I'm assuming that what I've been told is true:
We can only detect pulsars if their beams of electromagnetic radiation is directed towards Earth.
That pulsars are the same as neutron stars, only that they emit beams of EM radiation out of their magnetic poles.
So, isn't it possible that neutron stars emit EM radiation in the same fashion as pulsars, just not in the right direction for us to detect it?
Pulsars are a label we apply to neutron stars that have been observed to "pulse" radio and x-ray emissions. Although all pulsars are neutron stars, not all pulsars are the same. There are three distinct classes of pulsars are currently known: rotation-powered, where the loss of rotational energy of the star provides the power; accretion-powered pulsars, where the gravitational potential energy of accreted matter is the power source; and magnetars, where the decay of an extremely strong magnetic field provides the electromagnetic power. Recent observations with the Fermi Space Telescope has discovered a subclass of rotationally-powered pulsars that emit only gamma rays rather than in X-rays. Only 18 examples of this new class of pulsar are known.
While each of these classes of pulsar and the physics underlying them are quite different, the behaviour as seen from Earth is quite similar.
Since pulsars appear to pulse because they rotate, and it's impossible for the the initial stellar collapse which forms a neutron star not to add angular momentum on a core element during its gravitational collapse phase, it's a given that all neutron stars rotate.
However, neutron star rotation does slow down over time. So non-rotating neutron stars are at least possible. Hence not all neutron stars will necessarily be pulsars, but most will.
However practically, the definition of a pulsar is a "neutron star where we observe pulsations" rather than a distinct type of behaviour. So the answer is of necessity somewhat ambiguous.
Do there exist neutron stars without relativistic jets? Also, could jets be locked in alignment with the spin axis, resulting in a beam that does not pulse for any line of sight? For some reason discussion has been focused on Earthbound detectability of these jets. Instead, I'm looking for an answer using astrophysics that deals with all lines of site, not just those pointing toward us.
I think the expectation here is a radio-quiet neutron star. Though most of the neutron stars are pulsars, these are the special types that are more likely to satisfy the constraints. Either they don't emit relativistic jets, they have their magnetic axis aligned to the rotational axis, or the radio beams are always directed away from Earth. There's also another possibility that we haven't detected any emissions yet (I mean, we haven't swept the whole sky). For instance, the fact that Geminga is a pulsar was quite unknown for 20 years. Later, it was discovered to have a periodicity of 237 milliseconds.
As far as I've known, these radio-quiet neutron stars haven't been declared as a non-rotating neutron star yet. Instead, their periodicity and a few other details have been listed as unknown. Examples include RX J0822-4300 and RX J185635-3754 (it was accounted as a candidate for quark star, however Chandra and Hubble observations excluded it from the list)
There are a few papers related to these species, which I fear is quite beyond my knowledge...
For a neutron star to be called a pulsar, we need to detect a periodic signal pulse from the object. The "lighthouse model" explains this as a spinning object, with a magnetic field off-kilter from the spin axis, beaming radiation out from the poles. So, there are certainly some neutron stars where lighthouse beams are spinning around but never point at the earth, and we don't see them. In some cases, we observe a pulsar in a binary with another neutron star, but can't detect any radiation from the companion.
However, neutron stars (and thus pulsars) do emit other thermal radiation, it's just hard to detect that if they are far away. The surfaces are really small. Or we see some surface radiation, plus a brighter blip from the "lighthouse". For example, several nearby pulsars ( http://en.wikipedia.org/wiki/The_Magnificent_Seven_(neutron_stars) ) are detected mostly from their constant thermal radiation in x-rays. But they also have small periodic pulsations on top of the constant emission - the "pulsed fraction" is 1% to about 20% of the total ( http://arxiv.org/abs/0801.1143v1 ) - so they are still called pulsars.
