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Originally Posted by bojan
Good point. However...
A question from me now (I am now in Alex's mode  ).
Instead of expected onion-shape [BTW, layers of light for millisecond pulsating are expected to be very thin (1 ms equals ~300km), objects that small are not observable from those distances],we should be able to see some sort of bright ring, where rotating beam is hitting the shell of previously ejected material from a progenitor star.
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You would not be able to observe a light echo from a rotating beam. The echo is a function of the expanding wave front perpendicular to the observer, not the shape of the intervening matter.
A rotating beam sweeps out a disk. Since we can observe the pulsar, our line of sight corresponds to the edge of the disk. Hence we would not be see a light echo.
If on the other hand the pulsar is sending out spherically expanding wavefronts (pulses) then there exists a wavefront perpendicular to our line of sight. If there is matter between the observer and the pulsar, the size of the echo is a function of the distance travelled by the wavefront.
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Would the bright rings observed at SN 1987A in LMC be a good explanation for this?
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Malin's famous light echo rings of SN 1987A highlight the mechanism.
The two light echo rings correspond to the presence of two separate sheets of intervening matter. The larger ring is due to matter closer to Earth, the component of spherical wavefront perpendicular to the Earth has travelled further resulting in the larger ring.
Note the spherically expanding wavefront is due to the supernova blast itself. To date there is no evidence of a neutron star let alone a pulsar.
Regards
Steven