How Are Galaxies Receding Faster Than Light Visible To Observers?

We know that some galaxies are moving away from us faster than the speed of light and we know it by measuring the redshift, but how's that possible?

The following papers give good explanations:

http://users.etown.edu/s/stuckeym/AJP1992a.pdf

http://arxiv.org/pdf/astro-ph/0011070v2.pdf

In summary, Hubble Law: $v = H(t)D$, where $v$ is recession velocity, $D$ is distance, and $H(t)$ is the Hubble "constant" at a given time, requires that beyond a certain distance velocity is greater than the speed of light. If recession velocity at the location of a traveling photon were greater than the speed of light the entire time the photon from a distance galaxy were traveling, we would never observe the photon. A photon emitted from a galaxy moving away from us faster than light, initially is also receding from us. However, the photon may eventually get to a region of spacetime where recession from us is $<c$. In this case, the photon can reach us. The exact relationship between red shift and velocity depends upon the cosmological model, but according to the above references, galaxies with red shifts greater than ~3 were and are receding from us faster than light.

If they're moving away say at 2c, how would the light of the galaxy? even reach us?

Only if the photons from the galaxy reach a region of spacetime where recession velocity is $<c$.

How do we measure "redshift" for something faster than light?

Red-shift is measured as the change in wavelength of the light, but rather than interpreting the results using special relativity (which would result in $v<c$ for all red shifts), the results are interpreted in the context of a cosmological model and general relativity.


Light from beyond the Hubble sphere (the place where recession velocity equals the speed of light) reaches us daily.

I'm not good enough a physicist to come up with a nice layman's explanation for this fact, but it might help to think in comoving coordinates: This is a special coordinate system where the coordinate grid expands with space, ie even though the proper distance between galaxies will increase, their coordinates won't change.

In this coordinate system, light does not get frozen at the Hubble sphere (as one might possibly expect), but steadily moves from emitter to eventual observer, regardless of any change in proper distance.

The moving steadily towards us should actually also hold true for light emitted from beyond the cosmic event horizon (the thing that actually delimits the observational universe) - it just takes the light a longer-than-infinite time to reach us ;)

As to the second part of your question about the redshift: That doesn't depend on recession velocities, but rather on relative velocities as computed by parallel transport along the light path (and should stay below $c$ until you hit the event horizon).