[WorkLobster]

One thing I don't understand about what this page seems to suggest: shouldn't there be a bright ring of starlight at some non-zero angle away from dead ahead?

Given a finite collection of objects out to a certain radius (stars), relativistic length contraction will compress it along the direction of travel, so an observer looking out from the centre should see the density increase to a maximum when perpendicular to the contracted direction (in a way that's sort of the opposite of synchrotron radiation ending up tightly directed forward and backward). I guess the aberration described in your link will bend this fore-wards from the perpendicular, but it seems like it should still be visible.

[superposeur]

If you travel through a localized clump of stars then yes, as you describe, the clump would be pancake-shaped. However, the Lorentz transform of an infinite lattice is another infinite lattice, just one in which the spacing between stars in one of the three directions is smaller. So, in particular, the average density everywhere remains uniform (no matter where you are situated within the lattice).

The reason you don’t see an isotropic distribution of light from this uniform density is the distortion due to aberration + the synchrotron effect you mention (which makes the stars in the forward direction brighter).

So, in conclusion no “critical angle” but the dots of light appear more densely concentrated toward front and they are brighter, bluer.

[mr_toad]

Some science fiction describes the phenomena as a starbow.