Neutron Star, Pulsar, Magnetar and Redbacks and Black Widows
When a star fuses matter it creates a outward pressure against the gravity that its mass causes, which tries to crush inwards. Eventually, the star will run out of matter it can fuse, and the star will begin to collapse inwards.
If the remaining core is less than 1.4 times the mass of our Sun, then a white dwarf will be born, a ball of mostly oxygen and carbon around the size of our planet.
If the star was massive, and there is more than 1.4 times the mass of the Sun left, then gravity can continue to crush down, crushing up atoms into a giant ball of neutrons. The limit between a white dwarf and a neutron star is known as the Chandrasekhar Limit.
Neutron stars despite being more massive, are much smaller, ranging from the size of the moon down to the size of a large city. Like white dwarfs, Neutron stars also have limits, one of the most massive found is J0740+6620, 2.17 times the mass of the Sun, squeezed into just 30km in diameter.Â
Beyond that, Black Holes form !Â
When a neutron star is formed, it does so with a bit of a spin, while many spin within seconds, some extreme stars spin in the milliseconds. Emanating from it’s polar regions are vast jets of particles and sub atomic particles which act rather like a lighthouse. Every neutron star does this, but not all of them are aligned in such a way that we catch the beam. So, the ones we can see, we call Pulsars.Â
Magnetars are just the extreme end of the Pulsars, those millisecond pulsars generate huge magnetic fields, and hence we call them Magnetars, but they are all neutron stars.
Now for the Spider Connection
These millisecond pulsars are often span up so much because when the neutron star was formed, it was part of a binary star system, and if those stars happen to be close enough, the neutron star can accrete a lot of material from the other star, causing massive supernova styled explosions and spinning up the neutron star, additionally, it can continue to feed it after its birth.
There are two types of systems, a neutron star that ended up with a low mass small red dwarf partner, which we call a black widow, and a neutron star that partners with a much larger mass star, which is the redback.
These are both rare and of great interest to astronomers, due to the fact neutron stars are generally not visible optically (due to their size) and only the pulses or the gravitational effects on partner stars is noticeable. So to have a confirmed pulsar (ie neutron star) with a star orbiting it can reveal a lot of information, otherwise impossible to obtain.