Why do neutron stars emit beams of x-ray radiation at their poles???

Answer 1

These guys have a magnetic field on steroids, which can accelerate charged particles to relativistic velocities. The spinning magnetic field creates a strong electric field which throws out high energy charged particles (eg. electrons) at the poles. The particles then emit high frequency photons in their direction of travel. Sort of like the auroras in reverse.

Answer 2

In case you want to do a search on it, the specific phenomenom is called synchrotron radiation.

http://en.wikipedia.org/wiki/Synchrotron_radiation

Answer 3

Cause they can