Can a galaxy have a recession velocity greater than the speed of light?

[nnxion]

Hi all. I was reading: http://www.astro.ucla.edu/~wright/doppler.htm but I'm failing to understand this part:

When z is larger than 1 then cz is faster than the speed of light and, while recession velocities faster than light are allowed, this approximation using cz as the recession velocity of an object is no longer valid. Thus for the largest known redshift of z=6.3, the recession velocity is not 6.3*c = 1,890,000 km/sec. It is also not the 285,254 km/sec given by the special relativistic Doppler formula 1+z = sqrt((1+v/c)/(1-v/c)). The actual recession velocity for this object depends on the cosmological parameters, but for an OmegaM=0.3 vacuum-dominated flat model the velocity is 585,611 km/sec. This is faster than light.

My understanding is that a galaxy cannot move faster than c (the speed of light). Why then could a galaxy moving close to c have a recession velocity greater than the speed of light? What would happen to the value of redshift?

 

[Danger]

I think that this is once again a case of mistaking the expansion of space-time for physical movement within the universe. The galaxies can recede relative to us at superluminal velocity because the amount of space between us is enlarging. They're not moving very fast in relation to the space-time that they're in.

 

[nnxion]

Okay thanks for clearing that up. Another question then: When is the value of redhift largest? When a galaxy is receding faster than light? When does redshift get shifted to infinite wavelength? Does every object that's at a same distance from us (earth) have the same redshift?

 

[Garth]

Okay thanks for clearing that up. Another question then: When is the value of redhift largest? When a galaxy is receding faster than light? When does redshift get shifted to infinite wavelength? Does every object that's at a same distance from us (earth) have the same redshift?

The cosmological red shift of the light from an object observed today, where the scale factor is R(t₀), which was emitted when the object was situated when the scale factor was R(t_e) is given by
$$1 + z = \frac{R(t_0)}{R(t_e)}$$

so z tends to infinity as R(t_e) tends to zero, i.e. for an object at the Big Bang itself. The nearest we can actually get to observing the Big Bang directly is the Cosmic Microwave Background which is observed at a red shift of over 1000.

I hope this helps.

Garth

 

[matt.o]

Objects at the same distance from Earth may have different redshifts caused by their respective peculiar motions through space (along the line of sight). For instance, galaxies orbiting within a cluster of galaxies show a distribution of redshifts that are well approximated by a Gaussian (assuming the cluster is relaxed, ie. not merging with another cluster), with the mean redshift approximately equal to the redshift due to cosmological expansion (ignoring the fact that the cluster as a whole may have some peculiar velocity along the line of sight).