbon-oxygen white dwarf doesn't actually reach the Chandrasekhar limit, at which point it would collapse to a neutron star, although neon-oxygen white dwarfs may.

The supernova will ablate some material from the surface of the companion star, but will not disrupt it, so the companion continues its evolution in largely the same manner as an isolated, non-binary star, although its prior close binary evolution leaves it in a slightly different state to a true single star. There's some evidence for this ablation in Tycho's supernova, e.g.

http://blogs.discovermagazine.com/80beats/2011/04/28/tychos-supernova-went-boom-after-slurping-up-some-of-its-neighbor/

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Nice explanation of what a Type Ia is, but it doesn't exactly answer the bottom line question, does it? –  Larian LeQuella Sep 5 '11 at 13:52
    
Did you read to the last paragraph? –  strmqm Sep 5 '11 at 16:03
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My BAD! :( I got so caught up in the explanation of what a Type Ia is that my mind wandered off like it - OH LOOK A BUNNY! –  Larian LeQuella Sep 5 '11 at 17:41
    
Minor point: Yes, the Type I/II distinction is a lack or presence of hydrogen, but Ia's don't have much helium either. Their spectra are dominated by Si II and other metals. –  Chris White Dec 26 '12 at 7:45
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