(1) There is an EXTREMELY high density mass of neutrons
with a Mass 
and radius between 10 and 80km.
This is like taking the Sun and shrinking it down to the size of campus. If the Sun were shrunken to this same density, it would be around 5 km in radius.
(2) This neutron star is extremely HOT. Used to be the core of a massive star and SN II. Note, the ``black-body'' radiation is tiny since the surface area is so small. Would never expect to detect one of these via its blackbody radiation.
(3) The Neutron star is rotating extremely quickly
This is the return of Conservation of Angular Momentum
As the ``Moment of Inertia'' (I) for a rotating object decreases, the object spins faster. Everyone knows this from watching those ice skaters.
Arms out 
large I, low spin rate
Arms in small I, high spin rate (toss cookies)
More explicitly,
where L= angular momentum; I= moment of inertia; and 
``angular velocity'' (spin rate)
Q. If a sphere collapses from a radius of 
km
to 10km by what factor does its spin rate increase?
Conservation of angular momentum means:
The Sun rotates at 
. Compress
it to 10 km and conserve angular momentum, it would spin up
to 
(and fly apart).
It turns out that the magnetic field gets compressed as the star shrinks and the field density goes way up.
So, at the center of a SNII remnant we expect to find a Rapidly Spinning, Extremely Dense ball of Neutrons with a Huge Magnetic Field
This was worked out back in the 1930's but it was assumed it was impossible to ever test it and it also seemed like science fiction even to the researchers who worked in the area.
But, Jocelyn Bell and Tony Hewish out together a rickety barbed-wire fence in a field in the countryside near Cambridge (England) in 1967 to do some routine radio observations.
They discovered a source in the constellation Vela that let out a little pulse every 1.3 seconds, then they realized it was every 1.337 seconds, then 1.3372866576 seconds. Eventually they realized that the best clocks of the time were not accurate enough to time this object which they christened a ``LGM''.
The announcement of this discovery was withheld for awhile while they tried to decide if they had discovered extra-terrestrial life. But soon others were discovered. This discovery set off more than a year of wild speculation as to the nature of the rapidly varying sources. But the possibility that it was a neutron star pretty quickly rose to the top.
Looked at the Crab nebula (ejected shell of the 1054 AD SN explosion) and detected another pulsing source with a period of 0.033 seconds (or, 30 pulses per second). This cinched it.
Michael Bolte