Measuring distances: the furthest away objects

[First up, apologies for the unscheduled hiatus. Being sick and moving house (mercifully not simultaneously) sort of quashed any blogging plans I may have had. OK, so I don't mean so much quashed as put out of my mind entirely, but whatever.

Also, thanks to changing life routines, I think I'll be changing my update schedule from Wednesday nights to weekends. For the time being it seems more manageable.]

This week I thought I'd talk about something a little bit outside the realms of foreseeable future SF: extragalactic distances. I say outside in the sense that there is currently no plausible way to travel to neighbouring galaxies, let alone galaxies at the edges of the observable universe.

How far is far?

The thing to understand here is that the universe is really big. Like, amazingly, mind-blowingly large. Douglas Adams said it well:

Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.

Light travels 300 000 km in one second (in a vacuum). It takes about eight minutes for light to travel from the sun to Earth. About five and a half hours from light to travel from the sun to Pluto. It takes a hundred thousand years for light to travel from one edge of our galaxy to the far edge (along the disc). By this stage, I'm sure you've heard the term light year. It's the distance that light can travel in one year and is about 9 460 000 000 000 kilometers (about 10¹³ km or ten trillion kilometres). The nearest galaxy is two and a half million light years away. See how all these distances stack up?

Most astronomers don't actually measure or think about distances in light years. They're somewhat useful for conceptualising things, but parsecs (abbreviated to pc) are more common. One parsec is 3.26 light years. That puts the nearest galaxy, Andromeda almost 800 kpc away (kpc is kiloparsec where the kilo indicates a factor of 1000). Mostly galaxy distances are measured in megaparsecs (Mpc) where one megaparsec is a million parsecs.

Even larger distances are measured using a scale called redshift. The universe is expanding. When light leaves a distant galaxy and travels towards us, it takes time. Possibly millions or billions of years, depending on just how distant that galaxy is. In all that time while it's travelling, the universe continues expanding. The expansion stretches out the light so by the time it gets to us, it has a longer wavelength. Longer wavelength means redder (on the visible spectrum, although in reality this light could have started at any wavelength, depending on what emitted it, and could finish up stretched out all the way into the radio region). Hence the term "redshift".

Doing the Measuring

I touched upon spectroscopy when I talked about the Doppler effect in this astronavigation post. Basically, you look for some known lines (often hydrogen lines) and see how far they've shifted towards the red end of the spectrum.

So we should just be able to use this to measure distances, since we know how fast the universe is expanding, right? Not quite. In the post I linked above, I talked about Doppler shift. This is different to redshift but it can look very similar. Far away galaxies can be moving relative to their neighbours (galaxies in a cluster orbiting a central galaxy, for example). These local motions are called peculiar velocites. This means that you could work out spectroscopic redshifts for galaxies in a cluster, which are all around the same distance from us, but get different results because of their peculiar velocities.

Instead we have to use a combination of different methods, two of which I'll talk about now. The same principle underlies both. Basicaly, in the 70s and 80s, it was discovered that there are a few "scaling relations" which galaxies obey. For example the Tully-Fisher relation relates a spiral galaxy's luminosity (how much light it gives out in total) and the rotational velocity of it's stars (how quickly they orbit the centre).

A spiral galaxy. Although, for a Tully-Fisher measurement, you'd
want it to be side-on, not face-on. But face-on looks prettier.
Source: Hubblesite.org

We can measure the rotational velocity of the stars in a spiral galaxy using the Doppler effect (even though the galaxy is moving away, the stars on one side will be moving towards us and on the other side away from us -- the difference between the two sides can be used to work out the rotational velocity). Once we know that, we get a prediction for the luminosity of the galaxy. However, the galaxy is far away and looks dim, much like a light in a high-ceilinged hall that isn't too bright too look at although it would hurt your eyes if you were up close. Exactly how dim a galaxy looks depends exactly on how far away it is. So if we know how bright it should be, we can compare with how bright it appears and work out how far away it is. Huzzah.

There is a similar, albeit slightly more complicated, relationship for elliptical galaxies called the Fundamental Plane.

Both the Tully-Fisher relation and the Fundamental Plane are constantly being improved upon as we build better telescopes that give more precise measurements and also as we understand the underlying physics governing them better. (At the moment, we're not super sure why they exist.) However, we're still able to use them to measure things like Hubble's constant. Who knows, maybe there are super advanced aliens out there who can set up extragalactic wormholes and need to know how far away to place them.

Probably not, though. I did say this post was outside the realm of plausibility.