Neutron stars are extremely dense: they are only 10 kilometers or so in size, but have the mass of an average star (usually about 1.5 times more massive than our Sun).
“A single [neutron star] can hold the mass of up to 5 suns in a sphere about 12 kilometers across” (Krieger 2006). Neutron stars were supergiant stars whose exploded “ultradense cores becom[e] neutron stars the size of a small town” (Kaler, Jim. Ask Astro. Astronomy, 32, Issue 1. 2004). (This phenomena can also create a black hole.)
Neutron stars are made of neutrons. Their superdense status is responsible for some of the most exotic phenomenon in the universe, such as pulsars. In 2006, astronomers discovered a “densely packed sphere of neutrons spinning so fast that its equator may whirl at 15% the speed of light. The object breaks a 23-year-old record for fastest stellar spin by a sizeable margin” (Irion 2006.)
Neutron stars have consumed all of their own fuel and so tap into other sources for energy. “Thanks to this efficient release of gravitational energy, the temperature at the center of a newborn neutron star can reach 500 billion kelvins… It’s likely that neutron stars are born magnetized… A newborn neutron star is incredibly hot -- it is, after all, the surviving core of a star that has just collapsed and exploded as a supernova. Gravitational energy released during the star's collapse represents almost 10 percent of its rest-mass energy... Rotation offers another energy source for neutron stars. They spin rapidly at birth because the collapsing pre-supernova star "spins up"-- much as a spinning ice skater does when she pulls in her arms…Some neutron stars do produce energy by thermonuclear fusion on their surfaces.” (Sigg 2005).
Both white dwarfs and neutron stars are the remnants of stars about the size of our sun. Neither are sustained via nuclear reactions at the core. The matter in both objects is compressed to extreme densities, and therefore both are useful for studying matter at high energies.
White dwarfs are dim; neutron stars are invisible, but they all have masses similar to the sun. Like a neutron star, a white dwarf has no energy source other than what is left over from its birth. White dwarfs are dead stars, and, like neutron stars, are incapable of nuclear reactions. Also like neutron stars, they are incredibly dense. Neutron stars and massive white dwarfs can sometimes, as a result of a close encounter, create an x-ray-emitting binary pair (Morledge, 2002). Both neutron stars and white dwarfs are useful for studying matter at high densities.
“A typical white dwarf is a little larger than Earth but has 60 percent the mass of the Sun. It forms after a star that is born with less than eight times the Sun's mass expands into a red giant. The red giant eventually casts off its atmosphere, exposing the hot, dense core -- the white dwarf. A white dwarf does not burn nuclear fuel, as the Sun and other stars do; instead, it shines because it is hot. Since white dwarfs no longer generate energy, their evolution resembles the fading fortunes these stars have faced during the 20th century: They start off hot and bright but soon cool and fade” (Croswell, 1996.)
White dwarfs theoretically turn to black dwarfs, but no such star exists; it takes so long for the process to occur, that all white dwarfs are still evolving.
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