Imaging galaxies receding at a velocity that exceeds c?

[hyksos]

There are galaxies that are so far away that metric expansion causes them to have a co-moving recessional velocity that exceeds the speed of light. However, those galaxies are also so far away that the time it took the light to reach us was itself billions of years in the passage of its journey here. For example, GN-z11 is "today" receding at a velocity that far exceeds light speed. But at the time in which it emitted that light received by our telescopes was a wopping 11.1 billion years ago. This was so long ago, that our solar system had not even begun to form. My understanding is that those distant objects can never be imaged and are forever cut off from us because their recession is moving them away from us faster than the speed of light.

Is it possible to image a galaxy that was receding at a velocity greater than c, at the time in which it emitted that light?

 

[CWatters]

Apparently GN-z11 was receding from us at 4C when it emitted the light we see today...

https://astronomy.stackexchange.com...urements-of-galaxies-moving-faster-than-light

 

[kimbyd]

Yes. Most galaxies we see are and always have been receding at faster than the speed of light.

 

[PeterDonis]

Most galaxies we see are and always have been receding at faster than the speed of light.

I'm not sure this is correct. In a universe where the expansion is decelerating (which it was in our universe until a few billion years ago), an object can emit light towards us when it is receding from us faster than light and still have that light reach us--because as the expansion decelerates, the light is able to move towards us. So light we are seeing that was emitted more than few billion years ago could have been emitted when the object that emitted it was receding from us faster than light.

But in a universe where the expansion is accelerating (which it has been in our universe since a few billion years ago, and is expected to be for the indefinite future), if an object emits light towards us, that light will never reach us. So any light we are seeing that was emitted less than a few billion years ago must have been emitted when the object that emitted it was receding from us slower than light.

 

[kimbyd]

So any light we are seeing that was emitted less than a few billion years ago must have been emitted when the object that emitted it was receding from us slower than light.

And most galaxies are further than that.

 

[PeterDonis]

most galaxies are further than that.

Ah, I've figured out what I was missing: a few billion years ago is still a small redshift (about 0.3 as best I can estimate), so most galaxies we can see are at a higher redshift than that. Or, to put it another way, the relevant fraction is not (a few billion years ago) / (the age of the universe), but (the redshift of a galaxy that emitted light towards us a few billion years ago) / (the largest redshift of any galaxy we can see). The latter fraction is much smaller than the former.

 

[kimbyd]

Ah, I've figured out what I was missing: a few billion years ago is still a small redshift (about 0.3 as best I can estimate), so most galaxies we can see are at a higher redshift than that. Or, to put it another way, the relevant fraction is not (a few billion years ago) / (the age of the universe), but (the redshift of a galaxy that emitted light towards us a few billion years ago) / (the largest redshift of any galaxy we can see). The latter fraction is much smaller than the former.

Yeah. I just didn't want to get into a full discussion because it's been asked and answered so many times.

Short version is that this is possible because the rate of expansion in the past was much higher than it is now.

 

[RUTA]

We just did these calculations in my modern physics class. For ΛCDM cosmology, Einstein's equations give $\dot{a} = H_o \sqrt{\frac{\Omega_M}{a} + \Omega_{\Lambda}a^2}$ where $a$ is the scaling factor, $H_o$ is the Hubble constant, $\Omega_M$ is the fraction of mass-energy from cold dark matter (CDM), and $\Omega_{\Lambda}$ is the fraction of mass-energy from the cosmological constant Λ with $\Omega_M + \Omega_{\Lambda} = 1$. To relate redshift $z$, time of emission $t_e$, current time (age of universe) $t_o = 13.8$ Gy, redshift $z$, the current value of the scaling constant $a_o$, and the value of the scaling constant at time of emission $a_e$, we have $\frac{1}{H_o t_o}\int\limits_{a_e}^{a_o} \frac{da}{\sqrt{\frac{\Omega_M}{a} + \Omega_{\Lambda}a^2}} = 1-\frac{t_e}{t_o}$. The current value of the scaling constant is chosen to be $a_o = 1$ giving $a_e = \frac{1}{1+z}$ so we have $\frac{1}{H_o t_o}\int\limits_{\frac{1}{1+z}}^{1} \frac{da}{\sqrt{\frac{\Omega_M}{a} + \Omega_{\Lambda}a^2}} = 1-\frac{t_e}{t_o}$. To get $H_o t_o$ just use the same equation with $a_e = 0$ and $t_e = 0$. Of course you have to do the integrals numerically, but Wolfram Alpha will do that for you. The most popular choices for $\Omega_M$ are 0.27 to 0.31.

 

[RUTA]

objects with mass cannot move faster than light speed

You can get the cosmological redshift via an integrated SR doppler shift over the light path (frame to adjacent frame), but technically yes, you should not apply the SR doppler shift between largely separated (per the curvature scale) frames in curved spacetime without specifying the means of parallel transport.

The objects with Hubble recession velocities larger than c are not themselves moving locally at speeds greater than c. For example, the photons are moving with Hubble recession velocities differing from c as they traverse the space between emitter and receiver, but are always moving at c locally. Think of an ant walking on an expanding rubber band. The ant's speed relative to the rubber band underneath its feet is not the speed of the ant relative to either end of the expanding rubber band. See Fig 2 in http://users.etown.edu/s/STUCKEYM/AJP1992a.pdf where the Hubble recession velocity of the photon is shown throughout its journey and equals -c upon arrival.

 

[kimbyd]

objects with mass cannot move faster than light speed

The speed of light limitation is a local limitation only in General Relativity. Far-away speed is ambiguous in a curved space-time.

The local limitation in GR basically means, "Nothing can outrun light rays." And these galaxies are not outrunning light rays.

 

[PAllen]

I'm not sure this is correct. In a universe where the expansion is decelerating (which it was in our universe until a few billion years ago), an object can emit light towards us when it is receding from us faster than light and still have that light reach us--because as the expansion decelerates, the light is able to move towards us. So light we are seeing that was emitted more than few billion years ago could have been emitted when the object that emitted it was receding from us faster than light.

But in a universe where the expansion is accelerating (which it has been in our universe since a few billion years ago, and is expected to be for the indefinite future), if an object emits light towards us, that light will never reach us. So any light we are seeing that was emitted less than a few billion years ago must have been emitted when the object that emitted it was receding from us slower than light.

Last time I checked the concordance model, the current standard cosmological distance at which comoving bodies have superluminal recession rate is about 4 gigaparsecs, while the current distance from which we will never receive signals is 5 gigaparsecs. Thus, there is still a window for superluminal recession rate galaxies to be eventually seen.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

Thread reopened after some cleanup.