Are there more Pulsars than we observe?

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TL;DR
If Pulsars are like lighthouses, we only see the pulses if they are directly towards us.
Hello All

Dame Jocelyn Bell Burnell (the lady who was robbed of the Nobel Prize) described Pulsars to be like lighthouses, emitting a beam of high intensity light modulated by their spin, which we see as they 'flash' towards us.

Would we only see the beam as pulses if the Pulsar was spinning in a plane that intersected the Earth, which seems pretty unlikely. Therefore are there in fact many more Pulsars out there which we never see?

best regards ... Stef
 
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The NASA animation and description are useful.

It doesn't give an estimate for the angular width (is that the correct phrase?) of the beam of energy, or even the theoretical min and max values. The wider this is, the more likely that beams will intercept the observer on Earth.
 
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Also, it apparently spins around too, giving it a greater chance of shining on us. And then there's the possibility of gravitational lensing catching one a really great distance from us.
 
We know of a few thousand pulsars, below is link to ATNF catalogue

https://www.atnf.csiro.au/research/pulsar/psrcat/

There are estimated 10^8 to 10^9 neutron stars in our galaxy. Only a small fraction will be pulsars, they spin down relatively quickly, but even so, probably plently left to discover.
 
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