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When observing a pulsar from Earth, can we determine what the angle between the rotation axis and magnetic axis is?
A late answer, but the answer is yes, this can in fact be done! The method is outlined in section 2 of the paper On the Evolution of Pulsar Beams
by Tauris and Manchester (1998), where the angle between the rotation axis and magnetic axis is labelled α:
The details are fairly complicated, but the basic idea is straightforward. To determine the angle, we're fitting a model of the pulsar's sweeping beams of emission to the signal we observe. What we need are measurements of the period of the signal, the width of the pulse (how wide is the segment of the beam that crosses us), and its polarization. The polarization reveals information about the magnetic fields the radiation passed through -- that is, what part of the pulsar beam are we seeing? Combining that with the period and pulse width reveal how far that beam is from the spin axis.
This isn't foolproof and it may not work with all pulsars. Some pulsars "glitch"
which can throw off everything. The results may also depend on model assumptions, sometimes by 20-30 degrees. That being said, it has been accurate enough to reveal a lot of interesting information about pulsar evolution. For example, for the first few thousand years the magnetic axis tends to migrate away from the spin axis until they are nearly orthogonal! Then for the next millions of years a magnetic braking effect slows the pulsar's spin rate and also brings the magnetic axis back towards the spin axis, until they are closely aligned. The pulsar's beam also becomes narrower. Pulsar magnetic alignment and the pulsewidth–age relation.