The Redshift Drift

Things are crazily busy, with me finishing teaching this week. Some of you may know, that I am writing a book, which is progressing, but more slowly than I hoped. Up to just over 60,000 words, with a goal of about 80 to 90 thousand, so more than half way through.

I know that I have to catch up with papers, and I have another article in The Conversation brewing, but I thought I would write about something interesting. The problem is that my limited brain has been occupied by so many other things that my clear thinking time has been reduced to snippets here and there.

But one thing that has been on my mind is tests of cosmology. Nothing I post here will be new, but you might not know about it. But here goes.

So, the universe is expanding. But how do we know? I've written a little about this previously, but we know that almost 100 years ago, Edwin Hubble discovered his "law", that galaxies are moving away from us, and the further away they are, the faster they are moving. There's a nice article here describing the importance of this, and we end up with a picture that looks something like this

Distance is actually the hard thing to measure, and there are several books that detail astronomers on-off love affair with measuring distances. But how about velocities?

These are measured using the redshift. It's such a simple measurement. In our laboratory, we might see emission from an element, such as hydrogen, at one wavelength, but when we observe it in a distant galaxy, we see it at another, longer, wavelength. The light has been redshifted due to the expansion of the universe (although exactly what this means can be the source for considerable confuddlement).

Here's an illustration of this;

Relating the redshift to a Doppler shift we can turn it into a velocity. As we know, the Hubble law is  what we expect if we use Einstein's theory of relativity to describe the universe. Excellent stuff all around!

One thing we do know is that the expansion rate of the universe is not uniform in time. It was very fast at the Big Bang, slowed down for much of cosmic history, before accelerating due to the presence of dark energy.

So, there we have an interesting question. Due to the expansion of the universe, will the redshift I measure for a galaxy today be the same when I measure it again tomorrow.

This question was asked before I was born and then again several times afterwards. For those that love mathematics, and who doesn't, you get a change of redshift with time that looks like this

(taken from this great paper) where z is the redshift, Ho is Hubble's constant today, while H(z) is Hubble's constant at the time the light was emitted from the galaxy your observing. 

The cool thing is that last term depends upon the energy content of the universe, just how much mass there is, how much radiation, how much dark energy, and all the other cool things that we would like to know, like if dark energy is evolving and and changing, or interacting with matter and radiation. It would be a cool cosmological probe.

Ah, there is a problem! We know that Hubble's constant is about Ho = 72 km/s/Mpc, which seems like a nice sort of number. But if you look closely, you can see that it actually had units of 1/time. So, expressing it in years, this number is about 0.0000000001 per year. This is a small number. Bottom.

But this does not mean that astronomers pack up their bags and head home. No, you look for solutions and see if you can come up with technologies to allow you to measure this tiny shift. I could write an entire post on this, but people are developing laser combs to give extremely accurate measurement of the wavelength in spectra, and actually measure the changing expansion of the Universe in real time!

Why am I writing about this? Because these direct tests of cosmology have always fascinated me, and every so often I start doodling with the cosmological equations to see if I can come up with another one. Often this ends up with a page of squiggles and goes no where, but some times I have what I thing is a new insight.

And this gives me a chance to spruik an older paper of mine, with then PhD student, Madhura Killedar. I still love this stuff!

Lyman alpha absorbers in motion: consequences of gravitational lensing for the cosmological redshift drift experiment

Madhura Killedar, Geraint F. Lewis

(Submitted on 23 Oct 2009)

The evolution of the expansion rate of the Universe results in a drift in the redshift of distant sources over time. A measurement of this drift would provide us with a direct probe of expansion history. The Lyman alpha forest has been recognized as the best candidate for this experiment, but the signal would be weak and it will take next generation large telescopes coupled with ultra-stable high resolution spectrographs to reach the cm/s resolution required. One source of noise that has not yet been assessed is the transverse motion of Lyman alpha absorbers, which varies the gravitational potential in the line of sight and subsequently shifts the positions of background absorption lines. We examine the relationship between the pure cosmic signal and the observed redshift drift in the presence of moving Lyman alpha clouds, particularly the collapsed structures associated with Lyman limit systems (LLSs) and damped Lyman alpha systems (DLAs). Surprisingly, the peculiar velocities and peculiar accelerations both enter the expression, although the acceleration term stands alone as an absolute error, whilst the velocity term appears as a fractional noise component. An estimate of the magnitude of the noise reassures us that the motion of the Lyman alpha absorbers will not pose a threat to the detection of the signal.