Pulsars ------- The discovery of pulsars, along with that of quasars and the cosmic microwave background, ranks highly among some of the most important discoveries in astronomy in the latter half of the twentieth century. The first pulsar was discovered in 1967 by Jocelyn Bell, Anthony Hewish and collaborators at Cambridge University. Bell's group was in the process of observing quasars, or distant, extremely bright galaxies whose source of energy to this day remains a bit of a mystery. In the astronomical data, Bell noticed an extremely regular, repetitive signal whose period was one and a third seconds. Its regularity lead Bell and Hewish to first conjecture that the source was artificial, but after a careful search, they ruled out such a possiblity and concluded that the pulses were astronomical in origin. Currently there are about 1000 known pulsars, similar to the one discovered by Bell and Hewish. The periods range from approximately 1 ms to almost 5 s. The periods are not entirely regular but rather increase at an extremely slow rate, taking anywhere from a hundred thousand to a thousand trillion years to gain a second. Early researchers realized that such incredibly fast and regular pulses would require a small rotating astronomical object that emitted a highly directional beam of radiation. As the object rotated, the beam would rotate with it, sweeping past our earth at regular intervals, much like a lighthouse. The only known objects available to rotate at such speeds are white dwarfs, black holes, or neutron stars. White dwarfs are too large to rotate more than once a second. Black holes, being singularities in space time itself, have no physical surface on which radiation emitters can reside. Thus the only remaining, and current, theory is that these pulsars are actually rotating neutron stars. Although the exact mechanism by which neutron stars emit the observed pulse like radiation is to this day a matter of debate, much is known about the physics of these stars which may in the future shed light on the source of their radiation. Neutron stars are extremely dense stellar objects that are produced in supernova explosions. They were first proposed by Baade and Zwicky in 1934 in their pioneering work on supernovae. Their masses are on the order of the mass of the sun even though their typical radii are only 10 km. This yields an average interior density of 300 trillion kilograms per cubic centimeter which is greater than the density of a large atomic nucleus. These neutron stars originally come about from supernovae under the gravitational collapse of the stellar core when it reaches a critical size. As the core collapses, the immense gravitational binding energy is converted into kinetic energy, allowing the core to rotate faster. The mechanism behind this rotation is conservation of angular momentum which in this case states that the angular velocity of the rotating core is inversely proportional to the square of its radius. This is actually a familiar effect and is entirely analogous to the way a person in a spinning chair spins faster when his or her arms are pulled inwards. Further gravitational collapse is prevented by quantum mechanical Fermi pressure of neutrons in the core. This pressure eventually exceeds the binding energy of nuclei at which point protons and electrons interact via the weak interactions of particle physics, ejecting a neutrino and leaving behind a neutron. The end result is a rapidly spinning dense condensate of neutron matter that comprises the neutron star. Neutron stars also carry very strong magnetic fields, on the order of a trillion Tesla. It is these magnetic fields, combined with the rotating nature of the neutron star, that are thought to be responsible for the radiation we observe from pulsars. It is well known from elementary electromagnetism that a rotating magnetic dipole (the pulsar) radiates electromagnetic waves at the same frequency as that of the rotation. In addition this dipole radiation can accelerate charge particles that may be in the vicinity of the pulsar to large, relativistic energies. It is conjectured that these accelerated particles account for the origin of high energy cosmic rays. As the pulsar radiates energy, the rotation frequency of the pulsar also decays, presumably due to torques applied by the magnetic fields themselves. This decay in rotation accounts for the observed increase in the pulse period over time. There are about thirty known pulsars that derive their source of power from an alternate mechanism, that of accretion rather than rotation. Accretion-powered pulsars have slightly longer and less regular pulse periods than rotation-powered pulsars. They are typically found in binary systems with a normal star or a red giant as a companion. Matter from the companion star flows into the neutron star and generates energy in the form of x rays or gamma rays. The study of pulsars, despite their mystery, has nonetheless lead to important results in related fields. Observations of doppler shifts in radiation as binary pulsars rotate around each other has verified predictions about the nature of gravitational radiation. Similar Doppler shifts lead to the discovery of the first planets outside our solar system. Furthermore pulsars can yield information about extremely dense states of matter, often at densities that are beyond the reach of particle physics. Their continued study will no doubt yield important clues about the structure of our universe at all scales.