A star like our Sun will become a white dwarf when it has exhausted its nuclear fuel. Near the end of its nuclear burning stage, such a star expels most of its outer material (creating a planetary nebula) until only the hot (T > 100,000 K) core remains, which then settles down to become a young white dwarf. A typical white dwarf is half as massive as the Sun, yet only slightly bigger than the Earth. This makes white dwarfs one of the densest forms of matter, surpassed only by neutron stars.
White dwarfs have no way to keep themselves hot (unless they accrete matter from other closeby stars); therefore, they cool down over the course of many billions of years. Eventually, such stars cool completely and become black dwarfs. Black dwarfs do not radiate at all.
Many nearby, young white dwarfs have been detected as sources of soft X-rays (i.e. lower-energy X-rays); soft X-ray and extreme ultraviolet observations enable astronomers to study the composition and structure of the thin atmospheres of these stars.
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