Pulsar planet
Pulsar planets are an exotic type of planets that are found orbiting pulsars, or rapidly rotating neutron stars.
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Formation
From a protoplanetary disk
The first type of pulsar planets are formed from the circumstellar disks around pulsar stars. These disks are thought to have formed from metal-rich debris left over from the supernova that formed the pulsar.
Pulsar planets would be unlikely to harbour organic life, because the high levels of ionizing radiation emitted by the pulsar and the corresponding paucity of visible light.
From the core of a star
Pulsar planets can also be the remaining cores of former stars that were the pulsar's orbital companions. They are typically quasi-degenerate worlds, such as in the system around millisecond pulsar PSR J1719-1438. The planet is estimated to have a density of at least 23 times that of water, a diameter of 55,000 km, a mass near that of a medium-sized gas giant planet, and a 2hr10min orbital period at 600,000 km. It is thought to be the diamond crystal core remaining from the evaporated white dwarf, with an estimated 1031 carat weight.
From the debris of a companion star
The third type of pulsar planet are those that were formed out of the debris of a destroyed companion star that used to orbit the pulsar. In PSR J1719-1438, the planet most likely is the companion, or what's left of it after being almost entirely blasted away by the extreme irradiation from the nearby pulsar. PSR B1620-26 b is most likely a captured planet.