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A pulsar is a rapidly rotating neutron star which emits large amounts of electromagnetic radiation (light, x-rays, radio waves, etc.) and particle jets. A neutron star is what is left over when a star 4 - 8 times the mass of our sun burns up most of its fuel and explodes in a supernova. The outer layers of the star shoot outwards rapidly, while the stellar core collapses to a sphere approximately 20 km in diameter. Some neutron stars do not rotate very rapidly but those that do are known as pulsars.
Suns more massive than 8 times the mass of our sun collapse to form black holes, which emit very little radiation because their gravity well is so deep that nothing can escape from it. Suns less than 4 times the mass of our sun turn into Red Giants and then brown dwarfs, without collapsing into a neutron star. But those suns that do collapse into neutron stars release a massive amount of energy in the process, due to the sheer energy of the collapsing matter. Sometimes a small initial rotation in the stellar core will amplify greatly as the collapse ensues, as an ice skater tends to spin more rapidly and they draw their arms closer in towards themselves.
The particle jets and electromagnetic radiation emanate from two locations on the spinning neutron star - the north and south magnetic poles. Because the gravity of the neutron star is so massive (thousands of times that of the sun), very little matter or light escapes from any other part of the pulsar. Because the magnetic poles are slightly misaligned with the axis of rotation, just like on Earth, we observe pulsars as light sources which blink on and off at a regular frequency, as the magnetic poles are spun around by the rotation of the star. This phenomenon was first observed by the graduate student Jocelyn Bell Burnell in late 1967.
Pulsars produce magnetic fields approximately a trillion times more intense than Earth's. Pulsars in binary configurations with normal stars are the most easily observable, as all neutron stars tend to pull matter off of their companion stars, resulting in a luminous accretion disk. Pulsars accreting matter from a companion star tend to rotate even more rapidly as they gain mass. Pulsars rotate somewhere between 10 and 1000 times a second, with some variants spinning even more rapidly. The rotation rates of some pulsars are so regular that they are known as the most accurate clocks in the universe. Among the most exotic of cosmological objects, pulsars give us a window into a bizarre world where high-intensity gravitational and electromagnetic fields are exposed to relativistic speeds, thus testing the very limits of our understanding of physics.