A pulsar is a specific type of neutron star, so let’s start there. Neutron stars are made when a star slightly more massive than our Sun dies and goes supernova. In a supernova event, large amounts of radiation explodes out from the star, causing a brilliant flash of light which can sometimes outshine an entire galaxy.
At the same time, gravity causes the core of the star to collapse into a neutron star. Neutron stars are made almost entirely of neutrons (hence the name), and are MUCH smaller in size than their parent stars. Since a neutron star keeps most of the angular momentum from its parent star but has a significantly smaller radius, it spins with very high rotational speeds. These speeds typically lead to rotational periods ranging from milliseconds to seconds.
In addition to spinning quickly, neutron stars also commonly have very strong magnetic fields that can accelerate electromagnetic particles and eject them out along the magnetic poles of the star at extremely high velocities. This results in neutron stars emitting spinning beams of radiation, or light.
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