If a white dwarf is a "dead" star, why is it so hot?
Is a white dwarf a "dead" star? Is a dead star defined as one that has burned through all its fuel? If a white dwarf is a dead star, why is it located on the hotter side of the HR diagram in my textbook? Hasn't it burned through all its fuel?
A white dwarf is a stellar remnant and can be considered as a dead star in this regard. A "dead" star is one that has no more nuclear fusion going in it. When a star dies, it leaves some remnant behind. Depending on the mass of the star, the remnant can be a white dwarf, neutron star or a black hole.
White dwarfs are what was once the core of a star. During a star's life, nuclear fusion goes on in the core (and not in the entire star). The temperatures are extremely high in the core (15 million degrees Kelvin for main sequence stars burning hydrogen, and 100 million degrees for stars burning helium). As a result, when a low mass star dies by shedding its envelope leaving behind the core as a white dwarf, it is very hot at around 100 million degrees. In addition, the core has become very compact (size of the Earth). This is the reason why the white dwarf is located on the bottom left part of the HR diagram: left because it is very hot, and bottom because its luminosity is very small (compared to normal stars) due to its small size.
Left to itself, the white dwarf slowly cools since there is no longer any energy production taking place in it. So, after a few million years, the white dwarf which was very hot when it was born in a planetary nebula will become quite cool.
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