If a pulsar's rotational and magnetic axes were aligned and both aimed at us, would we see a steady radio source?

Question

In other words, a non-pulsing pulsar?

Answer 1

Two things would be required. First, your line of sight would have to be close to looking along the magnetic axis of the neutron star. Second, that magnetic axis would have to be closely aligned with the rotation axis of the pulsar.

If both of these are pseudo-randomly distributed and the pulsar beam is narrow, then this is inherently a very unlikely scenario. The cumulative probability of a randomly oriented axis in space having an inclination $<i$, where $i=0$, means aligned, is $1 - \cos i$. And if both line of sight and magnetic-rotation axes require close alignment, you are dealing with the product of two of these factors.

One factor that may work in favour of seeing such objects is that it seems likely that pulsars drift towards alignment of the rotation and field axes as they get older (e.g. Young et al. 2010), but on the other hand, the pulsar beam is expected to get narrower and the pulsar activity weakens and eventually switches off on a similar timescale. It is also possible that young pulsars are more likely to have misaligned, almost orthogonal rotation and field axes, in which case the scenario is impossible for young pulsars.

Still, this is an interesting question. If pulsars are born with random alignments, you might expect a small number to be born with aligned rotation and field axes, and for a small number of those to have beams aligned with our line of sight. They would be characterised by very little modulation of their emission.