A Neutron Star is at the heart of Pulsars, they are the end remains of a dead giant star that has finished burning it energy/fuel and this is all what is left. They may only be the size of a city (say 20km) but they can be so dense and heavy. A teaspoon of a neutron star would weigh far than a tea spoon, actually, it would weigh a billion tons. The reason for their weight is that all the neutron are packed so tight together. Ref: Space
A Neutron Star gets its name from what the star consists of, surprise! surprise!, neutrons. A neutron is produced when the neutron and electrons are crushed together. A star can only become a Neutron Star when the solar mass of the star is between 1 and 3 solar masses. Anything higher will create a Black Hole. Neutron Stars can be found in Pulsar, Magnetars and at the centres of Supernova remnants. Ref: N.A.S.A. The Crab Nebula Supernova Remnant has a Pulsar at the centre of it.
The below picture shows you the size of a pulsar compared to New York City, in particular Manhatten Island. The image is a screenshot from a video that N.A.S.A. produced on YouTube to explain Pulsars. Clicking on the picture below will take you to the YouTube page.
Pulsar or in its longer form 'Pulsating star' is the remnants of a supernova explosion at the end of a Star's death. It is one form of end of a star, the others being a black hole or a planetary nebula. A planetary nebula is what happens when a dying star is not big enough to go supernova.
Compared to a planet or an asteroid, a Pulsar is incredibly small, it can be nothing that the size of a large city such as London or New York. Although they might be as big as a city, their mass could be many million times the mass of the Earth. The reason for the difference is the extreme amount of gravity that is pulling in on itself. At the heart of a pulsar is a neutron star, a star that is made entirely of neutrons.
What causes a pulsar to spin is the fact that the neutrons are so tightly packed. Futurism gives the example of a figure skater spinning faster as curls up using a concept called Angular momentum. If you watch this YouTube video, it'll explain Angular Momentum better than writing words. The fastest spinning neutron star in a pulsar is snappily named PSRJ 1748-2446 and is in the constellation of the archer, Sagittarius.
The picture below is from NASA and is an artists impression of a new kind of Pulsar. The ball at the centre of the pulsar is the neutron star. The pink is the gamma rays that shoot out from the pulsar. The blue lines are the magnetic field lines.
Given its name, its no surprise that the pulsar will rotate and so that the gamma rays won't always fire in the same direction. We are only able to detect a pulsar when its beams are firing towards us.
Pulsars were first discovered by Jocelyn Bell Burnell and Antony Hewish on November 28th,1967 when they started getting signals from space. They thought they'd discovered signals from an alien life form trying to communicate with us. When another signal was found of the same type in another part of the sky that the theory of aliens was discounted.
Pulsars although they are the remnants of the dead, they have been discovered to have orbiting planets. One such pulsar, PSR 1257+12, now known as Lich, in the constellation of Virgo has been discovered to have a planet around it. The pulsar was rotating at such as fast speed that scientists were able to detect the miniscule fluctuation that a planet causes when its orbits round the planet. The planets are bathed in the spinning streams of radiation channelled out from the star and so there are zero chance of there being life.
The first extrasolar planet (exoplanet) discovered around a Sun like star, was officially known as 51 Pegasi b and unofficial as Bellerophon after the Greek Mythological character who tamed Pegasus, the winged horse that Perseus used during his mission to save Andromeda from being killed. There is not a slight chance that the planet would have life but since then Extrasolar Planets have been discovered around so many other stars that we shouldn't feel disheartened by the fact there wasn't any chance of finding a planet that could support aliens life there.
Magnetars are power Neutron Stars with powerful magentic fields. They are 100 times stronger than an average neutron star and have a quadrillion times the power of the Earth's Magnetic field. If the Magnetar was as close to the Earth as the moon, the magnetic strips on your credit cards would be beyond use. If the Magnetar was half the distance, it would lift metal objects off the ground. If the magnetar was 600 miles away, the iron would be stripped from our bodies. There's no magnetars so don't have nightmares. Ref: Futurism (Link as above).
To give you an idea of how powerful a Magnetar is, the Sun's magnetic field is measured as 5 Gauss. Which given its the Sun, you'd think it pretty power. A magnetar are thousand times more powerful than a normal neutron star which in turn has a Gauss of a million billon. A known Magnetar is 1E 2259 that is in the constellation of Cassiopeia in the Northern Hemisphere. Ref: N.A.S.A.
The image is courtesy of Nova Celestia which has free use image policy.